All will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $73.98 and costs an additional S0.09 per mille driven. Thesecond plan has an initial fee of $59.98 and costs an additional $0.13 per mile driven, How many miles would All need to drive for the two plans to cost thesame?

answer: t = 9

Part A: Rebecca's credit card balance can be calculated using the equation x = (51 - 1) 0.02 if her finance charge is $51.

Part B: By making the purchase on the final day of the billing cycle rather than the first day, Rebecca will be able to avoid paying $27 in finance charges.

How do equations work?

A mathematical statement proving the equality of values between two or more mathematical expressions is called an equation.

Equation symbols (=) are used to represent equations.

A finance charge is what?

The interest and other fees levied on credit cards are included in a finance charge.

Typically, the finance charge is based on a stated APR (annual percentage rate).

The month's billing cycle lasts for 28 days.

Balance at current starting = x.

APR = 24%, or annual percentage rate.

The monthly percentage rate (MPR) equals 2% (24% divided by 12).

The final day's purchase cost $1,400.

$51 is the total finance fee for the month.

($1,400 x 2% x 1/28) = $1 finance fee for the last-minute purchase.

$50 ($51 - $1) serves as the initial balance's finance charge.

The starting balance at this time is x = $2,500 ($50 x 2%).

Current Beginning Balance Equation: x = 51 - 1 0.02

($1,400 x 2%) Equals $28 in total loan charges for the last-minute purchase.

Finance charge savings from buying on the last day equals $27 ($28 - $1).

By buying the $1,400 gift for her friend on the last day of the billing cycle rather than the first, Rebecca can avoid paying $27 in finance charges.

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Answer:

6 grams of sugar in 3/4 liter.

Explanation:

Recall that two 1/4 portions is equal to 1/2.  So if 1/2 liter has 4 grams, 1/4 liter will have 2 grams of sugar.

Every 1/4 liter will have 2 grams of sugar.

Therefore, 3/4 liter will have 3 times as much sugar as 1/4 liter.  The amount of sugar in 3/4 liter will be 3 times 2 grams or 6 grams of sugar in 3/4 liter

Answer:

86.6 feet (3 s.f.)

Step-by-step explanation:

Please see attached picture.

tan60°= height of tower/ 50

Height of tower

= 50tan60°

= 50√3

= 86.6 ft (3 s.f.)

tanѲ= opp/ adj

The best description about the sampling distribution of means for the student's sample is mu x = 45, sigma x = 3.75, shape of distribution unknown.

Sampling distribution is defined as the probability distribution of a statistical measure which is got by the repeated sampling of a specific population.

Given that,

μ = 45 minutes and σ = 15 minutes

Sampling distribution of means for the student's sample is :

μₓ = μ = 45

σₓ = σ / √n, where n is the sample size.

σₓ = 15 / √(16) = 15 / 4 = 3.75

Now since the sample size 16 which is less than 30, shape of the distribution is unknown.

Hence the sampling distribution is, μₓ = 45, σₓ = 3.75, and the shape of distribution is unknown.

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Answer:
21 tables

Step-by-step explanation:

First, let’s simplify the ratio by dividing both sides by 11.

Once we’ve done that, we're left with a ratio of 3 tables for every 7 chairs.

Because 49 is divisible by 7, we will divide seven and get a quotient of 7.

All that’s left is to multiply 7 by 3, and get our final answer of 21 tables sold.

Answer:

We found, based on beach strandings, that more than 1,000 turtles are dying a year, after becoming tangled up, but this is almost certainly a gross underestimate. Young turtles and hatchings are particularly vulnerable to entanglement.” In recent years, global turtle population numbers have been falling.

Answer:

Answer: 10

Step-by-step explanation:

Let L be the length of the rectangle, and W be the width.

From the problem, we know that:

The perimeter of the rectangle is 72, which means that:

2(L + W) = 72

L + W = 36

The width is 4 less than 3 times the length:

W = 3L - 4

Substituting W = 3L - 4 into the first equation, we get:

L + 3L - 4 = 36

4L = 40

L = 10

Therefore, the length of the rectangle is 10. Answer:  10

Answer:

\(\frac{4}{6}\)

Step-by-step explanation:

Answer:

3x³ + 15x²

taking common 3x²

3x²(x+3) is your answer

Answer :

3x²(x+3) is the answer

Answer:

he's at work for 9 hours 55minutes

Carlos works for 8 hours and 55 minutes.

Given that, Carlos starts work at 21:20 and finishes at 06:15 the next day.

A clock or a timepiece is a device used to measure and indicate time. The clock is one of the oldest human inventions, meeting the need to measure intervals of time shorter than the natural units such as the day, the lunar month and the year.

The 24-hour clock is more often shown on digital clocks and is written in a 4-digit form, with the first two digits representing the hour and the last two representing the minutes.

From 21:20 to 06:15 there are 8 hours and 55 minutes.

Therefore, Carlos works for 8 hours and 55 minutes.

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Answer:

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

Given:

First, convert the two side length as below:

Now find the third side:

Hence the third side is 5√7 feet.

Answer:

TRUE

Step-by-step explanation:

Angle <A and angle <B are complementary, which means their sum must be = 90

Angle <B and angle <C are supplementary which means their sum must be = 180

Now let's see

m∠A=3x+17, m∠B=55−x, and m∠C=67(x/3−1)

first find the sum of A and B

3x + 17 + 55 - x = 90 add like terms

2x + 72 = 90 subtract 72 from both sides

2x = 18 divide both sides by 2

x = 9

TRUE OR FALSE is asked for

m∠A=44, m∠B=46, and m∠C=134

to find that we just replace c with 9 with every expression given for angles

m<A = 3x + 17

m<A = 3*9 + 17 = 44

m<B =  55 - x

m<B = 55 - 9 = 46

m<C = 134, we don't really need to calculate one by one since the angle are complementary and supplementary.

The answer is TRUE

The statement is true if A and ∠B are complements, while ∠B and ∠C are supplements.

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

We have:

∠A and ∠B are complements, while ∠B and ∠C are supplements.

∠A + ∠B = 90 degree

3x + 17 + 55 - x = 90

2x = 18

x = 9

Angle ∠B and angle ∠C are supplementary:

∠B + ∠C = 180

55 -x + 67(x/3  - 1) = 180

x = 9

Put the value of x and find angles A, B, and C.

m∠A = 44

m∠B = 46

m∠C = 134

∠A + ∠B = 90

∠B + ∠C = 180

The above statement is true.

Thus, the statement is true if A and ∠B are complements, while ∠B and ∠C are supplements.

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The perimeter of the triangle is 24.3 units.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

Triangle vertices:

(1,5), (1,-4), (-4,-4)

Now,

Using the distance formula,

The distance between (1, 5) and (1, -4).

D(1) = √(1 - 1)² + (5 + 4)²

D(1) = √9²

D(1) = 9

The distance between (1, -4) and (-4, -4) is:

D(2) = √(1 + 4)² + (-4 + 4)²

D(2) = √(5²

D(2) = 5

The distance between (-4, -4) and (1, 5) is:

D(3) = √(-4 - 1)² + (-4 - 5)²

D(3) = √(25 + 81)

D(3) = √106

Now,

The perimeter of the triangle.

P = d(1) + d(2) + d(3)

P = 9 + 5 + √106

P = 9 + 5 + 10.30

P = 24.3

Thus,

The perimeter of the triangle with vertices (1,5),(1,-4),(-4,-4) is 24.3 units.

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Answer:

Step-by-step explanation:

x=0

The statement that must be true since the average rate of change T(d) for the interval d = 4 and d = 10 is 0 is this:

C: The same number of tickets was sold on the fourth day and tenth day.

The average rate of change is a measurement that shows how much the function of a unit changes over a given interval. In the above question, we can see that the average rate of change given the two intervals is zero and this means that there was no change among the variables.

Thus, we can conclude that the number of tickets that were sold on day 4 was also the number of tickets sold on day 10.

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Answer:

The coefficients are;

1,28,378 and 3,276

Step-by-step explanation:

For the binomial expansion, when we talk of the coefficients, we mean the whole numbers that stands before the alphabets

For example, the coefficient of x in 2x is 2

Back to the question;

(x + y)^28

= 28C0 x^28y^0 + 28C1 X^27y^1 + 28C2 x^26y^2 + 28C3 x^25y^3 + ..........

So the coefficients we are looking for are;

28C0 = 1

28C1 = 28

28C2 = 378

28C3 = 3,276

Kindly note that 28C0 is read as 28 combination zero and so on

Answer:

dunno

Step-by-step explanation:

hope this helps has hdhd

Answer:

1 2/3

Step-by-step explanation:

ggez

Final Answer:  a. The number of units that should be sold in order to maximize the profit is 7 thousand units.

b. The  maximum profit is approximately $5.51

Conceptual part:   a. In order to find maximum profit we need to differentiate the profit function

\(dp/dx = (-3x^2+18x+21)/-x^3+9x^2+21x+1\) = 0

\(-3x^2+18x+21=0\)

\((x-7) (x+1) = 0\)

as profit can't be negative.

hence x=7.

b. We can determine the maximum profit by substituting x=7 in profit function.

\(p(7) = ln(-7^3+9*7+21*7+1)\)

\(p(7) = ln(246)\)

p(7) = 5.51

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Answer:

B

Step-by-step explanation:

Answer:

B. \(\frac{x^2}{3^2} +\frac{y^3}{2^2} =1\)

Step-by-step explanation:

The simplified version of (sec a - cosec a) / (sec a + cosec a)  is cosec 2a(cosec 2a - 2) / (sec²a - cosec²a).

The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.

Given:

(sec a - cosec a) / (sec a + cosec a)

Multiply the numerator and denominator by (sec a - cosec a)

(sec a - cosec a) / (sec a + cosec a)  × (sec a - cosec a)

(sec²a + cosec²a -2sec a cosec a) / (sec²a - cosec²a)

As we know,

\(sec^2a + cosec^2a = sec^2a \ cosec^2a\)

sec² a cosec² a - 2sec a cosec a /  (sec²a - cosec²a)

sec a cosec a (sec a cosec a - 2) / (sec²a - cosec²a)

cosec 2a(cosec 2a - 2) / (sec²a - cosec²a)

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Thus, the annual arithmetic mean number of degrees awarded in computer science over the most recent seven years is approximately 7,525.14.

To find the annual arithmetic mean number of degrees awarded in computer science over the most recent seven years, we need to add up the total number of degrees awarded over those years and then divide that total by seven (the number of years being considered).

So, adding up the numbers given in the question, we get:

4,820 + 13,188 + 4,614 + 5,920 + 12,372 + 5,885 + 5,877 = 52,676

Now, to find the mean, we divide this total by seven:

52,676 ÷ 7 = 7,525.14

So, the annual arithmetic mean number of degrees awarded in computer science over the most recent seven years is approximately 7,525.14.

If we wanted to understand more about how the number of degrees awarded in computer science has changed over time, we would need to look at additional data and analyze it in more detail.

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Let:

Wi = Initial weight

Wf = Final weight

x = amount of mass the substance lost

Therefore:

solve for x:

The perimeter is the sum of all sides. Then the perimeter of the kite is 27 units, then the correct option is C.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The length of the kite (x) will be given by the Pythagoras theorem

H² = P² + B²

H² = 15² + 8²

H² = 225 + 64

H² = 289

 H = 17

Then

\(\rm x = \dfrac{H}{2} \\\\x = \dfrac{17}{2}\\\\x = 8.5\)

And another length of the kite is 5 units.

Then the perimeter of the kite will be

Perimeter = 2(8.5 + 5)

Perimeter = 27

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The given statement "For every positive x ∈ Q, there is a positive y ∈ Q for which y < x" is true when we use proof by contradiction.

Assume that there exists a positive rational number x for which there is no positive rational number y such that y < x.

Let's consider the set of all positive rational numbers less than or equal to x

S = {y ∈ Q | y ≤ x}

Since there is no positive rational number y such that y < x, the set S must be non-empty, because if S was empty, then x would not have any rational number less than or equal to it.

Let y be the maximum element of the set S. Since y is the maximum element of S, we have y ≤ x, and for any other element z ∈ S, we have z ≤ y.

Since y is rational and y < x, there must exist a positive rational number z such that y < z < x. But z cannot be an element of S, because if z ∈ S, then z would be greater than y, contradicting the fact that y is the maximum element of S. This contradicts our initial assumption that there exists a positive rational number x for which there is no positive rational number y such that y < x.

Therefore, the statement "For every positive x ∈ Q, there is a positive y ∈ Q for which y < x" is true.

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Answer:4.2

Step-by-step explanation:

Answer:

a)ab and yz, ac and xy, bc and xz

b)yz  =   xy  =   xz          30 = 37.5 = 45      3 = 3 = 3      

ab      ac        bc          40     50       60     4    4    4

c)they are similar because all sides break down to ¾  

Step-by-step explanation: i did this on my test

a) The pairs of proportional triangle is

AB and YZ,

AC and XY,

BC and XZ

b) The fraction of side is

YZ / AB = XY / AC= XZ / BC = 3/4.

c) Yes the similarity of Triangle.

Similar triangles are triangles that have the same shape but differ in size. Similar items include all equilateral triangles and squares with any side length. In other words, if two triangles are identical, their corresponding angles and sides are congruent and in equal proportion. The " sign here denotes the resemblance of triangles.

In Triangle ABC and YZX

a) So, the pairs of proportional triangle is

AB and YZ,

AC and XY,

BC and XZ

b) The fractions with your side pairs is

YZ / AB = 30 / 40 = 3/4

XY / AC = 37.5 / 50 =  3/4

XZ / BC = 45/ 60 = 3/4.

c) As, the ratio of sides are proportion.

So, by SSS similarity criteria the triangles are similar.

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Answer:

Step-by-step explanation:

If XY is bisector of angle AXN then:   \(\dfrac{YN}{AY}=\dfrac{XN}{AX}\)

\(\dfrac4{12}=\dfrac{XN}{18}\\\\XN=\dfrac4{12}\cdot18\\\\XN=6\)                                                            

Two other examples of linear relationships are changes of units and finding the total cost for buying a given item x times.

Two examples of linear relationships that are useful are:

Changes of units:

These ones are used to change between units that measure the same thing. For example, between kilometers and meters.

We know that:

1km = 1000m

So if we have a distance in kilometers x, the distance in meters y is given by:

y = 1000*x

This is a linear relationship.

Another example can be for costs, if we know that a single item costs a given quantity, let's say "a", then if we buy x of these items the total cost will be:

y = a*x

This is a linear relationship.

So linear relationships appear a lot in our life, and is really important to learn how to work with them.

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