Marcus looked up the path that he had taken on his run this morning on the map shown below.

Using some logarithm properties we will get the expanded expression:

log(y^10) = 10*ln(y)/ln(10)

So there are two logarithm properties that we can use here, these are:

logₙ(x) = ln(x)/ln(n)

and:

logₙ(x^a) = a*logⁿ(x)

Now let's go to our expression, it is:

log(y^10)

Using the second property we can remove the exponent, then we will get:

log(y^10) = 10*log(y)

Now we can use the first rule, remember that log(x) has a base of 10, then we can write:

10*log(y) = 10*ln(y)/ln(10)

That is the expession expanded.

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Answer:

To find the value of A, we can substitute g(-3) = 2 into the given equation and solve for A.

g(q) = (2q-4) / (q-A)

2 = (2(-3)-4) / (-3-A)

Multiplying both sides by (-3-A), we get:

2(-3-A) = -10 - 2A

Expanding the left side, we get:

-6 - 2A = -10 - 2A

Adding 2A to both sides, we get:

-6 = -10

This is a contradiction, which means that there is no value of A that satisfies the given conditions. Therefore, the answer to the question is:

There is no value of A that satisfies the given conditions.

Answer:

Distance = Speed × Time.

Let's break down the problem into two parts:

a) At what time will the cyclists meet on the way?

Let's assume t represents the time in hours when the cyclists meet.

The distance Joel travels in t hours is given by: Distance = Speed × Time = 12t km.

The distance Ryan travels in t hours is given by: Distance = Speed × Time = 8t km.

Since they are cycling towards each other, the sum of their distances should equal the total distance between Kingston and Sunny Place, which is 35 km.

So, we can set up the equation: 12t + 8t = 35.

Simplifying the equation, we have: 20t = 35.

Dividing both sides of the equation by 20, we get: t = 35/20 = 1.75 hours.

Therefore, the cyclists will meet on the way after 1.75 hours, which is equivalent to 1 hour and 45 minutes.

b) How far will each cyclist have traveled when they meet?

To find the distance traveled by each cyclist, we can substitute the value of t into their respective equations:

Distance traveled by Joel = 12t = 12 × 1.75 = 21 km.

Distance traveled by Ryan = 8t = 8 × 1.75 = 14 km.

Therefore, when the cyclists meet, Joel would have traveled 21 km and Ryan would have traveled 14 km.

The surd forms are simplified to give;

21. 10√6 - 12√10

23. -56a  - 5√2a - 25

25. -4√15x - 25x + 3

Surds are described as values in square root that can no longer be simplified into whole numbers or integers

They are also seen as irrational numbers.

From the information given, we have that;

√15(2√10 - 4√6)

Expand the bracket and multiply the surd forms

2√150 - 4√90

Factorize the forms

2√25 ×√6 - 4√9 × √10

find the square root

10√6 - 12√10

23. (√2a - 5)(7√2a - 5)

expand the bracket

7√4a² - 5√2a - 35√4a² + 25

find the square root, we have;

7×2a - 5√2a - 35×2a + 25

collect the like terms

14a - 70a - 5√2a - 25

-56a  - 5√2a - 25

25. (√3 + √5x)(√3 - 5√5x)

expand the bracket

3 - 5√15x + √15x - 5√25x²

find the square root

3 - 5√15x + √15x - 25x

collect the like terms

-4√15x - 25x + 3

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Answer:

I'm pretty much confused abt this one bc I didn't get an exact answer. Anyway I think it's 13.1

Step-by-step explanation:

The pic

Step-by-step explanation:

[tex] {( ({3})^{4} })^{8} \\ = {3}^{32} [/tex]

The vertical shift and vertical shrink of the exponential function are 2 and 1/2 respectively and the graph of the function is attached below

An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.

The vertical shift and vertical shrink of the function f(x) = 1/2(4 - eˣ) are 2 and 1/2

The vertical shift = 2

vertical shrink = 1/2

Kindly find the attached graph below

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Answer:

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According to the problem, 2 laps make a difference of 10% as:

Hence the total distance in terms of laps is:

Find the total distance:

Answer:

The correct answer is C, Graph D.

x^2 - 4x + 4 = (x - 2)^2.

The sequence 1, 6, 30, 60, . . . is not a geometric sequence

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

1, 6, 30, 60, . . .

To check if the sequence is geometric, we calculae the common ratio of the sequence using

r = next term/previous term

Using the above as a guide, we have the following:

r = 6/1 = 6

r = 30/6 = 5

r = 60/30 = 2

The common ratios of the sequence calculated above are different

This means that the sequence is not geometric

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The solution of the inequality given is b < 64

the graph is attached

In the equation, let us replace b with x

To solve the inequality x/8 < 8 for x, we need to isolate x on one side of the inequality.

We can do this by multiplying both sides of the inequality by 8, which will cancel out the 8 in the denominator on the left side:

Therefore, the solution to the inequality x/8 < 8 is x < 64.

This means that any value of x that is less than 64 will make the inequality true.

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Answer:

x=109 y=100

Step-by-step explanation:

Answer:

x=100

y=109

Step-by-step explanation:

For any quadrilateral (4-sided shape) inscribed in a circle (all 4 vertices of the quadrilateral are on the edge of the circle),  there is a special relationship between certain pairs of angles within the quadrilateral.

Specifically, opposite angles (angles across from each other) must sum (add) to 180 degrees.

The angle measuring 80 degrees is opposite the angle measuring x degrees, so x + 80 = 180, implying x = 100.

In this case, the angle measuring 71 degrees is opposite the angle measuring y degrees.  So, 71 + y = 180, which implies y = 109.

The point estimate of the population​ proportion, the margin of error for the following confidence​ interval, and the number of individuals in the sample are:

The point estimate of the population proportion:

= (lower bound + upper bound) / 2

= (0.640 + 0.910) / 2

= 0. 775

The margin of error for the confidence level :

= p - hat - lower bound

= 0. 775 - 0. 640

= 0. 135

The number of individuals in the sample with the specified characteristic (x ) :

= n x p - hat

= 1, 200 x 0. 775

= 930 people

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Answer:

2:35

Step-by-step explanation:

it takes 2 hours to get to Muar so 9:45

he spends 1 hour 40 in muar so 11:35

he went at 60 Km/h before so he returns at 40Km/h so it takes 3 hours so 2:35

The inequality represented by the given graph as required to be determined in the task content is; y ≥ 0.5x.

It follows from the task content that the inequality which is represented by the given graph is required to be determined.

By observation; the slope of the border line is; 0.5 and the y-intercept is; 0.

Ultimately, the corresponding equation to the border line is; y = 0.5x.

Hence, since the region above the line is shaded and the line is a solid line; the required inequality is; y ≥ 0.5x.

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Multiplying is necessary because each larger unit contains a certain number of the smaller units and we need to account for that conversion factor.

For example, when converting from meters to centimeters where we know that 1 meter is equal to 100 centimeters.

To convert 3 meters to centimeters, we need to multiply by the conversion factor of 100 which gives us:

= 3 meters * 100 centimeters/meter

= 300 centimeters

So, without the multiplication, we would not account for the fact that each meter contains 100 centimeters. This principle applies to all conversions from larger units to smaller units and it is important to remember to ensure accurate conversions.

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To solve for x in terms of y in the equation 23x + 15y = 2, we can start by isolating the term with x on one side of the equation. We can do this by subtracting 15y from both sides of the equation to get 23x + 15y - 15y = 2 - 15y, which simplifies to 23x = 2 - 15y.

Next, we can solve for x by dividing both sides of the equation by 23 to get 23x/23 = (2 - 15y)/23, which simplifies to x = (2 - 15y)/23.

Therefore, the solution for x in terms of y is x = (2 - 15y)/23.

The dimensions of the sign are as follows, using an overall scale factor of 12 on the original graphic:

The scale factor refers to the ratio of an original scale, object, or drawing to its model or final version.

The scale factor may enlarge or reduce the original dimensions.

The dimensions of the street sign graphic on computer = 4 inches by 5 inches

Scale factor of the graphic on print = 3

The first smaller dimensions:

4 x 3 inches and 5 x 3 inches

= 12 inches by 15 inches

The second larger dimensions:

Scale factor = 4

12 x 4 inches by 15 x 4 inches60 i

= 48 inches by 60 inches

Overall scale factor of the original graphic to the last model = 12 (3 x 4)

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Answer:

We can use the given formula to calculate the decibel level D when the intensity level I is 63,096 times Io:

D = 10log(I/lo)

Where Io is the reference intensity level and is typically taken to be the threshold of hearing, which is 10^−12 watts/m^2.

So, substituting the values, we get:

D = 10log(63,096*Io/Io) = 10log(63,096)

Using a calculator, we find:

D ≈ 47.1 dB

Rounding this to the nearest whole number, we get:

The decibel level is 47 dB when I is 63,096 times Io.

I hope this helps mate.

Using a system of equations, the quantities of each type of gas sold by the gas station for the business day are as follows:

A system of equations refers to two or more equations solved concurrently.

A system of equations is also known as simultaneous equations because they can be solved at the same time.

                              Regular    Premium

Price per gallon      $2.20       $2.75

Total number of gallons of gas sold = 340

The total receipts for the 340 gallons = $803.

Let the number of gallons of the regular gas = x

Let the number of gallons of the premium gas = y

x + y = 340 ...Equation 1

2.2x + 2.75y = 803 ...Equation 2

Multiply Equation 1 by 2.2:

2.2x + 2.2y = 748 ...Equation 3

Subtract Equation 3 from Equation 2:

2.2x + 2.75y = 803

-

2.2x + 2.2y = 748

0.55y = 55

y = 100

x = 240 (340 - 100)

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Spinner B is the spinner that has a probability of 1/3 of spinning orange.

a) For one of the spinners, the probability of spinning orange is 1/3. To identify which spinner this is, we need to find the spinner that has exactly one orange sector out of three total sectors.

From the given spinners, Spinner B is the only spinner that has one orange sector out of three, so Spinner B is the spinner that has a probability of 1/3 of spinning orange.

b) For two of the spinners, the probability of spinning orange is more than 40%. To find these spinners, we need to look for the spinners that have at least three orange sectors out of a total of eight sectors (since 3/8 is greater than 40%).

From the given spinners, Spinner A and Spinner C both have three orange sectors out of eight total sectors, so they are the two spinners for which the probability of spinning orange is more than 40%.

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Answer: A

Step-by-step explanation:

well i did alll of them and got A

There were no more books checked out in March than in April.

The pictograph provided shows the number of books checked out from the library during the months of December, January, February, March, and April. Each picture represents 5 books.

The pictograph tells us that for each of these months, 5 books were checked out. So, in March, 5 books were checked out, and in April, 5 books were also checked out.

To find the difference between the number of books checked out in March and April, we subtract the number of books checked out in April from the number of books checked out in March:

5 books (March) - 5 books (April) = 0 books

Therefore, The result shows that there were no more books checked out in March than in April. Both months had the same number of books checked out, which is 5.

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$3.90

29.20-13.60=15.6

15.6/4= 3.90

The amount of water that the plastic container can hold is -p + 3.

To determine the amount of water that can be held, we will first assume that the container can hold x quantity of water.

So, the glass jug can hold:

p + 6 - x

2 glass jugs and 2 plastic containers can hold 6p quarts of water.

= 2(p + 6 - x) - 2x = 6p

2p + 12 - 2x -2x = 6p

2p + 12 -4x = 6p

12 - 4x = 6p - 2p

-4x = 6p -2p - 12

-4x = 4p -12

x = 4p - 12/-4

x = -p - 3

or -p + 3

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The converse of the statement "A → B: If x = 3, then x + 8 = 11" is Option(c) which is "B → A: If x + 8 = 11, then x = 3."

The "Converse" of a "conditional-statement" can be expressed by interchanging the hypothesis and the conclusion of "original-statement".

In this case, The "conditional-statement" is given to be "A → B: If x = 3, then x+8=11", which is read-as that if "x" is equal to 3, then expression "x + 8" is equal to 11.

So, The converse statement would say that if "x + 8" is equal to 11, then x must be equal to 3.

Therefore, the correct option is (c).

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The sculpture's base length = 9 cm and the height of sculpture is found as 6 cm.

The base and apex are joined to form a pyramid. To identify them from the base, the triangular sides are also also referred to as lateral faces. In a pyramid, the apex, which creates the triangle face, is connected to each base edge.

Put the values and find the length.

162 = 1/3 (x)² (x-3)

162 * (3) =  (x)² (x-3)

486 = x²(x-3)

486 = x³ - 3x²

x³ - 3x² - 486 = 0

(use a graphing tool or calculator equation mode).

x = 9

Thus,

side length of sculpture = 9 cm

height of sculpture = 9 - 3   = 6cm

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Correct question:

Nathan has a sculpture in the shape of a pyramid. The height of the sculpture is 3 centimeters less than the side length,x,of its square base. Nathan uses the formula for the volume of a pyramid to determine the dimesnsioms of the sculpture.

V=1/3 a^2h

Here, a is the side length of the pyramids square base and h is it’s height.

If 162 cubic centimeters of clay were used to make the sculpture, the equation x^3 + _x^2+ _ =0 can be used to find that the length of the sculptures.  base is _ centimeters.

The estimate of the cost for a 20-ft cord is given as follows:

$74.66.

To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.

The points in the context of the problem are given as follows:

(3, 12.75), (5, 16), (6, 25.99), (50, 185).

Inserting these points into a calculator, the regression equation is given as follows:

y = 3.6794x + 1.06462.

Hence the estimate of the cost for a 20-ft cord is obtained when x = 20 as follows:

y = 3.6794(20) + 1.06462

y = $74.66.

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Answer: 8.7

Step-by-step explanation:

Given:

hypotenuse = 9

Angle x =75

opposite of angle = x

Solution:

From SOH CAH TOA, use SOH

sin x = [tex]\frac{opposite}{hypotenuse}[/tex]                  > substitute

sin 75  = [tex]\frac{x}{9}[/tex]                           > multiply both sides by 9

9*sin 75 =x

x=8.7

Answer:

10868

Step-by-step explanation:

11x26=286

286x38=10868