MODELING REAL LIFE: You have a total of 42 math and science problems for homework. You have 10 more math problems than science problems. How many problems do you have in each subject. a) Use x to represent math problems and y to represent science problems. Write an equation that represents the number of problems you have.

Step-by-step explanation:

please review the attachment. That's the answer.

Answer:

For the nearest 10th of a centimeter, the value of h is 460 cm

Step-by-step explanation:

To find length of h we can use Law of Sines  . The Law states that for a triangle with sides a, b, and c and angles A, B, and C opposite to those sides, the following equation holds:

a/sin A = b/sin B = c/sin C

In ΔGHI, let h be the length of the side opposite angle H, and let i be the length of the side opposite angle I.

Now:

h/sin 122° = i/sin 26°

We can find h by cross multiplying:

h = i * sin 122° / sin 26°

  =459.9

Here,

h = 459.9 cm

By taking approximation we get 460 cm

Answer:

This answer is actually 1280.3

Step-by-step explanation:

Work Shown:

4.5% of 125 = 0.045*125 = 5.625

That rounds to 5.63

Answer:

5.625

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: Let's follow the same steps as in the previous example:

Identify the constants and the variables.

The known constant here is 4. Shailyn read 4 fewer books than Oswaldo. Let's call the number of books Oswaldo read "o".

Identify the operations.

The phrase "four fewer" tells us we need to subtract.

Rewrite the phrase as an expression.

"Four fewer books than Oswaldo" is o - 4.

So, the expression that shows how many books Shailyn read last year is o - 4.

Step-by-step explanation:

The function operation (f/g)(x) in the functions f(x) = √( x² - 1 ) and g(x) = √( x - 1 ) is √( x + 1).

A function is simply a relationship that maps one input to one output.

Given the functions in the question;

To evaluate (f/g), replace the function designators in f/g with the actual functions.

(f/g)(x) = f(x) / g(x)

(f/g)(x) = ( √( x² - 1 ) ) / ( √( x - 1 ) )

Now, rewrite 1 as 1²

(f/g)(x) = ( √( x² - 1² ) ) / ( √( x - 1 ) )

Factor using difference of square

(f/g)(x) = ( √( (x - 1)(x + 1 ) ) / ( √( x - 1 ) )

Combine into a single radical

(f/g)(x) = √( ( (x - 1)(x + 1) ) / ( x - 1 ) )

Now, cancel out the common factors (x-1)

(f/g)(x) = √(  (x + 1) / 1 )

(f/g)(x) = √( x + 1)

Therefore, the function operation (f/g)(x) is √( x + 1).

Option A) √( x + 1) is the correct answer.

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well, in 2007 it was 12000, so initially that's what it was, and in 2019 it went to 23000, so that's 12 years later, and in 2040, that'll be 33 years later.

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 23000\\ P=\textit{initial amount}\dotfill &12000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &12\\ \end{cases} \\\\\\ 23000 = 12000(1 + \frac{r}{100})^{12}\implies \cfrac{23000}{12000} =\left(1+ \cfrac{r}{100} \right)^{12} \\\\\\ \cfrac{23}{12}=\left(\cfrac{100+r}{100} \right)^{12}\implies \sqrt[12]{\cfrac{23}{12}}=\cfrac{100+r}{100}[/tex]

[tex]100\sqrt[12]{\cfrac{23}{12}}=100+r\implies 100\sqrt[12]{\cfrac{23}{12}}-100=r\implies \boxed{5.57\approx r} \\\\[-0.35em] ~\dotfill\\\\ \qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &12000\\ r=rate\to 5.57\%\to \frac{5.57}{100}\dotfill &0.0557\\ t=years\dotfill &\stackrel{year~2040 }{33}\\ \end{cases} \\\\\\ A \approx 12000(1 + 0.0557)^{33} \implies \boxed{A \approx 71782}[/tex]

The reasons for (1) and (2) are added below

One reason why it might be reasonable to model the relationship between time and height of the candle with a linear function is that the rate of change of the candle's height appears to be constant over time.

One reason why it might NOT be reasonable to model this relationship with a linear function is that the candle's height cannot continue to decrease indefinitely.

This means that the candle's height is bounded and cannot continue to decrease linearly forever.

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Answer:you never asked for like in what minutes or hours?

Step-by-step explanation:

The car, traveling at a speed 5 mph faster than the truck, will take more than 4.6 hours to be more than 23 miles ahead.

This question pertains to relative speed. When the car is traveling at 55 mph and the truck at 50 mph, the car is effectively moving away from the truck at (55 mph - 50 mph) = 5 mph. To calculate the time it will take for the car to be more than 23 miles ahead, we can use the formula: Time = Distance/Speed. So the time it would take is Time = 23 miles / 5 mph = 4.6 hours. Therefore, it will take the car more than 4.6 hours to be more than 23 miles ahead.

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The measure of angle ∠ACB is 45 degrees

From the question, we have the following parameters that can be used in our computation:

A (-3, 2), B (0, 0), C (2, 3)

The graph is attached

The lines AB and BC are perpendicular lines

This means that

∠B = 90 degrees

Calculate the length AB and BC using

distance = √[(x2 - x1)² + (y2 - y1)²]

So, we have

AB = √[(-3 - 0)² + (2 - 0)²] = √13

BC = √[(0 - 2)² + (0 - 3)²] = √13

The angle C is then calculated as

tan(C) = AB/BC

tan(C) = √13/√13

tan(C) = 1

Take the arctan of both sides

C = 45

Hence, the measure of ∠ACB is 45 degrees

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Answer: the answer is 5/12

The two integers are 5 and 10.

What do you mean by Integers?

An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.

Integer is a Latin word which means 'whole' or 'intact'. This means integers do not include fractions or decimals.

A number is positive if it is greater than zero, so it said to be positive integers

A number is negative if it is less than zero, so it said to be negative integers.

A number line is a visual representation of numbers on a straight line. This line is used for the comparison of numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally.

Given:

Let x be the positive number

2x be the other positive number

Find the first integer

[tex]\frac{1}{x} - \frac{1}{2x} = \frac{1}{10}[/tex]

[tex]\frac{2x - x}{2x^2} = \frac{1}{10}[/tex]

[tex]\frac{x}{2x^2} = \frac{1}{10}[/tex]

[tex]\frac{1}{2x} = \frac{1}{10}[/tex]

2x = 10

x = 5

Therefore, the first positive integer is 5.

Find the other integer

2x = 2(5) = 10

Therefore, the other integer is 10.

To check:

[tex]\frac{1}{x} - \frac{1}{2x} = \frac{1}{10}[/tex]

[tex]\frac{1}{5} - \frac{1}{10} = \frac{1}{10}[/tex]

[tex]\frac{2}{10} - \frac{1}{10} = \frac{1}{10}[/tex]

[tex]\frac{1}{10} = \frac{1}{10}[/tex]

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Answer:

B

Step-by-step explanation:

the zeros are the values of x on the x- axis where the graph crosses

the graph crosses the x- axis at 1 and 3

then the zeros are x = 1 , x = 3

The vertices of the image of triangle ABC are A''(x, y) = (- 6, 8), B''(x, y) = (- 8, 4) and C''(x, y) = (- 4, 4).

Any triangle can be generated by three points that are not collinear, in this problem we need to determine the image of a triangle, which is the result of two rigid transformations: (i) Reflection over the y-axis, (ii) Dilation centered at the origin with a scale factor of 2, whose definitions are shown below:

Reflection over the y-axis:

(x, y) → (- x, y)

Dilation centered at the origin with a scale factor of 2:

(x, y) → (2 · x, 2 · y)

If we know that A(x, y) = (3, 4), B(x, y) = (4, 2), C(x, y) = (2, 2), then the image of the vertices are determined below:

Reflection over the y-axis

A'(x, y) = (- 3, 4), B'(x, y) = (- 4, 2), C'(x, y) = (- 2, 2)

Dilation centered at the origin with a scale factor of 2

A''(x, y) = (- 6, 8), B''(x, y) = (- 8, 4), C''(x, y) = (- 4, 4)

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Answer:

Flase, no real numbers (2+-8)

Step-by-step explanation:

First, you conjoined the equations (-6x+2=-6x-8).  Then you conjoined the variables first, (-6x+6x=0). Now you have 2=-8, which is not true.

Equivalence means to be same, whether it be value, temperature, size, etc.

Let's make an equation to solve this problem. We first would need to take the total (12 pounds) and divide that total by the amount each slice must weigh (1.5 pounds) to get an equal number of slices.

To check our work, we can take number of slices (8), and multiply that by the weight of each slice (1.5 pounds) to get the original weight of the watermelon.

Now, we know for sure that Mr. Ramirez can make 8 watermelon slices each weighing 1.5 pounds if he has a 12-pound watermelon.

The required value of the given expression which satisfy it is b = 3/5.

To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.

We have,

3 - 2(b - 2) = 2 - 7b

= 3 - 2b - 4 = 2 - 7b

= 5b = 3

= b = 3/5

Thus, required value of the b for the given function is b = 3/5.

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The probability that there are fewer than 2 tornadoes in a 22-year period is, 0.214

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

Since the probability of a tornado in any given year is 0.08,

the probability of no tornado in any given year is;:

=  1 - 0.08

= 0.92.

Let X be the number of tornadoes in a 22-year period.

X follows a binomial distribution with n = 22 and p = 0.08.

We want to calculate the probability that there are fewer than 2 tornadoes in a 22-year period.

This can be written as:

P(X < 2) = P(X = 0) + P(X = 1)

Using the binomial probability formula, we can calculate:

P(X = 0) = (22 choose 0) x (0.08)⁰ x (0.92)²² ≈ 0.038

P(X = 1) = (22 choose 1) x (0.08)¹ x (0.92)²¹ ≈ 0.176

Therefore,

P(X < 2) = P(X = 0) + P(X = 1) ≈ 0.214

So the probability that there are fewer than 2 tornadoes in a 22-year period is approximately 0.214 or 21.4%.

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The solution is the union of the solutions from both inequalities. That is, x is either greater than 3.2 or less than -0.75. So, the final solution is: -0.75 < x < 3.2.

What is  inequalities?

An inequality is a mathematical statement that represents a comparison between two values, and indicates the relationship of one value being greater than, less than, or equal to the other. It is usually represented using symbols such as ">" (greater than), "<" (less than), ">=" (greater than or equal to), "<=" (less than or equal to), and "≠" (not equal to). For example, the inequality "2x + 3 > 7" expresses that the value of the expression "2x + 3" is greater than 7 for some values of x.

Inequalities are used to describe a range of values that satisfy a certain condition. The solution to an inequality is a set of values that make the inequality true.

To solve the inequality "5x - 4 > 12 or 12x + 5 < -4", we can start by solving each inequality separately and then combining the solutions to find the final solution.

Adding 4 to both sides, we get 5x > 16

Dividing both sides by 5, we get x > 3.2

So, the solution to this inequality is x > 3.2

Subtracting 5 from both sides, we get 12x < -9

Dividing both sides by 12, we get x < -0.75

So, the solution to this inequality is x < -0.75

Final solution: Combining the solutions from both inequalities:

Since "or" is used in the inequality, the solution is the union of the solutions from both inequalities. That is, x is either greater than 3.2 or less than -0.75. So, the final solution is: -0.75 < x < 3.2.

So the solution to the inequality "5x - 4 > 12 or 12x + 5 < -4" is -0.75 < x < 3.2.

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Answer: no

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

1 plus 1 due to the characterisation of the number 1 increasing by 1 gives you 2

Answer: 44.20-10.68=33.52

He need 33.52$

Step-by-step explanation:

Answer:

Step-by-step explanation:

Here's a step by step solution with more details:

Let's call the length of the two equal sides of the triangle as x.

The third side, which is 1 1/3 cm longer, will have a length of x + 1 1/3 cm.

The perimeter of the triangle is 5 2/5 cm, so we can write an equation using the lengths of the sides:

x + x + (x + 1 1/3) = 5 2/5

Simplifying the equation:

2x + 1 1/3 = 5 2/5

Subtracting 1 1/3 from both sides:

2x = 4 1/5

Dividing both sides by 2:

x = 2 2/5

So the two equal sides of the triangle are 2 2/5 cm and the third side is 2 2/5 + 1 1/3 = 3 7/15 cm.

Answer:

One equal side = [tex]1\frac{16}{45}[/tex]cm and third side is [tex]2\frac{31}{45}[/tex]cm

Step-by-step explanation:

This is describing an isosceles triangle

1[tex]\frac{1}{3}[/tex] = [tex]\frac{4}{3}[/tex]

5[tex]\frac{2}{5}[/tex] = [tex]\frac{27}{5}[/tex]

Let

x = one of the two equal sides of the triangle

∴ Third side of triangle = [tex]\frac{4}{3} + x[/tex]

Perimeter of a triangle = Sum of all three sides:

[tex]\frac{27}{5}[/tex] [tex]= x + x + (\frac{4}{3} + x)[/tex]

Expand the parenthesis using the Distributive Law and bring all the like terms together:

[tex]=\frac{27}{5} = 2x + \frac{4}{3} + x[/tex]

[tex]= \frac{27}{5} = 3x + \frac{4}{3}[/tex]

[tex]= \frac{27}{5} -\frac{4}{3} = 3x[/tex]

The two denominators of the two fractions have to be manipulated to be made the same:

[tex]= (\frac{3}{3})(\frac{27}{5}) - (\frac{5}{5})(\frac{4}{3}) = 3x[/tex]

[tex]= \frac{81}{15} - \frac{20}{15} = 3x[/tex]

[tex]= \frac{81 - 20}{15} = 3x[/tex]

[tex]= \frac{61}{15} = 3x[/tex]

Cross-multiplication is added:

[tex]= (61)(1) = (15)(3x)[/tex]

[tex]= 61 = 45x[/tex]

Isolate x and make it the subject of the formula:

x = [tex]\frac{61}{45}[/tex]

x = One of the two equal sides = [tex]1\frac{16}{45}[/tex]cm

∴Third side:

= [tex]\frac{61}{45} + \frac{4}{3}[/tex]

= [tex]\frac{61}{45} + (\frac{15}{15})(\frac{4}{3})[/tex]

= [tex]\frac{61}{45} + \frac{60}{45}[/tex]

= [tex]\frac{61 + 60}{45}[/tex]

= [tex]\frac{121}{45}[/tex]

= [tex]2\frac{31}{45}[/tex]cm

find the length of the x

a^2 + b^2 = c^2

12x^2 + b^2 = 13^2

144 + b^2 = 169

b^2 = 25

b = 25; x = 5

use the formula

a = (1/2)(24)(5)

a = (1/2)(120)

area = 60

The statement regarding the census in this problem is classified as a True statement.

Population: Collection or set of individuals or objects or events whose properties will be studied.

Sample: The sample is a subset of the population, and a well chosen sample, that is, a representative sample will contain most of the information about the population parameter. A representative sample means that all groups of the population are inserted into the sample.

A Census is when a group of the population is chosen, that is, a sample is chosen, hence the statement for this problem is true.

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Using commutative and associative properties of addition, the solution for given expression is -5.

What is commutative and associative property?

The associative and commutative characteristics are universal principles that apply to addition and multiplication. The associative property states that rearranging the numbers will get the same result, while the commutative property states that rearranging the numbers will yield the same result.

These properties tell that one can add in any order, the result will always be the same.

We are given an expression as 8+(-8-5).

So, in this instead of adding from left to right, we can see that the 8 + (-8) will be zero and only -5 will be left as an answer.

Hence, the solution for given expression is -5.

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