Write and solve an equation for the given situation. Alan rented a car while on vacation in Florida. He was charged a one-time fee of $43 as well as $1.10 for each mile driven. If his final bill was $111.20, how many miles did he drive?

We will have the following:

*First: We determine the measure of angle L:

So, the measure of angle L is 23°.

*Second: We will use the measure of MN and the angle of L to determine the length of the hypotenuse:

So, the length of the hypotenus is approximately 20.5 units.

Here is the graph that shows the scenario:

To show that the quadrilateral on the tile floor is a parallelogram, you can use the opposite sides theorem, opposite angles theorem, consecutive angles theorem, and Diagonal bisector theorem.

1. Opposite sides theorem: If both pairs of opposite sides of the quadrilateral are congruent (equal in length), then it is a parallelogram.

2. Opposite angles theorem: If both pairs of opposite angles of the quadrilateral are congruent (equal in measure), then it is a parallelogram.

3. Consecutive angles theorem: If the consecutive angles of the quadrilateral are supplementary (their sum is 180 degrees), then it is a parallelogram.

4. Diagonal bisector theorem: If the diagonals of the quadrilateral bisect each other (divide each other into two equal parts), then it is a parallelogram.

Choose the most appropriate theorem based on the given information and apply it to prove that the quadrilateral is a parallelogram.

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The  probability space and that e1 and e2 are events satisfying e1 ∪ e2 = s, p(e1) = 1/5, and p(e1 ∩ e2) = 1/30.The  p(e2) is 0.8333.

In chance principle, a probability space or a probability triple. is a mathematical construct that offers a formal model of a random manner or "test". for example, you can still outline an opportunity area that fashions the throwing of a die.

A chance area fashions random occasions and is made of three parts: pattern space: the set of all possible results. as an example, in case you toss a coin twice, the pattern space is {HH, HT, TH, TT}. The sample space is every so often denoted by way of the Greek letter omega (Ω).07-Jan-2017

A finite probability space is a fixed S and a feature p: S → R ≥zero such that p(s) > 0 (∀s ∈ S) and ∑ p(s) = 1. We re. page 1. A finite probability area is a set S and a characteristic p: S → R≥0 such that p(s) > 0. (∀s ∈ S) and ∑

Given E1 and E2 events S is the probability space

And given E1∪ E2 =S

P(E1)=1/5 and P(E1 ∩ E2 )=1/30

From given P(E1∪ E2)=P(S)

From probability axioms P(S)=1

Therefore P(E1∪E2) =1

      P(E1)+ P(E2)- P(E1 ∩E2)= 1

      (1/5) + P(E2) - (1/30) = 1

   P(E2 )= 1-(1/5) +(1/30)= 0.8333

Therefore P(E2)= 0.8333

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The number of people that must be in the group is 15.

The expression for the total cost of Deal A is: $9p + $15

The expression for the total cost of Deal B is: $6p + $3p

Where p is the number of people in the group

When both promotions cost the same, both expressions would be equal:

$9p + $15 =  $6p + $3p

In order to determine the value of p, take the following steps:

Combine similar terms

$6p + 3p - 9p = 15

p = 15

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The ordered pair (-2, 2) satisfies both inequalities y < -x + 1 and y > x.

The correct option is A: (-2, 2).

To determine which ordered pairs satisfy both inequalities y < -x + 1 and y > x, we need to check each pair's coordinates in both inequalities.

Let's test each ordered pair:

A: (-2, 2)

For y < -x + 1: 2 < -(-2) + 1 → 2 < 3 (True)

For y > x: 2 > -2 → 2 > -2 (True)

B: (1, 1)

For y < -x + 1: 1 < -(1) + 1 → 1 < 0 (False)

For y > x: 1 > 1 → 1 > 1 (False)

C: (0, 0)

For y < -x + 1: 0 < -(0) + 1 → 0 < 1 (True)

For y > x: 0 > 0 → 0 > 0 (False)

D: (-1, -1)

For y < -x + 1: -1 < -(-1) + 1 → -1 < 2 (True)

For y > x: -1 > -1 → -1 > -1 (False)

From the above calculations, we can see that only the ordered pair (-2, 2) satisfies both inequalities y < -x + 1 and y > x. Therefore, the correct answer is option A: (-2, 2).

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The complete question:

Which ordered pairs make both inequalities y < -x + 1 and y > x true?

A: (2, 2)

B: (1, 1)

C: (0,0)

D: (-1, -1)

A binomial is a factor of a polynomial has been determined by using the

polynomial division method.

To determine if a binomial is a factor of a polynomial, you can use the polynomial division method. The basic idea is to divide the polynomial by the binomial and check if the remainder is zero. If the remainder is zero, then the binomial is a factor of the polynomial. Here's the step-by-step process:

Write the polynomial and the binomial in standard form, with the terms arranged in descending order of their exponents.

Perform the long division of the polynomial by the binomial, similar to how you would divide numbers. Start by dividing the highest degree term of the polynomial by the highest degree term of the binomial.

Multiply the binomial by the quotient obtained from the division and subtract the result from the polynomial.

Repeat the division process with the new polynomial obtained from the subtraction step.

Continue dividing until you reach a point where the degree of the polynomial is lower than the degree of the binomial.

If the remainder is zero, then the binomial is a factor of the polynomial. If the remainder is non-zero, then the binomial is not a factor.

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Answer:

Answer:

7.3

Step-by-step explanation:

11.6 - 4.3 = 7.3

Helping in the name of Jesus.

The odds that a woman will get divorced from her first marriage by the time she is 40 depend on various factors such as location, cultural norms, socioeconomic status, and individual circumstances.

Therefore, a specific value cannot be provided without more information about the population being studied.

However, according to statistics from the United States Census Bureau, the estimated probability of a first marriage ending in divorce by the 20th wedding anniversary is about 52%. This suggests that the odds of a woman getting divorced from her first marriage before age 40 are relatively high.

It's worth noting that divorce rates and probabilities can vary widely based on factors such as age, education level, income, and race/ethnicity. Additionally, divorce is a complex and often emotionally charged issue that is influenced by a wide range of individual and societal factors.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data.

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a) Q1 = 66 and Q3 = 84

b)  the interquartile range is 18.

What is the domain and range?

The domain and range are fundamental concepts in mathematics that are used to describe the input and output values of a function or relation.

The domain of a function refers to the set of all possible input values, or x-values, for which the function is defined.

The range of a function refers to the set of all possible output values, or y-values.

To identify the lower and upper quartiles and calculate the interquartile range for the given scores, we need to arrange the scores in ascending order.

Arranging the scores in ascending order: 62, 66, 71, 80, 84, 88

(a) Lower and Upper Quartiles:

The lower quartile, denoted as Q1, is the median of the lower half of the data. It divides the data into two equal parts, with 25% of the scores below and 75% above.

Q1 = 66 (the value in the middle of the lower half of the data)

The upper quartile, denoted as Q3, is the median of the upper half of the data. It divides the data into two equal parts, with 75% of the scores below and 25% above.

Q3 = 84 (the value in the middle of the upper half of the data)

(b) Interquartile Range:

The interquartile range (IQR) is the difference between the upper quartile (Q3) and the lower quartile (Q1). It measures the spread of the middle 50% of the data.

IQR = Q3 - Q1

= 84 - 66

= 18

Therefore, a) Q1 = 66 and Q3 = 84

b)  the interquartile range is 18.

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At t = ±0.6 seconds its velocity will be zero.

When an object is moving, its velocity serves as a measure of how quickly its location is changing as it is seen from a given point of view and as time is measured using a specific unit of measurement.

The velocity of a particle is the derivative of its position with respect to time, so to find the velocity we need to take the derivative of x with respect to t.

dx/dt = 20 - 15t^2

To find when the velocity is zero, we set dx/dt = 0 and solve for t:

0 = 20 - 15t^2

15t^2 = 20

t^2 = 20/15

t = ±√(20/15)

So, the velocity is zero at approximately t = ±0.6 seconds.

Correct Question :

a particle's position is given by = 20t − 5t^3 meters. at what time is its velocity zero? give your answer to the nearest unit.

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Answer:

28.2743 square feet (28 square feet, rounded)

Step-by-step explanation:

The area of a circle is given by the equation

Area = πr^2

Plug in 3 for the radius

Area= π(3)^2

3 squared is 9

Area= 9 π

Area= 28.2743 square feet

Rounded to the nearest square foot, the area of the circle is 28 square feet.

the sampling distribution of the sample means is 0.03

According to the central limit theorem (n>= 30), the sampling distribution of the sample mean is approximately normal with a mean of 4.9 and a standard deviation of 3.

So:

x = standard dev/sample size

= 3 / 100

= 0.03; it is normal due to its large sample size.

Distribution is the technique of promoting and handing over services and products to clients. The term is related to marketing channels that are used to reach customers in special methods and exceptional areas. distribution characteristic, a mathematical expression that describes the chance that a machine will take on a particular value or set of values. The traditional examples are related to games of hazard.

distributing objects is an act of spreading them out similarly. Algebraic distribution method to multiply every one of the phrases inside the parentheses by way of another time period this is outside the parentheses. To distribute a term over several different terms, you multiply each of the alternative phrases by the primary term. the statistical distribution suggests which values are common and uncommon. there are numerous styles of statistical distributions, along with the bell-shaped everyday distribution.

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Step-by-step explanation:

It is a 5th degree binomial. The highest exponetial power of the polynomial is 5, therefore we are dealing with a 5th degree polynomial. "Polynomial" is a general term. Trinomial and binomial categorize it even more by the number of terms the polynomial has. There are two terms, so we are dealing with a binomial. The prefix bi means "two"

Answer:

Binomial with degree 5

Step-by-step explanation:

The polynomial 3x⁵ + 3 is a binomial with degree 5.

Why?

This option is correct because:

\(\rule{150pt}{2pt}\)

In general, two congruent segments have the same measure. Since no more information about the figure is given, we would need to estimate the measurement of each of its segments.

A) Notice that

B)

C)

D)

E)

The end of the process, a total of 340 people will know the art of quilling.

Let's analyze the problem step by step.

In the first generation, Amanda teaches the art of quilling to 4 students. So there are 4 people who know the art of quilling at the end of the first generation.

In the second generation, each of the 4 students from the previous generation teaches the art of quilling to 4 more students. Therefore, in the second generation, there are 4 students from the first generation multiplied by 4 students taught by each of them, resulting in a total of 4 * 4 = 16 people who know the art of quilling.

This pattern continues for the next two generations. In the third generation, each of the 16 students from the second generation teaches 4 more students, resulting in a total of 16 * 4 = 64 people who know the art of quilling in the third generation.

Finally, in the fourth generation, each of the 64 students from the third generation teaches 4 more students, resulting in a total of 64 * 4 = 256 people who know the art of quilling in the fourth generation.

Now, let's express this using a geometric series:

The first term, a, is 4 (number of people in the first generation).

The common ratio, r, is 4 (each person in the previous generation teaches 4 more people).

The number of terms, n, is 4 (there are 4 generations).

Using the formula for the sum of a geometric series, we can calculate the total number of people who know the art of quilling:

S = a * (\(1 - r^n\)) / (1 - r)

S = 4 * (\(1 - 4^4\)) / (1 - 4)

S = 4 * (1 - 256) / (1 - 4)

S = 4 * (-255) / (-3)

S = 4 * 85

S = 340

Therefore, at the end of the process, a total of 340 people will know the art of quilling.

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Answer:

Well the slope of this is 49 and y intercept is 28, hooe this helped

Answer:

Slope: 2/2 = 1

y-intercept: 2

Step-by-step explanation:

Answer:

About $3.90

Step-by-step explanation:

6.37/1.65

The 12.04m is far from the base to wall.

The word "base" in mathematics is used to refer to a particular mathematical object that is used as a building block. The most common uses are the related concepts of the number system whose digits are used to represent numbers and the number system in which logarithms are defined.

Let the base of the 17ft long ladder be placed x ft away from the wall so that it exactly reaches the top of a 12- foot tall wall.

By Pythagorean theorem

12²+X²=17²

x²=17²-12²=145

x=√145=12.04

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Answer:

13% decrease. (13.4193548...% to be specific)

Step-by-step explanation:

The difference is 1550-1342=208. 208 as a percentage of 1550 --> 208/1550= 0.134193548... = 13% to the nearest whole number. So, it is a 13% decrease.

Answer:

En matemáticas, se dice que dos números reales distintos de cero a y b son conmensurables si su razón ab es un número racional; de lo contrario, ayb se denominan inconmensurables. (Recuerda que un número racional es uno que equivale a la razón de dos números enteros). En matemáticas y, en particular, en la teoría de la medida, una función medible es una función entre los conjuntos subyacentes de dos espacios medibles que conserva la estructura de los espacios: la preimagen de cualquier conjunto medible es medible.

Answer:

5 hours

Step-by-step explanation:

Answer: h = 5

Step-by-step explanation: Starting temp + (change in temp per hour × elapsed hours) = current temp

So...

82+(0.6h)=85

Subtract 82 from both sides to isolate your variable term.

0.6h=3

Divide both sides by 0.6 to solve for hl.

h=5

5 hours have elapsed.

Check your answer. In 5 hours, at 0.6⁰ per hour, the temp would increase by 3 degrees. 82 + 3 = 85

Two types of transformations that can be used to transform f(x) to g(x) are horizontal and vertical stretching/shrinking.

What is transformation ?

A transformation is a function that changes the position, size, or shape of an object or a graph. In mathematics, transformations are often used to map a function from one coordinate space to another. There are several types of transformations, including translations, rotations, reflections, and scalings.

Part A: Two types of transformations that can be used to transform f(x) to g(x) are horizontal and vertical stretching/shrinking.

Part B:

Horizontal stretching/shrinking: k is the horizontal scale factor.

Vertical stretching/shrinking: k is the vertical scale factor.

Part C:

Horizontal stretching/shrinking: g(x) = f(kx)

Vertical stretching/shrinking: g(x) = kf(x)

Two types of transformations that can be used to transform f(x) to g(x) are horizontal and vertical stretching/shrinking.

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Step-by-step explanation:

(5×10³) × (9×10^7)

= 45 × 10^10

= 4.5 × 10¹¹

Answer:

Answer is A

Step-by-step explanation:

They start at -10 and if you add 10 you get 0. You increase

15 inches is the height of the pyramid

Step-by-step explanation:

The volume of a cube is a³

Given a = 5 inches

→ Volume = a³

= 5³

= 5×5×5

= 125 in²

The volume of a pyramid is \( \frac{1}{3} {a}^{2}h\)

Given a = 5 inches , h = height of pyramid

\( = > \frac{1}{3} {a}^{2} h\)

\( = > \frac{1}{3}(5)^{2}h\)

\( = > \frac{1}{3} \times 25 \times h\)

\( = > \frac{25}{3}h\)

then,

\(125 = \frac{25h}{3}\)

\( = > 25h = 125 \times 3\)

\( = > 25h = 375\)

\( = > h = \frac{375}{25} \)

\( = > h = 15\)

Hence, the height of pyramid is 15 inches

Answer:

-10

Step-by-step explanation:

f(-4)=-(-4)-5

f(-4)=-1

g(-6)=2(-6)+3

-12+3

g(-6)=-9

add together:

-1+-9

=-10

Answer: a = 9/x      b = -2/y

OR

-ax + by = -11

3 and 1

Answer: 17.333333.....

Step-by-step explanation:

You take 30-4. then divide 26 by 1.5 = 17.33333333333333333333333

Answer:

17 batches

Step-by-step explanation:

if you are left with 4 cups of flour, that means you used 26 cups to batch cookies.

1.5 cups = 1 cookie batch

26 cups = 26 * 1 / 1.5

26/1.5 = 260/15 = 52/3 = 17.3 or 17 batches.

Make sure to confirm this my man