For each function, what is the output of the given input?
For f(x) = 4x+7, find f(4)

Your answer for this question is 0

Answer: 120

Step-by-step explanation:

The number of ways to arrange n things of which 'a' things are identical , 'b' things are identical and so on...... :-

[tex]\dfrac{n!}{a!\ b!......}[/tex]

Given Word : DEGREE

Total letters = 6

Here letter E is repeated 3 times.

Then, the number of unique ways to arrange the letters in the word "DEGREE " will be :-

[tex]\dfrac{6!}{3!}=\dfrac{6\times5\times4\times3!}{3!}=120[/tex]

Hence, the number of distinct arrangements for the letters in the word "DEGREE "=120

The measure of the side AB will be 45. The correct option is A.

Pythagorean theorem states that in the right angle triangle, the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Use the Pythagorean theorem to calculate the length of AB as below,

OB² = AB² + OA²

(BC + OC)² = AB² + OA²

(27 + 24)² =  AB² + 24²

AB² = 51² - 24²

AB = 45 units

Therefore, the correct option is A. The value of length AB is 45.

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Answer:

1.  13, 17                       Option D

2. -2                            Option B

3. 2                             Option C

4. F(n) = 3+4(n-1)        Option D

Step-by-step explanation:

1.  

Given sequence is:   1, 5, 9....

Common difference =  5-1 = 9-5 = 4

Next term is :

9+4 = 13

and

13+4= 17

So, next two terms are:  13 & 17.

2.

Given sequence is :

102, 100, 98, 96....

Common difference = 100 - 102 = 98 -100 = 96 - 98 = -2

3.

Given rule is :

Aₙ  = -14 + (n - 1)(2)

Find the 9th term

so, we put n = 9

A₉ = -14 + (9-1)*2

A₉ = -14 + 8*2 = -14 + 16

A₉ = 2

Ninth term is 2.

4.

Given sequence is:

3, 7, 11, 15.....

Write the nth term

Formula is :

F(n) = a₁ + (n-1)d

Where a₁ is first term

n is number of terms

d is common difference

a₁ = 3

d = 7-3 = 11-7 = 15 - 11 = 4

So nth term is :

F(n) = 3 + 4(n-1)

That's the final answer.

Answer:

1.  13, 17    Option D

2. -2      Option B

3. 2      Option C

4. F(n) = 3+4(n-1)     Option D

Step-by-step explanation:

Final answer:

The probability that the roots of the equation [tex]x^2+Ax+A+3=0[/tex] are both real is approximately 0.6786. Then we calculate the length of the range [-3, 16] divided by the length of the entire interval [-12, 16].

Explanation:

To find the probability that the roots of the equation [tex]x^2+Ax+A+3=0[/tex] are both real, we need to determine the range of values for A that will result in real roots. For real roots, the discriminant (b^2-4ac) must be greater than or equal to 0. In this case, the equation can be rewritten as [tex]x^2+(1+A)x+(A+3)=0[/tex], so a = 1, b = (1+A), and c = (A+3). The discriminant is (1+A)^2 - 4(A+3), which must be greater than or equal to 0.

Expanding and simplifying, we get (A^2 + 2A + 1) - 4A - 12 ≥ 0. Combining like terms, we have [tex]A^2 - 2A - 11 > 0[/tex].

To solve the inequality, we can find the values of A that make the equation equal to 0. Factoring, we get (A - 4)(A + 3) ≥ 0. The solutions are A ≤ -3 or A ≥ 4.

Therefore, the probability that the roots of the equation are both real is the probability of A taking values in the interval [-12, -3] or [4, 16]. To find this probability, we divide the length of the interval [-3, 16] by the length of the entire interval [-12, 16].

P(A is in [-3, 16]) = (16 - (-3)) / (16 - (-12)) = 19 / 28 ≈ 0.6786.

Deshaun drove at a speed of 62 miles per hour for 99.2 miles. To calculate the time spent driving, use the formula Time = Distance / Speed. The time taken for his drive is approximately 1.6 hours.

The question pertains to calculating the driving time given the speed and distance traveled by Deshaun in his new car. He drove at a speed of 62 miles per hour for 99.2 miles. To find out how many hours he drove, we use the formula for time which is:

Here, the distance d is 99.2 miles and the speed v is 62 miles per hour.

So we calculate the time t as follows:

The time taken by Deshaun for his drive is approximately 1.6 hours.

Final answer:

Jeremy needs to create an inequality to represent his new earning goal higher than $160 a week, leading to the inequality 8x + 10y > 160. This can be graphed by first converting to intercept form, plotting the intercept and slope, drawing a dashed boundary line, and shading the region above this line.

Explanation:

Jeremy is working two jobs to save for his college education and needs to create an inequality to represent the amount he needs to make each week, now more than $160. Let's denote the number of hours Jeremy works busing tables as x and the number of hours he spends tutoring as y. He makes $8 per hour busing tables and $10 per hour tutoring.

To express Jeremy's goal of making more than $160 a week, we can write the following inequality:

8x + 10y > 160

To graph this inequality:

First, rewrite the inequality as y > (-4/5)x + 16 to get the intercept form.

Plot the y-intercept at (0, 16) on the graph.

Use the slope of -4/5 to determine another point. From (0, 16), move 5 units to the right (positive x-direction) and 4 units down (negative y-direction), then plot this second point.

Draw a dashed line through the two points to represent the boundary of the inequality (dashed because the inequality is strict and does not include the line itself).

Shade above the line to indicate that all solutions to the inequality lie in this area, where Jeremy would be earning more than $160.

Answer:

A. 0.4

Step-by-step explanation: