Amanda rented a bike from Ted's Bikes.

It costs $10 for the helmet plus $4.25 per hour.

If Amanda paid about $33.38, how many hours did she rent the bike?

a) Let h = the number of hours she rented the bike. Write the equation you would use to solve this problem.

The equation of the line in slope-point form is:

y - 7 = -4/5(x + 6)

The equation of a line in slope-point form is given by:

y - y₁ = m(x - x₁)

where:

(x₁, y₁) represents the coordinates of a point on the line.

m represents the slope of the line.

m = (y₂ - y₁)/(x₂ - x₁)

(x₁, y₁) represents the coordinates of the 1st point on the line

where (x₂, y₂) represents the coordinates of the 2nd point on the line

We have

(x₁, y₁) = (-6, 7)

(x₂, y₂) = (4, -1)

m = (y₂ - y₁)/(x₂ - x₁)

m = (-1 - 7) / (4 - (-6))

m = -8/10

m = -4/5

Using y - y₁ = m(x - x₁):

y - 7 = -4/5(x - (-6))

y - 7 = -4/5(x + 6)

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The solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

Given the inequality,

    f(x²-2) < f(7x-8) over D₁ = (-∞, 2)

We need to find the values of x that satisfy this inequality.

Since we know that f is increasing over its domain, we can compare the values inside the function to determine the values of x that satisfy the inequality.

First, we can find the values of x that make the expressions inside the function equal:

x² - 2 = 7x - 8

Simplifying, we get:

x² - 7x + 6 = 0

Factoring, we get:

(x - 6)(x - 1) = 0

So the values of x that make the expressions inside the function equal are x = 6 and x = 1.

We can use these values to divide the domain (-∞, 2) into three intervals:

-∞ < x < 1, 1 < x < 6, and 6 < x < 2.

We can choose a test point in each interval and evaluate

f(x² - 2) and f(7x - 8) at that point. If f(x² - 2) < f(7x - 8) for that test point, then the inequality holds for that interval. Otherwise, it does not.

Let's choose -1, 3, and 7 as our test points.

When x = -1, we have:

f((-1)² - 2) = f(-1) < f(7(-1) - 8) = f(-15)

Since f is increasing, we know that f(-1) < f(-15), so the inequality holds for -∞ < x < 1.

When x = 3, we have:

f((3)² - 2) = f(7) < f(7(3) - 8) = f(13)

Since f is increasing, we know that f(7) < f(13), so the inequality holds for 1 < x < 6.

When x = 7, we have:

f((7)² - 2) = f(47) < f(7(7) - 8) = f(41)

Since f is increasing, we know that f(47) < f(41), so the inequality holds for 6 < x < 2.

Therefore, the solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

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8x + y = 15

subtract 8x from sides, we have:

8x - 8x + y = 15 - 8x

y = 15 - 8x

Answer:2.95*\(10^{4}\)

Step-by-step explanation:

the solution of the equation (s, f) is (0.4, 0.3)

12s + 15f =9.30 ...equation 1

4s + 10f=4.60​ ...equation 2

Using elimination method:

To use this method, the variable we are to eliminate should have same coefficiet. SO eliminating s would mean mulitplying equation 2 by 3 so we would have same coefficient.

Multiply equation 2 by 3:

3(4s + 10f = 4.60​)

12s + 30f = 13.8 ...equation 2

combining both equations:

12s + 15f =9.30 ...equation 1

12s + 30f = 13.8 ...equation 2

subtract equation 1 from 2:

12s - 12s + 30f - 15f = 13.8 - 9.3

0 + 15f = 4.5

15f = 4.5

divide both sides by 15:

15f/15 = 4.5/15

f = 0.3

substitute for f in any of the equation:

using equation1:

12s + 15(0. 3) = 9.3

12s + 4.5 = 9.3

12s = 9.3 - 4.5

12s = 4.8

divide both sides by 12:

12s/12 = 4.8/12

s = 0.4

Hence, the solution of the equation (s, f) is (0.4, 0.3) or (4/10, 3/10).

Answer:

♨ \( \underline{ \underline{ \red{\large {\tt{Step - By - Step \: Explanation}}}}} : \)

☄ \( \underline{ \underline{ \large{ \pink{ \tt{G \: I\: V\: E \: N}}}}} : \)

☂ \( \underline{ \underline{ \large{ \purple{ \tt{T \: O \: \: F \: I \: N \: D}}}} }: \)

☃ \( \underline{ \underline{ \large{ \orange{ \tt{ S \: O \: L \: U \: T \: I \: O\: N}}} }}: \)

☼ \( \boxed{ \large{ \sf{Area \: of \: a \: parallelogram = base(b) \times height(h)}}}\)

~Plug the known values & then multiply!

⤑ \( \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \large{ \tt{16 \: cm \times 4cm}}\)

⤑ \( \: \: \: \: \: \: \: \: \: \: \: \: \ \: \: \: \: \: \: \: \: \: \: \: \ \boxed{\boxed{\large{ \tt{64 \: {cm}^{2} }}} }\)

☥ \( \large{ \boxed{ \tt{Our \: Final \: Answer : \boxed{ \underline{ \bold{ \red{ \tt{64 \: {cm}^{2} }}}}}}}}\)

♡ Hope I helped! ツ

Have a wonderful day / night !

✎ \( \underbrace{ \overbrace{ \mathfrak{Carry \: On \: Learning}}}\) ✔

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

Answer:

\(\huge \fbox \pink {A}\huge \fbox \green {n}\huge \fbox \blue {s}\huge \fbox \red {w}\huge \fbox \purple {e}\huge \fbox \orange {r}\huge \fbox \pink {:}\huge \fbox \pink{-}\)

Given:

base[b]=16cm

height [h]=4cm

we have

Area of parallelogram=base ×height

=16×4=64cm²is your answer.

Answer:

The 95% confidence interval for the population mean is

(79.2996, 81.9004)

Step-by-step explanation:

Step(i):-

Given that the sample size 'n' = 168

Let 'X' be a Random variable in a normal distribution

Given that mean of the sample x⁻ = 80.60

Given that the standard deviation of the Population = 8.60

Step(ii):-

The 95% confidence interval for the population mean is determined by

\((x^{-} - Z_{0.05} \frac{S.D}{\sqrt{n} } ,x^{-} + Z_{0.05} \frac{S.D}{\sqrt{n} } )\)

\((80.60 -1.96 \frac{8.60}{\sqrt{168} } ,80.60 + 1.96 \frac{8.60}{\sqrt{168} } )\)

(80.60 -1.3004 , 80.60+1.3004)

(79.2996 , 81.9004)

Final answer:-

The 95% confidence interval for the population mean is

(79.2996, 81.9004)

An order-preserving function is one where x < y implies f(x) < f(y). An isomorphism is a one-to-one order-preserving function between two partially ordered sets, while an automorphism is an isomorphism of a set to itself.

In the given excerpt, it explains the concepts of order-preserving functions, isomorphisms, and automorphisms in the context of partially ordered sets.

Order-Preserving Function:

A function f: P -> Q, where P and Q are partially ordered sets, is said to be order-preserving if for any elements x and y in P, if x < y, then f(x) < f(y). In other words, the function preserves the order relation between elements in P when mapped to elements in Q.

Increasing Function:

If P and Q are linearly ordered sets, then an order-preserving function is also referred to as an increasing function. It means that for any elements x and y in P, if x < y, then f(x) < f(y).

Isomorphism:

A one-to-one function f: P -> Q is called an isomorphism of P and Q if it satisfies two conditions:

a. f is order-preserving: For any elements x and y in P, if x < y, then f(x) < f(y).

b. f is onto (surjective): Every element in Q has a pre-image in P.

When an isomorphism exists between (P, <) and (Q, <), it means that the two partially ordered sets have a structure that is preserved under the isomorphism. In other words, they have the same ordering relationships.

Automorphism:

An automorphism of a partially ordered set (P, <) is an isomorphism from P to itself. It means that the function f: P -> P is both order-preserving and bijective (one-to-one and onto). Essentially, an automorphism preserves the structure and order relationships within the same partially ordered set.

These concepts are fundamental in understanding the relationships and mappings between partially ordered sets, particularly in terms of preserving order, finding correspondences, and exploring the symmetry within a set.

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By using the compass to measure a distance from the original line, and then transferring that distance to another point on the line, a parallel line can be drawn.

What is the parallel lines?

Parallel lines are two lines in a plane that never intersect.

1. Orientation of Lines:

Parallel lines are lines that never intersect and remain equidistant from each other at all points.

When constructing parallel lines, the lines are drawn in the same direction and maintain the same distance between them throughout their entire length. They do not meet or cross each other.

On the other hand, perpendicular lines are lines that intersect at a right angle (90 degrees). When constructing perpendicular lines, the lines are drawn so that they intersect at a right angle, forming four right angles at the point of intersection.

2. Tools/Methods Used:

Constructing parallel lines and constructing perpendicular lines may require different tools or methods.

To construct parallel lines, one common method is to use a straightedge and a compass. A straightedge is used to draw a straight line, and a compass is used to measure and transfer distances to create additional parallel lines.

Therefore, By using the compass to measure a distance from the original line, and then transferring that distance to another point on the line, a parallel line can be drawn.

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Answer:

the interest rate was 8% per year.

Explanation:

To begin with, we will find the total amount of interest paid:

$1914-$1650=$264.

Divide by 2 years:

$264/2=$132.

Hence now, we can find the interest rate:

$1650/100%=$16.5;

$132/$16.5=8%.

Answer:

he spent 2hours 50minutes snowboarding

the time he spent skiing and snowboarding minus the time he skied

5hours minus 2hours 10minutes

Answer:

15 and 20

Step-by-step explanation:

When dividing 88 by 5 we wil have;

88/5

= 17 3/5

= 17 + 0.6

=  17.6

So we are to find the two numbers that 17.6 falls in between

From the given option 17.6 falls between 15 and 20. Hence the required numbers are 15 and 20

The number of 100 dollar bills in one billion dollars  is 10 million hundreds or 70,900 hundred dollar bills.

To find the number of 100 dollar bills in one billion dollars, we can use the following steps:

First, we need to find the value of one billion dollars in terms of hundreds. Since each hundred dollar bill has a value of $100,

we can divide one billion by 100 to get the number of hundreds

\(:$$\frac{1\text{ billion}}{100}=10\text{ million}$$\)

So one billion dollars is equal to 10 million hundreds.

Now we need to find the volume of one hundred dollar bill. To do this, we multiply its length, width, and thickness:\($$6.14 \text{ in} \times 2.61 \text{ in} \times 0.00043 \text{ in}=0.00709 \text{ in}^3$$\)

The volume of one hundred dollar bill is approximately 0.00709 cubic inches.

Finally, we need to find the total volume of 10 million hundreds:\($$0.00709 \text{ in}^3 \times 10,000,000=70,900 \text{ in}^3$$\)

Therefore, the total volume of 10 million hundred dollar bills is approximately 70,900 cubic inches.10 million hundreds or 70,900 hundred dollar bills.

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Answer:

18

Step-by-step explanation:

g(y) = y² − 3y

g(6)=6²-3(6)

=36-18

=18

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Reverse the rows and photos in each row (ex 5 rows 10 photos=10 rows 5 photos) to get another 3 sets.

5 rows of 10 photos and last row with 3 photos,

6 rows of 8 photos and last row with 5 photos,

7 rows of 7 photos and last row with 4 photos,

Hence, reverse the rows and photos in each row (ex 5 rows 10 photos=10 rows 5 photos) to get another 3 sets.

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The reciprocal of 9 2/3 is 3/29

Answer:

Tyler will clim peak _____A____

The probability that it has a mass of more than 120 g is 13/40.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Statistics is the study of occurrences that follow a probability distribution.

Given,

frequency = 5   9   13   7   6

sum of frequency = 40

P(120<m<=180) = 13/40

P(180<m<=240) = 7/40

P(240<m<=300) = 6/40

Probability that it has a mass of more than 120 g = [P(120<m<=180) + P(180<m<=240) + P(240<m<=300) ]

⇒ 13/40 + 7/40 + 6/40

= 26/40

= 13/20

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The total weight in the bag is given as follows:

8.2 pounds.

The total weight is obtained applying the proportions in the context of the problem.

From the table, the weight of each equipment is given as follows:

Hence the total weight of a bag with 4 balls, 2 gloves, and 2 bats is given as follows:

4 x 0.35 + 2 x 0.77 + 2 x 2.63 = 8.2 pounds.

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Answer:

10000

Step-by-step explanation:

100 hugs x 100 hugs

= 10,000 hugs.

The mean absolute deviation (MAD) of the data set is equal to 180.625.

The mean absolute deviation of a data set is to find the average distance of each observation of the data set and the mean of the data set.

Mean absolute deviation = 1/n ∑ absolute value of (xi - x bar)

x bar =average value of the given data set

n= total number of data set

xi = data value in a given set

According to the question,

x bar = sum of all the data set / total number of the data set

x bar = 2052/16 = 128.25

Substitute the value in the formula, we have

Mean absolute deviation = 2890/16 = 180.625

Hence, the Mean absolute deviation of the data set is equal to 180.625.

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As per the given data, the Mean absolute deviation (MAD) of the data set is equals to 17.5

The term Mean absolute deviation in math is defined as the average distance of each observation of data set  and the mean of the data set.

Here we have given the following data.

=> 13, 0 , 14 , 36, 18, 9

Then the mean of the data is calculated as,

=> (13 + 0 + 14 + 36 + 18 + 9)/6

=> 90/6

=> 15

Now, we have to the Substitute the value in the formula, we have

And then the Mean absolute deviation is calculated as,

=> (90 + 15)/6

=> 105/6

=> 17.5

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Answer:

average mean not sure please

Answer: Actually, the correct answer is:

−0.1 + 1.7 = 1.6

So, y = 1.6.

Step-by-step explanation:

Given statement solution is :- It takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

To determine the number of months it takes to pay off the credit card and the total amount paid, including interest, we can follow these steps:

Step 1: Calculate the monthly interest rate.

The APR (Annual Percentage Rate) is given as 9.5%. To find the monthly interest rate, we divide this by 12 (the number of months in a year):

Monthly interest rate = 9.5% / 12 = 0.0079167

Step 2: Determine the monthly payment.

The monthly payment is given as $400.

Step 3: Calculate the interest and principal paid each month.

The interest paid each month can be calculated by multiplying the monthly interest rate by the current balance.

Principal paid = Monthly payment - Interest paid

Step 4: Track the remaining balance each month.

Starting with the initial balance of $1,367.90, subtract the principal paid each month to determine the new balance.

Step 5: Repeat Steps 3 and 4 until the balance reaches zero.

Continue calculating the interest and principal paid each month, updating the balance, until the remaining balance becomes zero.

Step 6: Determine the total number of months and the total amount paid.

Count the number of months it takes to reach a balance of zero. Multiply the number of months by the monthly payment ($400) to find the total amount paid.

Let's calculate the number of months and the total amount paid, including interest:

Month 1:

Interest paid = 0.0079167 * $1,367.90 = $10.84

Principal paid = $400 - $10.84 = $389.16

New balance = $1,367.90 - $389.16 = $978.74

Month 2:

Interest paid = 0.0079167 * $978.74 = $7.75

Principal paid = $400 - $7.75 = $392.25

New balance = $978.74 - $392.25 = $586.49

Month 3:

Interest paid = 0.0079167 * $586.49 = $4.64

Principal paid = $400 - $4.64 = $395.36

New balance = $586.49 - $395.36 = $191.13

Month 4:

Interest paid = 0.0079167 * $191.13 = $1.51

Principal paid = $400 - $1.51 = $398.49

New balance = $191.13 - $398.49 = -$207.36 (Paid off)

It takes 4 months to pay off the credit card. Now, let's calculate the total amount paid, including interest:

Total amount paid = 4 * $400 = $1600

Therefore, it takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

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Answer:

Not a function, but a relation

Step-by-step explanation:

It is not a function because every input must have one and only one unique output. In this case, one output has 4 different outputs, which means the set of ordered pairs can't be a function.

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Answer:

3.65

Step-by-step explanation:

The square root of 2 is 1.4 and the square root of 5 is 2.2 adding that together you get 3.6

Answer:

\(\frac{1}{6}\)

Step-by-step explanation:

Total no. of outcomes = 1,2,3,4,5,6

No. of times 5 is on the cube =1

Therefore, probability of getting a 5 = \(\frac{1}{6}\)