If f(x)=3x, g(x)=x+4 , and h(x)=x2−1 , find g[h(0)]

From the trigonometric function sec θ = 13/12, two more functions are derived -

Option C: cos θ = 12/13

Option D: tan θ = 5/12

What is trigonometric function?

Simply put, trigonometric functions also referred to as circular functions are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle.

The given trigonometric function is -

sec θ = 13/12

Sec function is written as the ratio of hypotenuse to adjacent.

sec θ = 1/cos θ

Cos function is written as the ratio of adjacent to hypotenuse.

cos θ = 12/13

To find the opposite, apply the Pythagoras theorem -

(Opposite)² = (Hypotenuse)² - (Adjacent)²

(Opposite)² = (13)² - (12)²

(Opposite)² = 169 - 144

Opposite = √25

Opposite = 5

Tan function is written as the ratio of opposite to adjacent.

tan θ = 5/12

Therefore, from sec function, cos and tan function are obtained.

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The probability that  a product attains a good review is 0.6125

The given information can be tabulated as follows.

Success type          High             Moderate              Low            Total

                               0.40                   0.35                 0.25             1

Good reviews          0.95                    0.60                0.10

Combined prob       0.4*0.95             0.35*0.6          0.25*0.1

                                0.38                    0.21                  0.025       0.6125

A)the likelihood that a product will receive a favorable review = Prob it is successful and receives a favorable review + Prob it is moderately successful and receives a favorable review + Prob it is unsuccessful and receives a favorable review = 0.6125

B) If a new design receives positive feedback, there is a 0.62 percent chance that it will be a highly successful product.

C) Chance of not receiving a favorable review: (0.40*0.05)

+0.35(0.4) +(0.25)*0.9\s= 0.385

Prob for successful but not receiving a favorable evaluation is 0.40(0.05) = 0.02; required prob is 0.0519.

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The area, in square inches, will be 156.25π

You would require the radius in order to get the circle's area. You would enter the circumference (25) into the equation for the circle's circumference, which looks like this:

C = 2πr

25π = 2πr

Then you would figure out how to solve for r. (the radius)

25π = 2πr

12.5π = πr

12.5 = r  

After that, you would enter the radius into the equation for a circle's area.

A = π(r^2)

A = 12.5^2π

A = 156.25π

Due to the fact that meters were used as the unit of measurement, your response would be 156.25 meters.

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Answer:-√ 5

Step-by-step explanation:

4√ 20 = 8√ 5
3√ 45 = 9√ 5
8√ 5 - 9√ 5 = -√ 5

Answer:

2

Step-by-step explanation:

count the grids, A is 4, B is 8, so scale =2

The range of the ticket prices after the discount is used is 1.

The difference between the lowest and highest values, is considered as range.

Given that, groups of 25 and more receive a 20% discount to the zoo. tickets range in price from $10.00 to $15.00 depending on your age.

The range of a data is given by, difference of lowest element and largest element.

Here, 20% discount is to be given, and ticket price ranges from $10 to $15

20% of 10 = 2

And

20% of 15 = 3

Therefore, range = 3-2

= 1

Hence, the range of the ticket prices after the discount is used is 1.

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Answer:

VALUES (5,6,12)

Step-by-step explanation:

Answer: b to the power of 3 / 8 Have a nice day!

Both Guillermo's and Cara's solutions are incorrect due to the incorrect substitution of values of a variable to find the dependent one.

Guillermo's solution is incorrect because he did not substitute the value of 'b' from the first equation into the second equation. Instead, he directly added 0.49b to both sides and solved for a, which gives an incorrect result.

Cara's solution is also incorrect because she did not substitute the value of 'a' from the first equation into the second equation. Instead, she used the equation a + b = 7 to solve for the value of b, which gave her an incorrect result.

We can find the correct solution as follows -

The system of equations is,

⇒ a + b = 7   .. (i)

And 1.29a + 0.49b = 6.63 .. (ii)

Now, we will solve the system of equations as follows -

⇒ a + b = 7  

⇒ a = 7 - b .. (i)

And, ⇒ 1.29a + 0.49b = 6.63 .. (ii)

Substitute the value of a from (i) in (ii), we get;

⇒ 1.29a + 0.49b = 6.63

⇒ 1.29(7 - b) + 0.49b = 6.63

⇒ 9.03 - 1.29b + 0.49b = 6.63

⇒ - 0.8b = 6.63 - 9.03

⇒ - 0.8b = - 2.4

⇒ 0.8b = 2.4

⇒ b = 2.4 / 0.8

⇒ b = 3

And, From (i);

⇒ a = 7 - b .. (i)

⇒ a = 7 - 3

⇒ a = 4

Hence, 4 pounds of apples and 3 pounds of bananas were bought.

Thus, both of their solutions are incorrect.

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The complete question is -

FIND THE ERROR In the system a + b = 7 and 1.29a + 0.49b = 6.63, a represents pounds of apples and b represents pounds of bananas a person bought. Guillermo and Cara are finding and interpreting the solution. Is either correct? Explain your reasoning.

a. Guillermo: 1.29a + 0.49b = 6.63 ⇒ 1.29a +0.49(a + 7) = 6.63 ⇒ 1.29a + 0.49a + 3.43 = 6.63 ⇒ 1.78a = 3.2 ⇒ a = 1.8

a + b = 7, so b = 5.2. The solution (1.8, 5.2) means that 1.8 pounds of apples and 5.2 pounds of bananas were bought.

b. Cara: 1.29a + 0.49b = 6.63 ⇒ 1.29(7-b) + 0.49b = 6.63 ⇒ 9.03- 1.29b + 0.49b = 6.63 ⇒ -0.8b = -2.4 ⇒ b=3

The solution b = 3 means that 3 pounds of apples and 3 pounds of bananas were bought. volunteers. The ratio of boys to girls is 7:5.​

There are other methods to write a division issue, such as using a / or a to denote "divided by." As a result, in the equation 473 / 2 = 1 the divisor is the quotient, the remainder is 236, and the divisor is 2.

Divide the dividend's first digit, which should be on the left, by the divisor, then write the result as the quotient on top. Write the difference below after subtracting the outcome from the digit. Bring down the dividend's next digit (if present).

Long division strategy: lengthy division techniques. The same symbols are used for long division as they are for short division: dividend (the number being divided) under the "bus stop," divisor (the number the dividend is being divided by), quotient (the solution) on top, and each place value aligned with the dividend.

Dividend Divisor = Quotient + Remainder is the formula for dividing two numbers.

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The complete question is "Divide the given numbers 473 and 6 using our free online Long Division Calculator and determine the Quotient and Remainder as Q 78 R 5 instantly without any hurdles."

Answer: Ordinal numbers are a designation of something's place in a series by a number, such as first or third.  Ordinal numbers can function as pronouns, nouns, and adjectives.

Answer:

Step-by-step explanation:

It means what place something is in. For example the ordinal of 1 is 1st 2 is 2nd and 3 is 3rd and so on. I hope this helps.

The value of d in the given angles using the concept of complementary angles is; d = 13

Complementary angles are defined as angles that add up to 90 degrees.

Now, we are told that one angle measures 18°, and another angle measures (6d − 6)°. This tells us that;

(6d - 6) + 18 = 90

Expanding the bracket gives us;

6d - 6 + 18 = 90

6d + 12 = 90

6d = 90 - 12

6d = 78

Use division property of equality to divide both sides by 6 to get;

6d/6 = 78/6

d = 13

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The values of x and y on solving the two simultaneous equations are x = 1 and y = 3.

The simultaneous equations to be solved are 4x + 2y = 10 and x + 2y = 7.

Rearranging the above equations, we have,

- 4x - 2y = - 10 -----(A)

x + 2y = 7  -------(B)

Solving them, we have, -3x = -3

x = 1 ------(C)

Substituting (C) in (B), we have,

1 + 2y = 7

2y = 6

y = 3 ------(D)

Now, let us substitute the x and y values in (A) and (B) and then check.

4x + 2y = 10

4 + 2(3) = 10

A is checked.

x + 2y = 7

1 + 2(3) = 7

B is checked.

Thus, the values of x and y are checked to be correct.

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Answer:

Step-by-step explanation:

12.7% = 12.7/100 = 0.127

The linear functions f(x) and g(x) are neither parallel nor perpendicular.

To obtain whether they are parallel of perpendicular, first we must obtain the slope of each line.

Given two points, the slope of a line is calculated as the change in y divided by the change in x.

Hence, the slope for each line is obtained as follows:

They would be:

Hence they are neither.

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Answer:

x ≥ 10

Step-by-step explanation:

A solid dot on 10 means 10 is included.

An arrow pointing to the right of 10 means all numbers greater than 10 are included.

Answer: x ≥ 10

Answer:10 =< x

Step-by-step explanation:
Shaded circle means include that number so it is a <= or >= sign
Goes to x.
Think about it a bit, not quite sure if 50 is involved in this inequality

Answer:

X < 250

Step-by-step explanation:

Inequalities:

> Greater/More than

< Less/Fewer than

= Equal to

>= Greater than/More than OR equal to

<= Less than/Fewer than OR equal to

Since it says fewer than, we'll use <

X in this case will be the actual number of people.

We know fewer than 250 will attend, making the inequality

X < 250

A rectangular prism has a volume of  2x ^ 3 + 19x ^ 2 + 24x

the volume of the rectangular prism is

The area contained by an object's limits in three-dimensional space is referred to as its volume.

Thus, a rectangular prism having the following dimensions: 2x length, (x2) width, and (x + 2) height

L x B x H = volume

= x× (x +8 )(2x + 3)

= x(x + 8)(2x + 3)

(2x + 3) * x ^ 2 + 8x(2x + 3)

2x ^ 3 + 19x ^ 2 + 24x

The area contained by an object's limits in three-dimensional space is referred to as its volume.

A rectangular prism's volume is thus 2x ^ 3 + 19x ^ 2 + 24x

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a) Equation would be 5x + (x - 6) + (x - 6) = 180°

b) m∠1 = 180° and  m∠2 = 30°

What is the measure of angle?

The term "degree measure" refers to the measurement of an angle in degrees. Because one entire revolution equals 360°, it is divided into 360 parts. Each stage of the revolution represents a degree.

a) The angle measures in a triangle must add up to 180°.

Therefore, the equation to find x is:

        5x + (x - 6) + (x - 6) = 180°

b) Solving for x, we get:

x = 36

Therefore, angle m∠1 = (5x) = (5 * 36) = 180° (major angle)

angle m∠2 = (x - 6) = (36 - 6) = 30° (minor angle)

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There are a total of 10 slips.

8 slip with 3 on it

2 slips with 9  on it

value = Probability of 3 x 3 + Probability of 9 x 9.

=  (8 / 11)  x 3 + (2/ 11)  x 9

24 / 11 + 24 / 11 = 4.36

probability

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

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Three letters will be selected from five letters. The number of possible selections is 10.

A combination is a method of picking elements from a collection where the order of selection is irrelevant. Assume we have three numbers P, Q, and R. The number of ways we can choose two numbers from each set is determined by combination.

Suppose we want to pick k elements from a set of n elements, then the number ways it can be chosen is:

C(n,k) = n! / k! (n-k)!

Where n! is n factorial.

In this case, there are 5 letters and we want to select three letters. Hence, k = 3, and n = 5.

C(5,3) = 5! / 3! (5-3)!

C(5,3) = 5! / (3! 2!) = 10

Thus, there are 10 possible selections.

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ΔABC and ΔDEF are not similar because corresponding angles are not equal.

Now, According to the question:

In triangle ABC :

The measure of angle A is 35º and

The measure of angle B is 20°.

In triangle DEF:

The measure of angle D is 35º and

The measure of angle F is 125

We know that :

Sum of interior angles of triangle is 180°

Now, In ΔABC:

∠A + ∠B + ∠C = 180°

35 +  20 + ∠C = 180°

55° +  ∠C = 180°

∠C = 180° - 55°

∠C = 125°

Now,  In ΔDEF:

∠D + ∠E + ∠F = 180°

35 + ∠E + 125 = 180°

160  + ∠E = 180°

∠E = 180° - 160°

∠E = 20°

So, ∠C ≠ ∠E  as ∠C = 125° and ∠E =20°

Hence, No, Triangles are not similar .

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The probabilities for this problem are given as follows:

It is a distribution with two bounds, given by a and b, in which each possible outcome is equally as likely.

The probability of finding a value of at lower than x is:

[tex]P(X < x) = \frac{x - a}{b - a}[/tex]

The bounds for this problem are given as follows:

a = 2, b = 70.

Hence the probability of less than 30 seconds is given as follows:

P(X < 30) = (30 - 2)/(70 - 2)

P(X < 30) = 0.4118 = 41.18%.

The uniform distribution is a continuous distribution, meaning that the probability of an exact value is of 0.

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The initial fee charged to customers for using the gym, given the graph showing the charges to customers is $ 20.

To find the initial membership fee, you should look at the y - intercept of the graph.

The y - intercept is the point where the x vale is 0 and this case this point shows the cost when the customers have not worked out in the gym for any hour yet.

This y - intercept is therefore $ 20 as this is the point on the graph where the value of x is 0.

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The question is:

What is the initial fee charged to customers for using the gym?

Answer:

A. 500 people will go out to the park when its 100F is incorrect.

Answer:

C) 11

Step-by-step explanation:

Exterior angles in a triangle = the sum of the interior angles of the triangle

Here, the exterior angle is ∠BCT while the interior angles are ∠CAB and ∠ABC

Using the above theorem we can say that ∠BCT = ∠CAB + ∠ABC

Plugging in the given expressions and values of the angles we acquire

9x + 6 = 3x + 2 + 70

==> combine like terms

9x + 6 = 3x + 72

==> subtract 3x from both sides

6x + 6 = 72

==> subtract 6 from both sides

6x = 66

==> divide both sides by 6

x = 11

The displacement vector of the object is (-3, 9) and the work done is 30 Joules

The term called vector in math is defined as a quantity or phenomenon that has two independent properties such as magnitude and direction.

Here we know that the value of force F is (-1, 3) and the point is (3, -9)

Then the displacement from origin to (3, -9) is calculated as,

=> d = (0-3, 0-(-9))

Then the value of d is ( -3, 9)

Here the formula to Work done is written as,

=> F x d

=> (-1, 3) x (-3, 9) = 3 + 27

=> 30 joules.

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Answer:

-20

Step-by-step explanation: