Maya is riding on a bike course that is 35 miles long. So far, she has ridden 14 miles of the course. What percentage of the course has Maya ridden so far

Answer:

Step-by-step explanation:

Its 4.51

The expression that could be used to calculate the amount Trina was charged in interest for the billing cycle is  (APR / 365) x 30 days x adjusted balance.

The adjusted balance method is one of the methods for computing the finance charge (interest and other fees) for credit cards.

The adjusted balance is the ending balance determined after adjusting the opening balance with purchases and payments.

Credit card interest method = adjusted balance method

Beginning balance = $780

Purchase = $170

Payment = $210

Adjusted balance, AB = $740 ($780 + $170 - $210)

APR = 17% = 0.17 (17/100)

The interest charged = (APR / 365) x 30 days x adjusted balance

= $10.34 [(0.17/365) x 30 x $740]

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Claire who took part in a cross-country race ran 21 km in 1 hour and 12 minutes.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Claire took part in a cross-country race and completed the course in 1 hour and 12 minutes which is (1 + 12/60) = (1 + 1/5) = 6/5 = 1.2 hours.

Her average speed for the race was 17.5 km per hour.

∴ The total distance she ran is,

= (17.5×1.2) km.

= 21 km.

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The piece-wise linear functions can be written as follows:

A linear function is modeled by:

y = mx + b

In which:

For x less than 5, the y-intercept is of b = 3 and the function also gos through (2,2), hence the slope is:

m = (2 - 3)/(2 - 0) = -0.5.

Hence the rule is:

\(f(x) = -0.5x + 3, x < 5\).

When x = 5, the function is constant at -5, hence:

\(f(x) = -5, x = 5\)

For x less than 5, the function goes through points (6,3) and (7,2), hence the slope is:

m = (2 - 3)/(7 - 6) = -1.

Then:

y = -x + b

When x = 6, y = 3, hence the y-intercept is given as follows:

3 = -6 + b

b = 9.

Hence the rule is:

\(f(x) = -x  + 9, x > 5\).

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The system of equation that does not belong to the other two is the third system of equations; y = -4·x - 3, y + 4·x = -5, This is so because, the third system has no solutions.

A linear system of equations consists of two or more linear equations that consists of common variables.

The possible equations are;

y = x + 6, y = -x + 2

3·x + y = -1, y = 4·x + 6

y = -4·x - 3, y + 4·x = 5

Evaluation of the system of equations, we get;

First system of equations;

y = x + 6, y = -x + 2

x + 6 = -x + 2

x + x = 2 - 6 = -4

2·x = -4

x = -4/2 = -2

x = -2

y = x + 6

y = -2 + 6 = 4

y = 4

The solution is; x = -2, y = 4

Second system of equation;

3·x + y = -1, y = 4·x + 6

3·x + 4·x + 6 = -1

7·x + 6 = -1

7·x  = -1 - 6 = -7

x = -7/7 = -1

x = -1

y = 4·x + 6

y = 4 × (-1) + 6 = 2

y = 2

The solution to the second system of equation is; x = -1, y = 2

Third system of equation;

y = -4·x - 3, y + 4·x = 5

y + 4·x = 5

-4·x - 3 + 4·x = 5

-4·x + 4·x - 3 = 5

0 - 3 = 5

-3 = 5

The third system of equation has no solution

The system of equations that does not belong with the other two is the third system of equation; y = -4·x - 3, y + 4·x = 5, that has no solution.

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Answer:

- The population in 2001 is 23.1 million

- It will reach 28.3 million in 2013

Step-by-step explanation:

Given

\(A =23.1e^{0.0152t}\)

Solving (a): Population in 2000.

This implies that

\(t = 2000 - 2000\)

\(t = 0\)

So, we have:

\(A =23.1e^{0.0152t}\)

\(A =23.1e^{0.0152*0}\)

\(A =23.1e^{0}\)

Solve the exponent

\(A =23.1*1\)

\(A =23.1\)

The population in 2001 is 23.1 million

Solving (b): When will it reach 28.3 million

This implies that:

\(A =28.3\)

So, we have:

\(A =23.1e^{0.0152t}\)

\(28.3 = 23.1e^{0.0152t}\)

Divide both sides by 23.1

\(1.225 = e^{0.0152t}\)

Take natural logarithm of both sides

\(ln\ 1.225 = ln(e^{0.0152t})\)

Rewrite as:

\(ln\ 1.225 = 0.0152t\ ln(e)\)

\(ln(e) = 1\)

So:

\(ln\ 1.225 = 0.0152t*1\)

\(ln\ 1.225 = 0.0152t\)

Make t the subject

\(t = \frac{ln\ 1.225}{0.0152}\)

\(t = \frac{0.2029}{0.0152}\)

\(t \approx 13\)

Add the value of t to 2013 to get the actual year

\(Year = 2000 +13\)

\(Year = 2013\)

It will reach 28.3 million in 2013

Answer: She missed 5 targets

Step-by-step explanation:

-75/ -15

5 targets missed

The y-coordinate of -3f(x-1) when x = 0 is -63

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

The table of values

So, we have

-3f(x - 1)

When x = 0, we have

y = -3f(0 - 1)

This gives

y = -3f(-1)

From the table, we have

y = -3 * 21

Evaluate

y = -63

Hence, the y-coordinate is -63

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Answer:

Step-by-step explanation:

a. 1/3

b. 1/2

c. 1/3

Answer:

yes, no, yes, no

Step-by-step explanation:

For it to be a line, that means that when x goes up by 1 y goes up by the same thing every time.

7a. from (1, 12) to (2, 8), the x coordinate goes up by 1 and the y coordinate goes down by 4. From (2, 8) to (3, 4) the y coordinate again goes down by 4 when the x coordinate goes up by 1. This pattern continues for the other points, so yes.

Do the same thing for the rest and you should get:

7b. No

7c. Yes

7d. No

Answer:

a=no

b=no

c=yes

d=no

Here we have a geometric sequence, the recursive formula is:

Aₙ = (1/3)*Aₙ₋₁

And the explicit formula is:

Aₙ = (1/3)*ⁿ⁻¹*540

Here we have the following sequence:

540, 180, 60, 20, ...

This seems to be a geometric sequence, to check this, we need to take the quotients between consecutive terms and see if we get the same thing.

180/540 = 1/3

60/180 = 1/3

20/60 = 1/3

So yes, this is a geometric sequence where the common ratio is 1/3, so each term is (1/3) times the previous one, so the recursive formula is:

Aₙ = (1/3)*Aₙ₋₁

And the explicit formula is:

Aₙ = (1/3)*ⁿ⁻¹*A₁

Where A₁ is the first term, in this case 540, so the formula becomes:

Aₙ = (1/3)*ⁿ⁻¹*540

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Answer:

1 1/45

Step-by-step explanation:

3 5/6 ÷ 3 3/4

~Turn into improper fractions

23/6 ÷ 15/4

~Copy Dot Flip

23/6 * 4/15

~Multiply

92/90

~Simplify

1 1/45

Best of Luck!

Answer:

20000

Step-by-step explanation:

115%-> 23000

100%->20000

The cost of the topsoil needed to fill the flower bed is $588.75.

A rectangular flowerbed measures 3 meters by 5 meters.

The bed must be dug out and filled with topsoil to a depth of 0.5 meters.

To find:

a) The volume of the topsoil needed to fill the flowerbed.

Volume of topsoil = length × breadth × height of flowerbed

= 3 m × 5 m × 0.5 m= 7.5 m³

Therefore, the volume of topsoil needed to fill the flowerbed is 7.5 cubic meters.

Now, let us calculate the cost of the topsoil needed.Cost of 1 meter of topsoil

To calculate the volume of topsoil required to fill the flower bed, you can use the cuboid volume formula:

Volume = Length x Width x Depth

Length = 3 meters

Width = 5 meters

Depth = 0.5 meters

Substituting the values ​​into the resulting formula:

Volume = 3 meters x 5 meters x 0.5 meters

Volume = 7.5 cubic meters

The volume of topsoil required for Bed 7.5 cubic meters.

b) To calculate the cost of topsoil required, the volume of topsoil should be multiplied by the cost per meter.

The cost is $78.50 per meter, so you can calculate the cost as follows:

cost = volume * cost per meter

Plug the value into the formula:

cost = 7.5 cubic yards * $78.50/ meters

cost = $588.75

= $78.50Cost of 7.5 meters of topsoil

= 78.5 × 7.5= $588.75

Therefore, the cost of the topsoil needed is $588.75.

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(f/g)(-5) is equal to 1/4, and the value -1 is not in the domain of f/g.

To find (f/g)(-5), we need to substitute -5 into the functions f(x) and g(x) and then divide f(-5) by g(-5).

Given:

f(x) = (4+x)(6+x)

g(x) = 1+x

Substituting -5 into the functions:

f(-5) = (4+(-5))(6+(-5)) = (-1)(1) = -1

g(-5) = 1+(-5) = -4

Now, we can calculate (f/g)(-5):

(f/g)(-5) = f(-5) / g(-5) = -1 / -4 = 1/4

Therefore, (f/g)(-5) equals 1/4.

Now let's determine the values that are not in the domain of f/g. The values that are not in the domain of f/g are the values that make the denominator g(x) equal to zero. In this case, the denominator is g(x) = 1+x.

To find the values that make the denominator zero, we solve the equation:

1 + x = 0

Subtracting 1 from both sides, we get:

x = -1

So, the value x = -1 is not in the domain of f/g because it would make the denominator equal to zero.

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Using the normal distribution, it is found that there is a 0.2798 = 27.98% probability that he’ll use all the toothpaste in the tube.

In a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

In this problem:

The probability that he’ll use all the toothpaste in the tube is 1 subtracted by the p-value of Z when X = 0.85, hence:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{0.85 - 0.78}{0.12}\)

\(Z = 0.583\)

\(Z = 0.583\) has a p-value of 0.7202.

1 - 0.7202 = 0.2798

0.2798 = 27.98% probability that he’ll use all the toothpaste in the tube.

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Answer:

3rd Option: 1

Step-by-step explanation:

Step 1: Define

(x + 4)/3x

x = 2

Step 2: Substitute and Evaluate

(2 + 4)/3(2)

6/6

1

Answer:

Paige is incorrect.  g(x) has a steeper slope

Step-by-step explanation:

The slope for f(x)  is

m =( y2-y1)/(x2-x1)

   = (17/2 - 5/2) / ( -1 - -6)

    = (17/2 - 5/2) / ( -1 +6)

    = (12/2)/5

    = 6/5

The slope for g(x)  is

m =( y2-y1)/(x2-x1)

   = (-1 - 13/3) / ( 6 - 2)

    =(-3/3 -13/3) / (6-2)

    (-16/3)/4

     -16/3 * 1/4

   - 4/3

Comparing the magnitudes

|6/5|   |-4/3|

|6/5*3/3|     |-4/3*5/5|

|18/15|           |20/15|

|20/15| is greater so it has a steeper slope

g(x) has a steeper slope

The true statement regarding the classical model is I only. The AS curve is vertical.

The classical model of economics suggests that the economy is always at full employment and the prices and wages are hence, flexible enough to adjust to changes in demand. According to classical theory, the aggregate supply (AS) curve is vertical, which means that the quantity of commodities produced is independent of the price level.

The vertical AS curve is a key feature in the model that distinguishes it from other economic models, such as the Keynesian model, which assumes that the AS curve is upward-sloping. In the Keynesian model, changes in the price level can affect the number of commodities produced, as firms may choose to decrease production if the price they can charge for their products falls.

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Answer:

15

Step-by-step explanation:

=> (-3)²+(-4+7)(2)

=> 9+(3)(2)

=> 9+6

=> 15

Answer:

$94.81

Step-by-step explanation:

the selling price (before discount 20%) =

$98.60 ÷ (100-20)%

= $98.60 ÷ 0.8 = $123.25

the store paid for the clarinet =

$123.25 ÷ (100+30)%

= $123.25 ÷ 1.3 = $ 94.81

Answer:

Step-by-step explanation:

20

A z-score of 0 indicates that the person's score is equal to the mean, so they are right at the Average Performance level.the z-score of a person who scored 300 on the exam is 0.

The z-score of a person who scored 300 on the exam, we can use the formula:

z = (x - μ) / σ

where z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation.

In this case, the person scored 300 on the exam, which is equal to the mean (μ). Therefore, we can substitute these values into the formula:

z = (300 - 300) / 40

Simplifying the equation, we have:

z = 0 / 40

Since any number divided by zero is undefined, we can conclude that the z-score of a person who scored 300 on the exam is 0.

The z-score measures the number of standard deviations a data point is away from the mean. In this case, a z-score of 0 indicates that the person's score is equal to the mean, so they are right at the average performance level.

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Step-by-step explanation:

to find f(5)   in f(x) , just put in '5' where 'x' is in the equation

f(5) = 3 (5) + 2 = 17

Answer:

f(5) = 17

Step-by-step explanation:

Let's evaluate the function for f(5)

Insert 5 everywhere x appears:

Therefore f(5) = 17

1. Figure STUV is congruent to Figure KLMN because rigid motions can be used to map Figure STUV onto Figure KLMN.

2. Figure STUV is also similar to Figure KLMN because rigid motions and/or dilations can be used to map Figure STUV onto Figure KLMN. The scale factor is 2.

When it is said that two figures are congruent, like the ones shown on the graph, This means that they have the same shape and size.

Similar figures have the same shape, but they may have different sizes and be located in different positions.

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The expanded form of the given decimal number is 706.039 = 700 + 0 + 6 +0.0 +0.03 +0.009

We break up a number according to its place value and expand it to show the value of each digit.

Given that to write expanded form of 706.039

Expanded Factors Form:

706.039 = 7 × 100  + 0 × 10 + 6 × 1  + 0 × 0.1 + 3 × 0.01 + 9 × 0.001

Expanded Notation Form:

706.039 = 700 + 0 + 6 +0.0 +0.03 +0.009

Hence, the expanded form of the given decimal number is 706.039 = 700 + 0 + 6 +0.0 +0.03 +0.009

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Answer:

8 people bought economy and 2 bought first class

Step-by-step explanation:

there are 10 person and total is 1580 so 250+ 9(135)=1460 which is wrong so we gonna try adding 2(250) and 8(135) which got us 1580