4 Brooke cycled at an average speed of 22 kilometers per hour from her house to the nearby park,
and cycled back at an average speed of 14 kilometers per hour vio the same route. She took
66 minutes to cycle back to her house. How long, in minutes, did she take to ode from her house
to the nearby park?

The expanded form of the given logarithm using the properties of logs is P=log(2)+log(3)+4.log(x).

A base must be raised to a certain exponent or power, or logarithm, in order to produce a specific number.

If bx = n, then x is the logarithm of n to the base b, which is expressed mathematically as x = logb n.

For instance, 23 = 8; hence, 3 is the base-2 logarithm of 8 or 3 = log2 8.

Common logarithms, with a base of 10, binary logarithms, with a base of 2, and natural logarithms, with a base of e 2.71828, are the four most popular varieties of logarithms.

So, we must keep in mind the following characteristics of the logarithms in order to solve the issue:

[tex]\begin{aligned}& \log (x . y)=\log (x)+\log (y) \\& \log \left(x^y\right)=y \cdot \log (x)\end{aligned}[/tex]

Then, the expression we have:

[tex]P=\log \left(6 x^4\right)[/tex]

The factor of 6=2*3:

[tex]P=\log \left(2 \cdot 3 x^4\right)[/tex]

Apply the product's feature:

[tex]P=\log (2)+\log (3)+\log \left(x^4\right)[/tex]

Apply the exponent's property now:

P=log(2)+log(3)+4.log(x)

Therefore, the expanded form of the given logarithm using the properties of logs is P=log(2)+log(3)+4.log(x).

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Correct question:

Expand the logarithm fully using the properties of logs. Express the final answer in

terms of log .

log 6x^4

A plausible lurking variable that could explain the cause and effect in the headline "Is Gluten the Culprit in Our Fight Against Obesity?" is overall diet.

It's possible that individuals who consume a diet high in gluten also consume a diet high in overall calories and processed foods, leading to weight gain and obesity. This would mean that it is not specifically gluten causing the obesity, but rather a combination of factors in the individual's diet.

A lurking variable is a variable that has a connection (e.g., may be correlated) with the response and the explanatory variable but is neither the explanatory variable nor the response variable.

Although it is not taken into account in the study, it might affect how the variables are related.

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The length of Nigel's bedroom is 11 feet while the width is 9 feet

An equation is an expression that shows the relationship between numbers and variables.

For Colleen room:

length = 8 ft, width = 12 ft

Perimeter = 2(length + width)

substituting:

Perimeter = 2(8 + 12) = 2(20)

Perimeter = 40 feet

For Nigel room:

length = l ft, width = 3/4 times that of Colleen = (3/4)(12) = 9 feet

Perimeter = 2(length + width)

But Colleen and Nigel room has same perimeter

substituting:

40 = 2(l + 9)

l + 9 = 20

l = 11 feet

The length is 11 feet.

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Answer: I believe the solutions your looking for would be x = 0 or x = −8

Step-by-step explanation:

x (x + 8) = 0

Step 1: Simplify both sides of the equation.

x² + 8x = 0

Step 2: Factor left side of equation.

x (x + 8) = 0

Here are factors equal to 0:

x = 0 or x + 8 = 0

x = 0 or x = −8

I hope this helps!

Answer:

Step-by-step explanation:

x inside the () is equal to -8

then that will be ( -8 + 8=0)

the x multiply by 0 is 0

You welcome

It take 43 seconds to the object to travel the full length.

Constant rate refers to a fixed rate of change over a specific period of time. It can be used to describe a variety of situations such as the rate of population growth, the rate of inflation, or the rate of decline in a company's profits.

Constant rate can be used to measure a variety of factors in order to track progress or gauge the success of a particular strategy.

This question uses the concept of constant rate.

Constant rate means that the marble is travelling at a constant speed over the entire length of the path.

This means that the time it takes to travel the full length is the same as the time it took to travel a certain portion of the path.

In this case, it took 43 seconds to travel a certain portion of the path, so it will take 43 seconds to travel the full length.

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Answer:

Jude: y = 5x

Ian: y = 45 - 10x

Step-by-step explanation:

Jude:

y = 5x

Ian:

y = 45 - 10x

Answer:

93.312

Step-by-step explanation:

This would be decay so we use the formula [tex]y=a(1-r)^{2}[/tex]

in this case a would equal $1200, r would equal 40% (as a decimal) or 0.4 and x would equal 5

[tex]y=1200(1-0.4)^5[/tex] plug this into your calculator and you will get 93.312

I hope this helps (Lmk if im wrong )

Point P cannot be located on either the x-axis or y-axis, as neither a nor b is 0.

The coordinate system's two axes, the x-axis and the y-axis, constitute a region called a quadrant.

If both a and b have the same sign, point P could be located in one of the four quadrants:

For First quadrant (a > 0, b > 0)

For Second quadrant (a < 0, b > 0)

For Third quadrant (a < 0, b < 0)

For Fourth quadrant (a > 0, b < 0)

Hence, Point P cannot be located on either the x-axis or y-axis, as neither a nor b is 0.

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Answer:

yes ✔‍♀️

Step-by-step explanation:

just flip it over and dividend by 1.2

Answer:

C

Step-by-step explanation:

A parachutist falls 11 seconds before the parachute opens, so 1936 ft far the parachutist fall during this time.

We have to find how far does the parachutist fall during this time.

The formula for estimating the time in seconds it will take an object to fall d feet is given below.

t = [tex]\sqrt{\frac{d}{16}}[/tex]

We merely need to enter the specified time t into the formula to find the distance answer.

11 = [tex]\sqrt{\frac{d}{16}}[/tex]

taking square on both side, we get

121 = d/16

Multiply by 16 on both side, we get

d = 1936 ft

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The complete question is:

The approximate time t in seconds that it takes an object to fall a distance of d feet is given by

t = [tex]\sqrt{\frac{d}{16}}[/tex]

Suppose a parachutist falls 11 seconds before the parachute opens. How far does the parachutist fall during this time?

Answer:

itll take 8 pounds for both DHL and MPS to cost the same

Step-by-step explanation:

since DHL charges $4 for the first pound and $0.22 for each additional pound, and MPS charges $12 for the first pound and $0.12 for each additional pound, we can write that as 4 + 0.22x = 12 + 0.12x, with the left side representing DHL and the right representing MPS.

If this equation is solved, you will find out that x = 8, which is the number of pounds that DHL and MPS will cost the same at. Therefore, they will charge the same amount for 8 pounds.

If Fran swims at 2.2 mph in still water and  Lazy River flows at a speed of 0.6 mph , the the time required by Fran to go 2.4 mi upstream is 1.5  hours and 2.4 mi downstream is 0.857  hours .

the speed of Fran in still water (rate) = 2.2 mph ;

the sped of the river (current) is = 0.6 mph  ;

The time  taken by Fran to swim 2.4 miles upstream and 2.4 miles downstream can be calculated by formula :

⇒ time = distance/(rate + current)  ;

the distance to be covered is = 2.4 miles ;

For the time taken by Fran to swim upstream , the speed of current is subtracted from the Speed of Fran ;

So , time = 2.4/(2.2-0.6) = 2.4/1.6 = 1.5 hours

For the time taken by Fran to swim downstream, the speed of current is added to the Speed of Fran ;

So , time = 2.4/(2.2 mph + 0.6) = 2.4/2.8 = 0.857 hours

Therefore , by Fran it will take 1.5 hours to travel 2.4 miles upstream and 0.857 hours to travel downstream .

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Assuming the interest is compounded monthly, the interest rate that would be required in order for Joshua to end up with $1,500 is 2.26%.

Mathematically, compound interest can be calculated by using this formula:

A(t) = P(1 + r/n)^{nt}

Where:

Substituting the given parameters into the compound interest formula, we have;

1,500 = 1,000(1 + r/12)^{12 × 18}

1.5 = (1 + r/12)^{216}

Taking the 216th root of both sides of the equation, we have:

1.00187891623 = 1 + 0.083333333r

0.083333333r = 1.00187891623 - 1

0.083333333r = 0.00187891623

r = 0.00187891623/0.083333333

r = 2.26

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Answer:

the interest rate that would be required in order for Joshua to end up with $1,500 is 2.26%.

Step-by-step explanation:

The population of rabbits in the Butler County, where the starting rabbit population of 6,004 increases by 8% per year in 10 years is about 13,362 rabbits

A population is the set that comprises of all individuals or items that share a common specified characteristics.

The current population of the rabbit = 6,004

The rate at which the population is increasing per year = 8%

The number of rabbits in 10 years is found using the formula for population growth as follows;

P = P₀ × e^(r·t))

Where;

P = The population or number after the time t

P₀ = The initial or starting population = 6,004 rabbits

r = The percentage growth rate = 8%

t = The time of growth = 10 years

e = Euler number

Therefore;

P₁₀ = 6,004 × e^(0.08 × 10) ≈ 13362

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The coordinates after a dilation of scale factor k = 4 are (-16, 48)

If we have a general point (x, y), and we apply a dilation of scale factor k and the center of dilation is the origin, then the coordinates of the image after the dilation are (k*x, k*y)

Here we start with the point (-4, 12), and we apply a dilation of scale factor 4 and the center is the origin, then the coordinates  of the image are::

(-4*4, 12*4) = (-16, 48)

The coordinates after the dilation are (-16, 48).

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∠XBC is 55 degrees because it is corresponding to ∠AXY..

The angle ∠BXC is 70 degrees

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, alternate exterior angles, linear angles, same interior angles, vertically opposite angles etc.

Therefore, XY and BD are parallel lines.

XB = XC

ΔXBC is an isosceles triangle.

Therefore, ∠XBC is 55 degrees because it is a corresponding angle to ∠AXY.

Let's find ∠BXC.

Therefore, the base angles of an isosceles triangle are congruent.

Hence,

∠XBC = ∠BCX = 55 degrees

Therefore,

55 + 55 + ∠BXC = 180

110 + ∠BXC = 180

∠BXC = 180 - 110

∠BXC = 70 degrees

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An expression that is equivalent to -56Z +28 can be -23z + 10 - 33z + 18

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

In this case, an expression that is equivalent to -56Z +28 can be:.

-23z + 10 - 33z + 18

= -23z - 33z + 10 + 18

= -56z + 28

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The radius of circle for the given length of rod is found as 1.65 ft

Perimeter of circle = 2 π r

In which,

When the length of the rod is bent to form the circle.

Length of rod = Perimeter of circle

10.38 = 2 π r

r = 10.38 /  2 π

r = 1.65

Thus, the radius of the circle for the given length of rod is found as 1.65 ft.

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Answer:

Without exponents: a * a * a * a * a

Fill in the blank: [tex]a^5[/tex]

Step-by-step explanation:

We have to use exponent rules:

[tex]x^y * x^y = x^{y+y} \\= x^{2y}[/tex]

So for this problem, we can apply that rule here:

[tex]a^3 * a^2 = a^{3+2}[/tex]

= [tex]a^5[/tex]

^ This will be the answer to the second question.

Now, to find the equation without exponents, we can use the information we have from above. We need to use this rule: [tex]x^2 = x * x[/tex]

Since our equation is [tex]a^5[/tex], we can rewrite it as a * a * a * a * a.

Answer:

The distance traveled by the car in each second is increasing by 4 cm each time. This is an example of an arithmetic sequence, where the common difference is 4 cm.

To find the total distance traveled by the car in 30 seconds, we can use the formula for the sum of an arithmetic series:

S_n = n/2 * (a_1 + a_n)

where S_n is the sum of the first n terms of the series, a_1 is the first term (4 cm in this case), a_n is the nth term, and n is the number of terms.

Substituting the values into the formula:

S_n = 30/2 * (4 + (4 + (30 - 1) * 4))

S_n = 30/2 * (4 + 4 + 116)

S_n = 30/2 * 124

S_n = 3720 cm

So the total distance travelled by the car in 30 seconds is 3720 cm.

Party planner 2 charges $15 more per person than party planner 1.

What is linear equation ?

Linear equation can be defined as the equation in which the highest degree is one.

Given ,

Melanie is comparing the price of two party planners. Party Planner 1 and Party Planner 2. Party Planner 1 uses the equation, y = 10x + 70,

where x is the number of people attending the party and y is the total cost.

y=15x+75 means that they charge $15 for every person but $75 right away. For planner 2, they charge $20 a person because comparing coordinates 1 and 2,

every 5 people charge $100. So to find the amount per person for planner 2, divide 100 by 5 and you'll get 20, and

since 20 is 5 more than 15. A is true.

Therefore, Party planner 2 charges $15 more per person than party planner 1.

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Answer:

x = 20

Step-by-step explanation:

Because these are alternate interior angles, 2x+20 and 3x are equivalent to each other. Therefore, we can set up this equation:

2x+20 = 3x

Now, we can solve this equation and find x:

20 = 3x-2x

x = 20

These provided angle measures (3x and 2x + 20) are a pair of alternate interior angles because they satisfy the following required conditions:

Since the two angles ARE alternate interior angles, they are EQUAL! Therefore, we can equate the two angles and solve for the variable (x).

{2x + 20 is equal to 3x} ⇒ 2x + 20 = 3x

The key step in solving the linear equation is to ISOLATE the variable completely by removing the coefficient until you have 1 as the coefficient.  

There are 4 possible ways to isolate the variable:

Once your variable is completely isolated, simplify (if possible) on the other side of the equation. If the opposite side of the variable is simplified, you can conclude your solution for the linear equation.

Now, let us solve the equation using the above step by step processes.

Isolating the variable from the constant(s) on the R.H.S:  

Simplify both sides of the equation:

Therefore, the solution to the linear equation (x) is 20.

__________________________________________________________

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The relative frequency of Selena's friends who speak more than one language is 3/16 or 0.1875

To create a relative frequency distribution, we first need to find the total number of responses by summing up the number of languages spoken by Selena's friends. In this case, the total number of responses is 2 + 1 + 1 + 1 + 2 + 3 + 1 + 2 + 1 + 1 = 16.

Next, we need to find the relative frequency for each category, which is the number of responses in that category divided by the total number of responses. To find the relative frequency of her friends who speak more than one language, we need to add up the number of responses in categories 2, 3, and above.

In this case, the number of responses in category 2 is 2, the number of responses in category 3 is 1, and there are no responses above 3.

So the relative frequency would be (2+1)/16 = 3/16 or 0.1875

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The number of sticks in pattern number n will be 6 + (n-1)(4).

What is a pattern?

A recurring arrangement of numbers, forms, colours, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern.

The given diagram states that -

The first figure of the triangle is made using - 6 sticks.

The second figure of the triangle is made using - 6 + 4 sticks.

The third figure of the triangle is made using - 6 + 4 + 4 sticks.

Similarly, the fourth figure of the triangle will be made using - 6 + 4 + 4 + 4 sticks.

So, the pattern followed here is -

First image = 6 + (1-1)(4)

Second image = 6 + (2-1)(4)

Third image = 6 + (3-1)(4)

Fourth image = 6 + (4-1)(4)

So, for pattern n the number of sticks will be -

nth image = 6 + (n-1)(4)

Therefore, the pattern is obtained as 6 + (n-1)(4).

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A graph of the inequality w ≤ 200 is shown in the image attached below.

In this scenario, we would solve the given inequality by making "w" the subject of formula as follows;

w/-10 ≤ -20

By multiplying both sides of the inequality by -10, we have the following:

-10 × w/-10 ≤ -20 × -10

w ≤ 200

Next, we would use an online graphing calculator to plot the inequality as shown in the graph attached below. Additionally, the circle is closed because of the less than or equal to (≤) symbol.

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Answer: The inequality one fifth times the difference of m and five is less than or equal to one tenth times the difference of m and twenty can be rewritten as:

(1/5)(m-5) <= (1/10)(m-20)

To find the integers in the set S that will make this inequality false, we need to find the values of m that do not satisfy it. We can start by simplifying the inequality:

(1/5)(m-5) <= (1/10)(m-20)

(1/5)m - (1/5)5 <= (1/10)m - (1/10)20

(1/5)m <= (1/10)m - (1/10)20 + (1/5)5

(1/5)m <= (1/10)m - 2 + (1/5)5

(4/5)m <= (1/5)5 - 2

m <= -5

So, the integers in the set S that do not satisfy the inequality are 20 and 40. These integers will make the inequality false.

Step-by-step explanation:

Answer: Let x be the speed of the eastbound train.

Then the speed of the westbound train is x+3 mph.

We can set up the following equation using the distance formula (rate x time = distance)

x*4 = 648/2 + (x+3)*4

Solving for x,

x= 42

So the speed of the eastbound train is 42 mph and the speed of the westbound train is 45 mph.

Step-by-step explanation:

If the average rate of inflation over the last hundred years was 3.22%, the amount of money one hundred years ago would be equivalent to a million dollars today is approximately 968,805 dollars.

If the average rate of inflation over the last hundred years was 3.22%, we have to determine the amount of money one hundred years ago would be equivalent to a million dollars today.

We know that formula of inflation is:

inflation = (FP−IP)/IP × 100

where, IP stands for the initial basket price or price index.

FP stands for the basket's final price or the price index.

From the question, inflation = 3.22%, FP = 1,000,000

Now putting the values in the formula

3.22 = (1,000,000 - IP)/IP  × 100

Divide by 100 on both side, we get

0.0322 = (1,000,000 - IP)/IP

Multiply by IP on both side, we get

0.0322IP = 1,000,000 - IP

Add IP on both side, we get

1.0322IP = 1,000,000

Divide by 1.0322 on both side, we get

IP = 968,804.5

IP = 968,805(approx)

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