The sum of two numbers is 72. The difference of the two numbers is 40. What are the two numbers.

Let
x
be the larger number and
y
be the smaller number.
Write an equation that expresses the information in the sentence "The sum of two numbers is 72."

Answer:

Terminal point: (√3/2, 1/2); tan θ = √3/3

Step-by-step explanation:

The terminal point is (√3/2, 1/2) and the value of tanθ is √3/3 option (A) is correct.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have:

θ = π/6

Taking tan on both sides:

tanθ = tanπ/6 = 1/√3 = √3/3

Terminal points:

= (cosπ/6, sinπ/6)

= (√3/2, 1/2)

Thus, the terminal point is (√3/2, 1/2) and the value of tanθ is √3/3 option (A) is correct.

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Answer:

y = 9x -1

Step-by-step explanation:

The formula is y=mx+b

m = slope

b = y-intercept

All ya gotta do is plug in the slope and y-intercept then you have an equation!

Hope that helps and have a great day!

Answer: ITS 10!!!!

Step-by-step explanation:

According to the equation, values of "Y" in the table would be 81, 126, 321, and 406 when X is 4, 5, 8, and 9 Respectively.

As given equation is "Y = 5x²+1"

According to the table, we will put values of X in the equation to find the value of Y.

When X = 4,

Y = 5(4)² + 1

Y = 81

When X = 5

Y = 5(5)² + 1

Y = 126

When X = 8

Y = 5(8)² + 1

Y = 321

When X = 9

Y = 5(9)² + 1

Y = 406

Therefore values of Y would be 81, 126, 321, and 406 when X is 4, 5, 8, and 9 Respectively.

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—------------- CORRECT QUESTION FORMAT IS GIVEN BELOW —-----------

(Q). Complete the table to evaluate the function Y = 5x² + 1.

(Table is given below as in image section)

The Social Exchange Theory of interpersonal relationship satisfaction suggests that individuals are motivated to stay in a relationship as long as they feel that the rewards of the relationship are greater than the costs.

In the Social Exchange Theory of interpersonal relationship satisfaction, you would feel happiest in relationships when you feel that the rewards of the relationship equal or exceed its costs.

The Social Exchange Theory states that people evaluate their relationships in economic terms, with rewards being the benefits of the relationship and costs being the negatives. Rewards can include affection, attention, emotional support, sex, and companionship. Costs can include time, effort, money, and negative emotions such as stress, anxiety, and sadness.

According to the theory, individuals will be motivated to stay in a relationship as long as they feel that the rewards of the relationship are greater than the costs.

The opposite is also true; if individuals feel that the costs of the relationship are greater than the rewards, they will be motivated to leave the relationship.

Therefore, people are constantly evaluating their relationships to determine whether they are getting what they need from the relationship and whether it is worth continuing.

The Social Exchange Theory of interpersonal relationship satisfaction suggests that individuals are motivated to stay in a relationship as long as they feel that the rewards of the relationship are greater than the costs.

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The expression "x < 10" will output any value of x less than 10, while the expression "10 <= x" will output any value of x greater than or equal to 10. Together, they will output the range of x that is greater than or equal to 0 and less than 10

The expression "x < 10" will evaluate to true if the value of x is any number less than 10. This includes values 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Therefore, the expression "x < 10" will output all values of x within the range 0 to 9, inclusive. The expression "10 <= x" will evaluate to true if the value of x is any number greater than or equal to 10. This includes values 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, and so on. Therefore, the expression "10 <= x" will output all values of x within the range 10 and greater. Combining these two expressions will output the range of x that is greater than or equal to 0 and less than 10.

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For Expression A, a strategy could be to use the distributive property and then using the fact that the unit can be written in any fraction. To evaluate we have the following:

For Expression B, we can see that 3/7 is the common factor of both summands, so we can use again the distributive property (but in the inverse way) and then add the two fractions that have the same denominator. We have:

Answer:

The function table for g(x) = -x + 4 is as follows:

X Y -5 9 -1 5 0 4 1 3 2 2

The odds ratio is \(1.36\) (option b) based on the given table. The odds ratio is a measure of the strength and direction of the association between two categorical variables.

In more detail, the odds ratio is obtained by taking the ratio of the odds of an event in one group (e.g., exposed) to the odds of the event in another group (e.g., unexposed). It provides information on how much more likely (or less likely) the event is to occur in one group compared to the other. An odds ratio greater than 1 indicates a positive association, where the event is more likely in the exposed group. Conversely, an odds ratio less than 1 suggests a negative association, indicating that the event is less likely in the exposed group.

To determine the odds ratio from the given table, you would need to look at the values in the table that represent the exposed and unexposed groups and their respective event frequencies. Without the specific data in the table, it is not possible to provide a more detailed explanation for why option b (\(1.36\)) is the correct answer.

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The independent variable in this study is the temperature of the water in each tank. The independent variable is the factor that is intentionally manipulated or changed by the researcher in order to observe its effect on the dependent variable. In this case, the researcher is testing the effects of habitat space on the size of fish populations, and they are manipulating the temperature of the water to see how it impacts the survival of the goldfish.

The researcher sets up four aquariums of the same size with six goldfish in each one. The independent variable, temperature, is kept different in each tank. This means that each tank is maintained at a different temperature throughout the experiment.

By manipulating the temperature in each tank, the researcher can observe how the different temperature conditions affect the survival of the goldfish. This allows them to determine whether the size of the fish populations is influenced by habitat space, as measured by the temperature of the water.

To summarize, in this study, the independent variable is the temperature of the water in each tank. The researcher is manipulating the temperature to observe its effect on the survival of the goldfish and determine the impact of habitat space on fish populations.

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L ≈ 35.8 ,the length of the arc to the nearest tenth is 35.8 units

The formula for calculating the length of an arc intercepted by a central angle is L=, where L is the arc's length,  is the circle's radius, and  is the central angle in radians. The length of the arc to the nearest tenth is 35.8 units. Given, In a circle with radius r = 6.5, an angle measuring  = 5.5 radians intercepts an arc. We know that the formula for calculating the length of an arc intercepted by a central angle is L=, where L is the arc's length,  is the circle's radius, and  is the central angle in radians. Substituting the values in the formula, we get:

L = rL = 6.5(5.5)L = 35.75 ≈ 35.8 (to the nearest 10th)

Therefore, the length of the arc to the nearest tenth is 35.8 units.

In a circle, the length of an arc intercepted by a central angle is determined by the central angle's size and the circle's radius. This is known as the arc's length formula. L=where L is the arc length,  is the radius of the circle, and  is the central angle in radians. We can use this formula to find the length of an arc intercepted by a central angle in a circle. Let's consider the following illustration to understand the concept better. In a circle with a radius of 6.5, an angle of 5.5 radians intercepts an arc. We'll use the arc length formula to find the arc's length, L.L= (Length of arc formula)Substitute the given value of r and  in the formula. L = 6.5 × 5.5L = 35.75The length of the arc is 35.75 units. We'll round this answer to the nearest tenth to get the final answer. L ≈ 35.8Therefore, the length of the arc to the nearest tenth is 35.8 units.

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Answer:

\(100x^2-4\pi x^2\)

Also can be said as:

\(4x^2(25-\pi )\)

Step-by-step explanation:

The question is asking you, "how much is left over."

In this scenario, you're going to have to subtract the area of the pool (P) from the total area of the backyard (B), which will leave you with the remaining area of the backyard (x).

This means your equation to solve this question is:

\(x=B-P\)

The value of B is the area of the backyard.

We are told that the backyard is a rectangular shape. So, we can use the formula of finding the area of a rectangle.

The formula is \(B=L*W\), where L is the length and W is the width.

Both the length and width are 10x, so we must plug that into this equation.

We end up getting:

\(B=10x*10x\)

Which can be simplified to:

\(B=100x^2\)

The value of P is the area of the pool.

The pool is a circular shape. So, to get the area of it, we must use the formula of finding the area of a circle.

The formula is \(P=\pi r^2\), where r is the radius.

Plugging in the radius of 2x, we get:

\(P=\pi (2x)^2\)

By solving this out, we end up with:

\(P=4\pi x^2\)

From the scenario, we have the equation:
\(x=B-P\)

And from steps 1 and 2, we have the values:

\(B=100x^2\) and \(P=4\pi x^2\)

Now we just plug those values in to get:

\(x=100x^2-4\pi x^2\)

And finally, the amount of the backyard remaining is:

\(100x^2-4\pi x^2\)

This answer may be simplified to:

\(4x^2(25-\pi )\)

Answer:

B

Step-by-step explanation:

It is determined by a triangular circle.

Answer:

It is $3.00 per hour

Step-by-step explanation:

Let C be the total charge and t be the rental time in hours.

C = ht + 43

Plugging the given values into the equation, we get:

64 = 7h + 43

7h = 21

h = 3

The hourly fee is $3.00 per hour.

The hourly fee for the rototiller is 3 dollars.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Given that, the rental company charged an initial fee of $43 with an additional fee per hour.

They paid $64 after renting the rototiller for 7 hours

Here, h represents the hourly fee

Now, 43+7h=64

7h=64-43

7h=21

h=$3

Therefore, the hourly fee for the rototiller is 3 dollars.

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\(\(h'(1)\)\) for the function \(\(h(x) = \frac{{f(x) + g(x)}}{{2f(x) + 3g(x)}}\),\) is  \(\(h'(1)\)\) for the function \(\(h(x) = \frac{{f(x) + g(x)}}{{2f(x) + 3g(x)}}\),\)

To find \(\(h'(1)\)\) for the function \(\(h(x) = \frac{{f(x) + g(x)}}{{2f(x) + 3g(x)}}\),\) we need to differentiate \(\(h(x)\)\) with respect to\(\(x\)\)and then evaluate it at \(\(x = 1\).\)

Using the quotient rule, the derivative of \(h(x)\) is given by:

\(\[h'(x) = \frac{{(2f(x) + 3g(x))(f'(x) + g'(x)) - (f(x) + g(x))(2f'(x) + 3g'(x))}}{{(2f(x) + 3g(x))^2}}\]\)

Now, let's substitute the given values:

\(\(f(1) = 3\), \(g(1) = 4\), \(f'(1) = 1\), and \(g'(1) = 5\).\)

Plugging in these values into the derivative expression, we get:

\(\[h'(x) = \frac{{(2f(x) + 3g(x))(f'(x) + g'(x)) - (f(x) + g(x))(2f'(x) + 3g'(x))}}{{(2f(x) + 3g(x))^2}}\]\)

\(\[h'(1) = \frac{{(2f(1) + 3g(1))(f'(1) + g'(1)) - (f(1) + g(1))(2f'(1) + 3g'(1))}}{{(2f(1) + 3g(1))^2}}\]\)

\(\[h'(1) = \frac{{(2(3) + 3(4))(1 + 5) - (3 + 4)(2(1) + 3(5))}}{{(2(3) + 3(4))^2}}\]\)

\(\[h'(1) = \frac{{(6 + 12)(6) - (7)(17)}}{{(6 + 12)^2}}\]\)

\(\[h'(1) = \frac{{108 - 119}}{{(18)^2}}\]\)

\(\[h'(1) = \frac{{-11}}{{324}}\]\)

Therefore, \(\(h'(1) = -\frac{{11}}{{324}}\).\)

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Answer:

10 is a real, rational, integer, whole and natural number,

5/6 is a rational number ,

24sqrt is irrational number,

0 is a real, rational, integer, whole and natural number ,

and

-81sqrt is a real, rational, integer, whole, and natural number.

Hope you have a nice day!

Answer:

x < 5/2

Step-by-step explanation:

The percent of his monthly income that will be budgeted for the utilities will be approximately 5.21%.

According to the question,

We have the following information:

Greg evaluated his spending and found that he was spending about $50 more per month on utilities than he has budgeted. He can transfer money from other categories to increase his utilities budget to $125 per month. If his total monthly income is $2,400.

Now, let's take the percent to be x.

We have the following expression:

2400*x/100 = 125

24x = 125

x = 125/24

x = 5.21%

Hence, the percent of his monthly income that will be budgeted for the utilities will be approximately 5.21%.

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The given statement in the form of inequality is given as -

c - 6 > 24.

An inequality is used to make unequal comparisons between two or more expressions. For example → ax + b > c

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the statement as -

"Six subtracted from c is greater than 24"

We can write the inequality as -

c - 6 > 24

Therefore, the given statement in the form of inequality is given as -

c - 6 > 24.

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{Question in english -

Six subtracted from c is greater than 24}

In a shipping network with n shipping locations, it can be proven that there are at least two shipping locations with the same number of roads by using Pigeonhole Principle.

To prove that in a shipping network with n shipping locations (n ≥ 2), there are at least two shipping locations with the same number of roads, we can use the Pigeonhole Principle.

1. Consider n shipping locations, with each location having a certain number of roads.

2. The minimum number of roads a shipping location can have is 0 (isolated), and the maximum number of roads it can have is n-1 (connected to every other location).

3. There are n possible shipping locations and n-1 possible road counts (from 0 to n-1).

4. According to the Pigeonhole Principle, if there are n pigeons (shipping locations) and n-1 pigeonholes (road counts), at least one pigeonhole must contain more than one pigeon.

5. Therefore, there must be at least two shipping locations with the same number of roads, no matter how the roads are organized.

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Answer:

y = \(\frac{4}{5}\) x - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (5, 3 ) and (x₂, y₂ ) = (0, - 1 )

m = \(\frac{-1-3}{0-5}\) = \(\frac{-4}{-5}\) = \(\frac{4}{5}\)

The line crosses the y- axis at (0, - 1 ) ⇒ c = - 1

y = \(\frac{4}{5}\) x - 1 ← equation of line

The three Fibonacci sequences represented in the given numbers are:  (1) 2, 5, 7, 12, 19, 31, (2) 5, 2, 7, 12, 19, 31, (3) 7, 5, 12, 19, 31 The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones.

In the given numbers, we can observe multiple sequences that follow this pattern.

Starting with 2, the sequence progresses by adding the two previous numbers: 2 + 5 = 7, 5 + 7 = 12, 7 + 12 = 19, and so on.

Starting with 5, the sequence follows the same pattern: 5 + 2 = 7, 2 + 7 = 9, 7 + 12 = 19, and so on.

Starting with 7, the sequence continues by adding the two preceding numbers: 7 + 5 = 12, 5 + 12 = 17, 12 + 19 = 31, and so on.

These sequences demonstrate the characteristic property of the Fibonacci sequence, where each number is the sum of the two preceding ones.

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The gallons of gas required by Ryan to travel 286 miles is 13.2 gallons.

As the stated question;

Total gallon of gas used to drive the 260 miles = 12 gallons

Let 'x' be the gallon of gas used to drive the 286 miles.

Then, bu using the proportion

12 / 260 = x / 286

Thus,

x = 286 x 12 / 260

x = 13.2 gallons

Thus, the amount of gas required by Ryan to travel 286 miles is 13.2 gallons.

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(a) To find the range of the function g(x), we need to determine all possible values that the function can take.

From the given definition, we see that g(x) is defined as 3 minus the square root of a quadratic expression. The square root of a quadratic expression can take both positive and negative values, so the range of g(x) will be all real numbers except for the values that make the quadratic expression negative. To determine these values, we solve the quadratic inequality:

5x^2 + 39x + 3 ≥ 0.

Using the quadratic formula or factoring, we find that the quadratic expression is positive or zero for all values of x. Therefore, the range of g(x) is (-∞, +∞), indicating that g(x) can take any real value.

(b) To find the value of g(0), we substitute x = 0 into the given expression:

g(0) = 3 - √(50^2 + 390 + 3) = 3 - √(0 + 0 + 3) = 3 - √3 ≈ 1.732.

Therefore, the value of g(0) is approximately 1.732.

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P(A) = 5/36, P(B) = 6/36, P(C) = 18/36, P(D) = 6/36, P(A|D) = 1/6, P(A|C) = 5/18

To compute P(A), we need to determine the number of favorable outcomes (where the sum of the two dice faces is 6) divided by the total number of possible outcomes. There are 5 favorable outcomes (1+5, 2+4, 3+3, 4+2, 5+1) out of 36 possible outcomes, so P(A) = 5/36.

P(B) can be calculated similarly. There are 6 favorable outcomes (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) out of 36 possible outcomes, resulting in P(B) = 6/36.

For P(C), we consider the outcomes where the sum is even. Half of the possible outcomes have an even sum, so P(C) = 18/36 = 1/2.

P(D) represents the probability of getting the same number on each die. There are 6 favorable outcomes (1+1, 2+2, 3+3, 4+4, 5+5, 6+6) out of 36 possible outcomes, giving us P(D) = 6/36.

To compute P(A|D), we need to find the probability of event A occurring given that event D has already occurred. Since D guarantees that the dice have the same number, only the outcomes (1+1, 2+2, 3+3, 4+4, 5+5, 6+6) are possible. Out of these 6 outcomes, only one (3+3) satisfies A, so P(A|D) = 1/6.

P(A|C) represents the probability of A occurring given that C has already occurred. Out of the 18 outcomes where the sum is even, 5 of them satisfy A (2+4, 4+2, 3+3, 1+5, 5+1). Hence, P(A|C) = 5/18.

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Answer:

A and C falls within the range.

Step-by-step explanation:

Have a nice day!

Answer:

A. 165.8°F

Step-by-step explanation:

The range for the thermometer must be from 165.3°F to 170.7°F and the only answer choice that falls between those two numbers is, A 165.8°F.

Answer:

x = 5

y = 3

Step-by-step explanation:

x + 4y = 17

2x + 5y = 25

We multiply the first equation by -2

-2x - 8y = -34

2x + 5y = 25

-3y = -9

y = 3

Now we put 3 in for y and solve for x

x + 4(3) = 17

x + 12 = 17

x = 5

Let's Check the answer

5 + 4(3) = 17

5 + 12 = 17

17 = 17

So, x = 17 and y = 3 is the correct answer.