A 32" flat screen television measures 32 inches across its diagonal. the diagonal makes a 35° angle with the bottom of the television
32"
h
a
35°
select all equations that can be used to solve for the height, h, of the television screen

Answer:

Solutions below.

Step-by-step explanation:

This question tests on the concept of Composite Functions

Composite functions are functions that is derived from another new and separate function.

Example: f(x) = 5x, g(x) = 9x , (f • g)(x) = f(g(x)) = f(9x) = 5(9x) = 45x

Given to us are 2 functions:

f(x) =

\( {x}^{2} - 7x + 4\)

g(x) =

\( - 2x\)

We are asked to find (f • g)(4). We first find (f • g)(x).

(f • g)(x) = f(g(x)) = f(-2x) =

\( {( - 2x)}^{2} - 7( - 2x) + 4 \\ = 4 {x}^{2} + 14x + 4 \\ = 2(2 {x}^{2} + 7x + 2)\)

Now, we will find the value of (f • g)(4) by substituting x = 4 into (f • g)(x).

(f • g)(4) =

\(2(2 {(4)}^{2} + 7(4) + 2) \\ = 2(2(16) + 28 + 2) \\ = 2(32 + 28 + 2) \\ = 2(62) \\ = 124\)

Answer:

X= 5/18

Step-by-step explanation:

Answer:

1. Using the jug 6 times and the bucket 3 times

2. Using the bucket 6 times, then using the jug two times

Step-by-step explanation:

Firstly, let’s remember that 1000 ml = 1l

Thus 2L = 2000 ml

And 15L = 15,000 ml

So the situation we are having now is that we want to fill a barrel of 15,000 ml using a jug of 1500 ml and a bucket with a capacity of 2000 ml

Firstly, the first way is using the bucket 6 times and the jug 2 times

What i mean by this is using the bucket 6 times bringing the total volume from the bucket as (6* 2000) = 12,000 ml

Then we are left with 15,000-12,000 = 3,000 ml

Now, she can fill the barrel with 2 times the full volume of the jug making 3,000

Secondly, she can also use the combination of both.

She can use the bucket 6 times and the jug 2 times

The total volume in each case here would be;

For the bucket; (2,000 * 6) = 12,000 ml

while for the jug, we have (1500 * 2) = 3,000 ml

And thus we shall be having a total of 12,000 + 3,000 = 15,000 ml this way

By solving the given question with compound interest, the correct option is A. 50, 51, 52.02, 53.06,...

What is compound interest?

Compound interest is the interest that is earned not only on the principal amount but also on any accumulated interest of previous periods.

Assuming that Mike doesn't make any additional deposits or withdrawals, the sequence that describes the total amount in Mike's account at the end of each year is:

Year 1: $51.00 (initial deposit of $50.00 plus 2% interest of $1.00)

Year 2: $52.02 ($51.00 from Year 1 plus 2% interest of $1.02)

Year 3: $53.06 ($52.02 from Year 2 plus 2% interest of $1.04)

Year 4: $54.12 ($53.06 from Year 3 plus 2% interest of $1.06)

Year 5: $55.21 ($54.12 from Year 4 plus 2% interest of $1.09)

And so on for each subsequent year. The amount in the account increases each year due to the compound interest earned on the initial deposit.

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The downhill side of the crane base should be raised by approximately 4.53 inches to level the crane on a 2.5° slope.

We can use trigonometry here. Let x be the length (in inches) that the downhill side of the base should be raised. The slope of the ground is given to be 2.5°,

tan(2.5°) ≈ 0.0436

Now, using the equation,

x / 12 = 9tan(2.5°)

Here, we converted the base's width from feet to inches (by dividing by 12) and calculated the crane's required vertical displacement (inches) using the angle's tangent. When we simplify this equation, we obtain,

x = 9tan(2.5°)12

x ≈ 4.53 inches

Therefore, the downhill side of the base should be raised by about 4.53 inches to level the crane.

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Complete question - A crane is being set up on a slope of 2.5 degrees. If the base of the crane is 9.0 ft​ wide, how many inches should the downhill side of the base be raised in order to level the​ crane?

If a negative relation exists between two variables, low scores on one variable will be associated with high scores on the other variable.

In a negative relationship between two variables, a decrease in one variable is accompanied by an increase in the other variable. This means that as scores on one variable decrease (i.e., low scores), the scores on the other variable tend to increase (i.e., high scores). The negative relationship implies an inverse pattern where the variables move in opposite directions.

The exact nature and strength of the negative relationship can vary, but the general trend is that low scores on one variable correspond to high scores on the other variable. This negative association provides insights into the behavior and interactions between the variables being examined.

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A sample size of at least 29 is necessary to achieve a margin of error of $8 for a 90% confidence interval of the mean daily spending on all holiday spending.

The following equation may be used to calculate a confidence interval's margin of error:

Margin of error = z *  \((\frac{standard\: deviation} {\sqrt{(sample\:\: size)} }\:)\)

We want the margin of error to be $8, so we can set up the following equation:

\($8 = 1.645 * (\$26 / \sqrt{(sample\: size))\)

To solve for the sample size, we need to isolate the variable "sample size" on one side of the equation:

\(\sqrt{(sample\: size)} = 1.645 * (\$26 / \$8)\\\sqrt{(sample\: size)} = 5.365\)

sample size = \((5.365)^2\)

sample size = 28.8

We can round up to the nearest whole number to ensure that the sample size is large enough:

sample size = 29

Margin of error refers to the range of possible values that a statistical result may vary from the actual population parameter. It is a measure of the precision of a survey or poll's results and indicates how much confidence one can have in the results.

When conducting a survey or poll, researchers typically take a sample from a larger population and use statistical techniques to estimate the parameters of interest, such as the mean or proportion. The margin of error is then calculated based on the sample size, level of confidence, and the variability of the data. It's important to consider the margin of error when interpreting survey results to avoid making incorrect conclusions or assumptions.

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Answer:

-19.68

-1/10x+8/5

25 1/3

-50

22.75

Step-by-step explanation:

Answer:

6) 22.75gallons

7) -50feets

8) 25⅓ inches

9)2/5

10) -19.68

Fernandez's!johojohohojojoj

Answer:

If AB is a tangent to the circle, the triangle ABO is right angled, as the angle where a tangent meets the circumference is always 90 degrees.

We also know that Pythogoras' theorem only holds for right angled triangles.

The hypotenuse is 12 + 8 as 12 is the radius so is 20.

16^2+12^2 = 256 + 144 = 400 = 20^2 so AB must be tangent.

The probability that the total number of rolls in the game, where a standard six-sided dice is rolled until a 6 is rolled, is odd is 1/6.

The probability that the total number of rolls in the game, where a standard six-sided dice is rolled until a 6 is rolled, is odd can be calculated using a geometric distribution.

To find the probability, we can consider the possible outcomes and their corresponding probabilities.

1. The first roll can either be a 6 or not a 6. The probability of rolling a 6 on the first roll is 1/6, and the probability of not rolling a 6 is 5/6.

2. If the first roll is not a 6, we repeat the process with the second roll. Again, the probability of rolling a 6 is 1/6, and the probability of not rolling a 6 is 5/6.

3. We continue this process until a 6 is rolled. Each time, the probability of rolling a 6 is 1/6, and the probability of not rolling a 6 is 5/6.

Since we are interested in the probability that the total number of rolls is odd, we need to consider the possible sequences of odd numbers of rolls.

Let's look at a few examples:
- It is possible to roll a 6 on the first roll, which means the total number of rolls is 1 (an odd number).
- It is also possible to roll a non-6 number on the first roll, then roll a 6 on the second roll, resulting in a total of 2 rolls (an even number).
- Another possibility is to roll a non-6 number on the first, second, and third rolls, and then roll a 6 on the fourth roll, resulting in a total of 4 rolls (an even number).

From these examples, we can observe a pattern: if the total number of rolls is odd, the last roll must be a 6. This means that the probability of the total number of rolls being odd is equal to the probability of rolling a 6 on the last roll.

Therefore, the probability that the total number of rolls is odd is 1/6.

In conclusion, the probability that the total number of rolls in the game, where a standard six-sided dice is rolled until a 6 is rolled, is odd is 1/6.

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Answer:

59+b or b+59

Step-by-step explanation:

If b is Beth, then 59+b is Andy.

The number of books Andy has is b+59 or 59+b

Sylvia's holdings in Maxima Growth add to her taxable income for the year assuming she decides not to sell the fund this year is $50.

Dividend income is a sort of revenue received by shareholders of certain companies. Dividend income is generated by company's profits and distributed on a per-share basis.

Some key features regarding income dividend are-

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The complete question is-

Sylvia owns 100 shares of Maxima Growth mutual fund.

In December she received a check for $50, payment of ordinary income dividend distributions and capital gains distributions.

Sylvia also noticed in her daily newspaper listings that Maxima Growth is now worth $2 per share more than what she purchased it for at the beginning of the year.

How much will Sylvia's holdings in Maxima Growth add to her taxable income for the year assuming she decides not to sell the fund this year?

Answer:

see explanation

Step-by-step explanation:

Using the sine/ cosine ratios in the right triangle and the exact values

sin30° = \(\frac{1}{2}\) , cos30° = \(\frac{\sqrt{3} }{2}\) , then

sin30° = \(\frac{opposite}{hypotenuse}\) = \(\frac{BC}{AB}\) = \(\frac{6}{AB}\) = \(\frac{1}{2}\) ( cross- multiply )

AB = 12

cos30° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{AC}{AB}\) = \(\frac{AC}{12}\) = \(\frac{\sqrt{3} }{2}\) ( cross- multiply )

2 AC = 12\(\sqrt{3}\) ( divide both sides by 2 )

AC = 6\(\sqrt{3}\)

Answer:

6.65

Step-by-step explanation:

0.95% of 700

= 0.0095*700

= 6.65

The value of 0.95% of the number 700 is 6.65.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the number 700 is 0.95%. The number will be calculated as below,

Number = 0.95% of 700

Number = 700 x 0.95/100

Number = 6.65

Therefore, the value of 0.95% of the number 700 is 6.65.

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Answer:

The slope of function a is less than the slope of function b

Step-by-step explanation:

The slope of the the graph is 1/4.  Rise over run.

The slope of the table is 3/4.  As the y increases by 3, the x increased by 4.

The equation of the graph is

y = 1/4 x -1

The equation of the table is

y = 3/4x -5

The y-ntercept of the table is -5.  It is the point (0,-5).  On the table, when x = -4 and you add 4, the next x value would be zero.  On the table, when y is = -8 and you add 3, you are at -5.  (0,-5)

The simplification of the radical expression √9. is 3.

Radical expressions are simplified by taking them down to their most basic form and, if feasible, altogether deleting the radical. When a radical expression appears in the denominator of an algebraic expression, the radical expression is simplified by multiplying the numerator and denominator by the appropriate radical expression (for example, conjugate in the case of a binomial and the same radical in the case of a monomial).

The given expression is √9.

The given expression can be written as:

√(3)(3) = 3

Hence, the simplification of the radical expression √9. is 3.

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The math equation for this example would be 12 courses divided by 4 courses = 3 semesters.

The formula for computing the minimum number of semesters it would take a student to take all of the courses is calculated by dividing the total number of courses by the number of courses that can be taken in a semester. For example, if a student needs to take 12 courses, and the maximum number of courses that can be taken in a semester is 4, then the minimum number of semesters it would take the student to take all of the courses is 3 semesters. The math equation for this example would be 12 courses divided by 4 courses = 3 semesters. In order to determine the exact number of semesters it would take a student to take all of the courses, the total number of courses must be divided by the number of courses that can be taken in a semester.

The formula for calculating the minimum number of semesters it would take a student to take all of the courses is Total Number of Courses divided by Number of Courses that can be taken in a semester. For example, if a student needs to take 12 courses, and the maximum number of courses that can be taken in a semester is 4, then the minimum number of semesters it would take the student to take all of the courses is 3 semesters. The math equation for this example would be 12 courses divided by 4 courses = 3 semesters.

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The surface area of the hemisphere with radius r = 19 cm. is 3400.62 square centimeters

The radius is given as:

r = 19

The surface area of a hemisphere is:

Area = 3πr²

So, we have:

Area = 3 * 3.14 * 19²

Evaluate

Area = 3400.62

Hence, the surface area of the hemisphere is 3400.62 square centimeters

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Therefore, the rank of matrix 'a' in this case would be 5.

To find the rank of a matrix, we need to perform row reduction to obtain its row echelon form (REF) or reduced row echelon form (RREF). However, since the matrix 'a' is not provided, I cannot perform the calculations or determine its rank.

The rank of a matrix is equal to the number of non-zero rows in its row echelon form or reduced row echelon form. If the system of equations 'ax = 0' has a two-dimensional solution space, it means that the rank of matrix 'a' is less than the number of columns (6) but greater than 4 (since the solution space is two-dimensional).

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The the maximum height reached by the rocket, to the nearest tenth of a foot is 914.14 ft.

The rocket launched from the top of the tower is covering a height y in feet in the time x in seconds.

Now, the equation of the motion is,

y=-16x²+227x+109

Differentiating respect to x,

dy/dx = -32x + 227

For maxima and minima,

Putting dy/dx = 0,

x = 227/32

Now, putting this value,

y= -16(227/32)²+227(227/32)+109

y = 914.14 ft.

So, the maximum height of the rocket is 914.14ft.

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Complete question - A rocket is launched from a tower. the height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. using this equation, find the maximum height reached by the rocket, to the nearest tenth of a foot.

Complete question -

y=-16x^2+227x+109

Answer: C. Buenos Aries-Tucuman-Bahia Blanca-Salta-Buenos Aries

Step-by-step explanation:

Edg 2022

Answer:

1.123

Step-by-step explanation:

first find the area of the circle which is 125.6/10 or 12.56.  Then divide take the square root which is around 3.54 and divide by pi which you get 1.1.23

Answer:

12.56 inches 10 × 12.56 = 125.6

The answer is 125.6 , If it is wrong i'm srry.

Step-by-step explanation:

After subtraction (3x+4) - (x+7), the resultant answer is 2x-3.

One of the four operations used in mathematics, along with addition, multiplication, and division, is subtraction.

Removal of items from a collection is represented by the operation of subtraction.

For instance, in the following image, there are 5 2 peaches, which means that 5 peaches have had 2 removed, leaving a total of 3 peaches.

So, we have:

(x+7) and (3x+4)

We have to subtract as:

(3x+4) - (x+7)

Now, subtract as follows:

(3x+4) - (x+7)

3x+4 - x-7

2x-3

Therefore, after subtraction (3x+4) - (x+7), the resultant answer is 2x-3.

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Answer:

1.2 x 10^4 = 12,000

4.5 x 10^-3 = 4.5 x 1/(10^3) = 4.5/1000 = 0.0045

3.8 x 10^3 = 3,000

7.5 x 10^3 = 7,000

largest is 1.2 x 10^4

Hope this helps!!

Step-by-step explanation:

An equilibrium solution of a differential equation refers to a solution where the derivative of the dependent variable with respect to the independent variable is always zero.

Thus, the correct options are:

- A solution y where y' (t) is always zero.

- A constant solution.

A constant solution is one in which the dependent variable remains constant with respect to the independent variable. In this case, the derivative of the dependent variable is zero, indicating no change over time. Therefore, a constant solution satisfies the condition of having y' (t) always equal to zero.

Additionally, if y' (t) is always zero, it means that the derivative of the dependent variable with respect to the independent variable is constant. This is because the derivative represents the rate of change, and if the rate of change is always zero, it implies a constant value. Therefore, a solution where y' (t) is constant also qualifies as an equilibrium solution.

Regarding the other statements:

- A solution y(t) that has a limit as t goes to infinity is not necessarily an equilibrium solution. The limit as t approaches infinity may exist, but it doesn't guarantee that the derivative is always zero or constant.

- The method of the integrating factor can solve not only first-order but also higher-order differential equations. This statement is true. The method of the integrating factor is a technique used to solve linear differential equations, and it can be applied to both first-order and higher-order equations.

- When solving separable equations through the method of separation of variables, we do not lose any solutions. This statement is false. The method of separation of variables guarantees the existence of a general solution, but it may not capture all possible particular solutions. Therefore, we may potentially miss some specific solutions when using this method.

- The equation y' = ky, where y(t) represents the size of a population at time t, models exponential population growth, not taking into account the carrying capacity of the environment. Therefore, the statement is false.

- The equation y = yx + x is not separable. Separable equations can be expressed in the form g(y)dy = f(x)dx, where the variables can be separated on opposite sides of the equation. In this case, the equation does not have that form, so the statement is false.

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Answer:

y = 20

x = 120

Step-by-step explanation:

2x + 3y = 300

3x + 5y = 460

mutliply eqn 1 by 3 and 2 by 2

6x + 9y = 900

6x + 10y = 920

y = 20

x =

Answer:

In order of the questions asked, the answers are, C, D, A, C

Step-by-step explanation:

After three half-lives have elapsed, 12.5% of the original nuclide remains, so the answer is C.

if 17 % is daughter nuclide, then 83% is parent nuclide, so , the answer is D

the isotope for dating organic remains is A. carbon-14

for 25% of original, 2 half-lives must have passed, so we get (2)(5730) = 11460

so the answer is C

The amount of diamonds produced in the first country is 1,000,000 carats, and in the second country, it is 5,000,000 carats.

Let's assume the amount of diamonds produced in one country is x carats. According to the given information, the other country produces about five times the amount produced in the first country. Therefore, the amount of diamonds produced in the second country can be expressed as 5x carats.

The total amount of diamonds produced in both countries is given as 6,000,000 carats. This can be represented by the equation:

\(x + 5x = 6,000,000\)

Combining like terms, we get:

\(6x = 6,000,000\)

To solve for x, we divide both sides of the equation by 6:

\(x = 1,000,000\)

Therefore, the amount of diamonds produced in the first country is 1,000,000 carats, and in the second country, it is 5 times that amount, which is 5,000,000 carats.

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EXPLANATION:

To solve the exercise we must make a rule of three.

The exercise is as follows: