A walking tour of Washington, D.C., costs $20 per person. Show that the relationship between the number of people in a tour group and the total cost is a proportional relationship. Write an equation for the relationship.

Graph of given system of equations is shown in figure with intersection point (2, 4).

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The system of equation is,

⇒ 2x + y = 8

⇒ - x + 2y = 6

By solving both equation , we get;

⇒ (x, y) = (2, 4)

Thus, The graph of system of equation intersect on point (2, 4).

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x2 + 5x - 25

= (x + 8)(x - 3)

So D, or (x + 8) is the answer.

Answer:

The slope is -4/5...

Step-by-step explanation:

y=mx+b

m=slope

b= y-intercept

The 99% confidence interval for the population mean of high school students who take the bus to school every day is approximately 0.445 to 0.543.

To construct a confidence interval for the population mean of high school students who take the bus to school every day, we can use the sample data and the formula for a confidence interval.

Given:

Sample size (n) = 650

Number of students who take the bus (x) = 321

To construct a 99% confidence interval, we need to determine the standard error and the critical value.

Step 1: Calculate the sample proportion (p-hat):

p-hat = x/n = 321/650 ≈ 0.494

Step 2: Calculate the standard error (SE):

SE = \(\sqrt{[(p-hat * (1 - p-hat)) / n]}\)

SE = \(\sqrt{[(0.494 * (1 - 0.494)) / 650]}\)

SE ≈ 0.019

Step 3: Determine the critical value (Z):

For a 99% confidence interval, the critical value is Z = 2.576 (from the standard normal distribution table).

Step 4: Calculate the margin of error (ME):

ME = Z * SE

ME ≈ 2.576 * 0.019 ≈ 0.049

Step 5: Calculate the confidence interval:

Lower bound = p-hat - ME

Upper bound = p-hat + ME

Lower bound ≈ 0.494 - 0.049 ≈ 0.445

Upper bound ≈ 0.494 + 0.049 ≈ 0.543

The 99% confidence interval for the population mean of high school students who take the bus to school every day is approximately 0.445 to 0.543. This means that we can be 99% confident that the true population mean lies within this interval.

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Answer:

28/63

Step-by-step explanation:

10/21*14/15=140/315=28/63

53 inches is the mean height of the students in the group.

Given data: \(54,48,52,56,55\)

We know that mean of the heights =  \(\frac{Sum of all the heights}{No. of students}\)

                                                         \(= \frac{54+48+52+56+55}{5}\)

                                                         \(= \frac{265}{5}\)

                                                         \(= 53\) inches

Thus, the mean height of the students is 53 inches

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Answer:

-11

28-17=11

17-17=0

0-11=-11

Answer:

108°

Step-by-step explanation:

LMN is the sum of LMP and NMP. Just add it up!

LMN = 85+23 = 108

Therefore, LMN is 108°

Answer:

equal to 1

Step-by-step explanation:

I believe this is the answer. Also I see that ur new. Well welcome to Brainly.

The 4 properties of the rhombus are:

A quadrilateral in Euclidean geometry is a rhombus. It's a parallelogram with all sides equal and diagonals intersecting at 90 degrees. In addition, opposing sides are parallel, and opposing angles are equal. This is a fundamental property of the rhombus. A rhombus is shaped like a diamond. As a result, it's also known as a diamond.

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The tree is 10 meters tall.

To find the height of the tree, we can use the concept of similar triangles. The ratio of the height of the tree to the length of its shadow should be equal to the ratio of the height of the post to the length of its shadow, since they are both located in the same plane and are being illuminated by the same light source.

Let's use proportions to solve this problem. We can set up the proportion:

height of tree / length of tree's shadow = height of post / length of post's shadow

Let h be the height of the tree. Then we have:

h / 15 = 2 / 3

Cross-multiplying, we get:

3h = 30

h = 10

Therefore, the tree is 10 meters tall.

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The amount is $3025 and the interest is $525.

When an amount earns a compound interest, it means that both the amount invested and the interest that has already been earned increases in value at each compounding period.

The formula for calculating future value with annual compounding:

FV = P (1 + r)^n

Where:

= 2500 x (1 + 0.1)^2

= 2500 x (1.1)^2 = $3,025

Interest = future value -  amount invested

$3025 - 2500 = $525

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Step-by-step explanation:

'x' distance from   4 to 9 is 5 units

'y' distance is  rom -6 to -6   is zero

the distance is then just the distance between the x coordinates = 5 units

Answer:

angle 2 =90 because it is a right angle

Answer:

MN

Step-by-step explanation:

Answer:

a) 3x² + 7x + 2

b) 4x² + 2x - 12

c) x² + 8x + 12

d) π (16x² + 144)

Step-by-step explanation:

a) Rectangle

A = bh

A = 3x + 1 (x + 2)

A = 3x² + 6x + 1x + 2

A = 3x² + 7x + 2

b) Parallelogram

A = bh

A = 2x + 4 (2x - 3)

A = 4x² + (-6x) + 8x + (-12)

A = 4x² + 2x - 12

c) Trapezoid

A = a + b/2 (h)

A = [(x + 3) + (x + 9)]/2 (x + 2)

A = (2x + 12)/2 (x + 2)

A = x + 6 (x + 2)

A = x² + 2x + 6x + 12

A = x² + 8x + 12

d) Circle

A = πr²

A = π (4x + 12)²

A = π (16x² + 144)

This will be you're simplest answer unless you multiple 16x² + 144 times pi (π) and round.

Answer:

12

Step-by-step explanation:

Length of the radius of the circle is equals to 6units.

" Length of the arc is defined as the distance between two point as a part of the circumference of the given curve."

Formula used

Length of the arc = rθ

r = radius of the circle

θ = central angle

Radius = \(\frac{diameter}{2}\)

According to the question,

Given,

Diameter = AB

Length of the arc = 6pi

Here central angle formed with diameter 'θ' = 180°

                                                                     = \(\pi\)

Substitute the value in the length of the arc formula we get,

   \(6\pi = r \pi\)

⇒ \(r = 6units\)

Hence, length of the radius of the circle is equals to 6units.

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The value of x is 9 when f(x) = - 10.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = -x - 1 _____(1)

f(x) = -10 ____(2)

Now,

From (1) and (2),

-x - 1 = -10

10 - 1 = x

x = 10 - 1

x = 9

Thus,

x is 9.

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Answer: 25

i just took the quiz, it’s 25.

The standard cell potential Ecell∘ for the equation Fe(s) + F₂(g) ⟶ Fe²⁺(aq) + 2F⁻(aq) is 2.87 V.

To calculate the standard cell potential (Ecell∘), we need to use the standard reduction potentials (E°) for the half-reactions involved in the cell. The reduction potential for the reduction half-reaction of Fe²⁺(aq) + 2e⁻ ⟶ Fe(s) is given as +0.44 V (taken from the standard reduction potentials table). The oxidation half-reaction of F₂(g) ⟶ 2F⁻(aq) + 2e⁻ has a reduction potential of +2.87 V.

To find the overall cell potential, we subtract the reduction potential of the anode (F₂) from the reduction potential of the cathode (Fe²⁺/Fe):

Ecell∘ = Ered(cathode) - Ered(anode)

Ecell∘ = (+0.44 V) - (+2.87 V)

Ecell∘ = -2.43 V

Since the standard cell potential is negative (-2.43 V), it indicates that the reaction is not spontaneous under standard conditions.

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the complete question is:

Calculate the standard cell potential Ecell∘, for the equation

Fe(s)+F2(g)⟶ Fe2+(aq)+2F−(aq)

Standard reduction potentials can be found in this table.

Ecell∘=V

Using translation concepts, the formula for function g(x) is given by the following option:

D. g(x) = 2^(x - 2)

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

From the graph of the functions, we have that:

This means that g(x) is a shift right of 2 units of f(x), that is:

g(x) = f(x - 2).

Hence:

g(x) = 2^(x - 2)

The formula for function g(x) is given by the following option:

D. g(x) = 2^(x - 2)

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Answer:

This is a function and there is no value of x for which we will get two or more different values of y.

Step-by-step explanation:

Now, this is a function and there is no value of x for which we will get two or more different values of y

The equation is y = 2x

bye

Sean would choose apples over pears if he were offered both, based on his preference order of apples > clementines > pears and the assumption that his preferences are transitive.

Sean's preference order for fruits is: apples > clementines > pears. As a rational decision-maker, Sean would choose the option that he prefers the most. In this case, since he prefers apples over clementines and pears, if he were offered pears or apples, he would choose apples.

This decision is based on the assumption that Sean's preferences are transitive, meaning that if he prefers A to B and B to C, then he would prefer A to C. Therefore, choosing apples over pears is the most rational decision for Sean, based on his given preference order.

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Answer:

35, 36, and 37

Step-by-step explanation:

We know our answer is correct because 35 + 36 + 37 equals 108.

Answer:

35,36,and 37

Step-by-step explanation:

We have the next expression:

Now, solve the parentheses using the next property:

Therefore:

Which represents the product of two powers.

But, we need to find two quotients:

Then, we can rewrite the next expression:

To make fractions, we use the next property:

Then:

The result expression for the product of two powers:

The result for the product of two quotients:

We have shown both inclusions: A∩(B∪C) ⊆ (A∩B)∪(A∩C) and (A∩B)∪(A∩C) ⊆ A∩(B∪C). Thus, we have proved the set equality A∩(B∪C) = (A∩B)∪(A∩C).

To prove the set equality A∩(B∪C) = (A∩B)∪(A∩C), we need to show two inclusions:

A∩(B∪C) ⊆ (A∩B)∪(A∩C)

(A∩B)∪(A∩C) ⊆ A∩(B∪C)

Proof:

To show A∩(B∪C) ⊆ (A∩B)∪(A∩C):

Let x be an arbitrary element in A∩(B∪C). This means that x belongs to both A and B∪C. By the definition of union, x belongs to either B or C (or both) because it is in the union B∪C. Since x also belongs to A, we have two cases:

Case 1: x belongs to B:

In this case, x belongs to A∩B. Therefore, x belongs to (A∩B)∪(A∩C).

Case 2: x belongs to C:

Similarly, x belongs to A∩C. Therefore, x belongs to (A∩B)∪(A∩C).

Since x was an arbitrary element in A∩(B∪C), we have shown that for any x in A∩(B∪C), x also belongs to (A∩B)∪(A∩C). Hence, A∩(B∪C) ⊆ (A∩B)∪(A∩C).

To show (A∩B)∪(A∩C) ⊆ A∩(B∪C):

Let y be an arbitrary element in (A∩B)∪(A∩C). This means that y belongs to either A∩B or A∩C. We consider two cases:

Case 1: y belongs to A∩B:

In this case, y belongs to A and B. Therefore, y also belongs to B∪C. Since y belongs to A, we have y ∈ A∩(B∪C).

Case 2: y belongs to A∩C:

Similarly, y belongs to A and C. Therefore, y also belongs to B∪C. Since y belongs to A, we have y ∈ A∩(B∪C).

Since y was an arbitrary element in (A∩B)∪(A∩C), we have shown that for any y in (A∩B)∪(A∩C), y also belongs to A∩(B∪C). Hence, (A∩B)∪(A∩C) ⊆ A∩(B∪C).

Therefore, we have shown both inclusions: A∩(B∪C) ⊆ (A∩B)∪(A∩C) and (A∩B)∪(A∩C) ⊆ A∩(B∪C). Thus, we have proved the set equality A∩(B∪C) = (A∩B)∪(A∩C).

Regarding the statement A∪(B∩C) = (A∪B)∩(A∪C), it is known as the distributive law of set theory. It can be proven using similar techniques of set inclusion and logical reasoning.

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Least Integer are -

(a) n = 7

(b) n = 9

(c) n = 0

(d) n = 4

What is a polynomial?

A mathematical statement made up of variables, coefficients, and non-zero integer exponents is known as a polynomial. A sum of terms is represented by this algebraic equation, where each term is the product of a coefficient and one or more variables raised to non-negative integer exponents. Any symbols or letters, such as x, y, or z, can be used as the variables.

What is a degree of a polynomial?

The degree of a polynomial is the highest exponent/power of the variable (or variables) in the polynomial expression. It represents the degree of the highest term in the polynomial.

The smallest integer n with which f(x) is O((\(x^{n}\)) for the given functions, we need to determine the highest power of x in each function. Let's analyse each function separately:

(a) f(x) = 2x² + x⁷log(x)

The highest power of x in this function is x⁷. Therefore, n = 7.

(b) f(x) = 3x⁹ + (log(x))⁴

The highest power of x in this function is x⁹. Therefore, n = 9.

(c) f(x) = (x⁴ + x² + 1)/(x⁴ + 1)

In this function, both the numerator and denominator have the highest power of x as x⁴. When we simplify the function, we can see that the highest power of x cancels out, resulting in a constant value of 1. So, f(x) is O(\(x^{0}\)) or simply O(1). Therefore, n = 0.

(d) f(x) = (x³ + 5log(x))/(x⁴ + 1)

The highest power of x in the numerator is x³, and the highest power of x in the denominator is x⁴. When we simplify the function, we can see that the x³ term becomes negligible compared to the x⁴ term as x approaches infinity. Therefore, f(x) is O(x⁴). Hence, the least integer n such that f(x) is O(\(x^{n}\)) is n = 4.

Therefore:

(a) n = 7

(b) n = 9

(c) n = 0

(d) n = 4

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Check the picture below.

\(tan(\theta )=\cfrac{\stackrel{opposite}{282}}{\underset{adjacent}{137}}\implies \theta =tan^{-1}\left( \cfrac{282}{137} \right)\implies \theta \approx 64^o\)

Make sure your calculator is in Degree mode.

If Sparky weights (lets call it K) 7 units and it is 7 times the Solo's weigth (lets call it S), then we can write:

Then, the weight of Solo is 1 unit.

199 feet in meters

1 foot = 0.3048 meters

\(0.3048(meters)\times199(feet)\)

\(=\fbox{60.66}\)