fill in the blanks for the geometric sequence
__, 5^4, __, __, 5^10

The given graph shows that the function is periodic and fluctuates between y = -2 and y = 2. So, the range of the function is [-2,2].

The graph covers one period, which is from x = -3 to x = 3, and then repeats itself indefinitely in both directions. So, the domain of the function is (-∞, ∞).

In general, the domain of a function consists of all the possible input values that the function can take. In this case, since the function repeats itself indefinitely, it can take any input value from negative infinity to positive infinity.

So, the domain is (-∞, ∞). The range of a function, on the other hand, consists of all the possible output values that the function can produce.

In this case, the function oscillates between y = -2 and y = 2, so the range is [-2,2]. The interval notation for the domain is (-∞, ∞) and for the range is [-2,2].

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Answer:

Step-by-step explanation:

If James gave each cousin 3 cupcakes, there would be 25 left. James is 71 cupcakes short of being able to give each cousin 15 cupcakes. You want to know the number of cousins and the number of cupcakes.

The given relations between the number of cupcakes (n) and the number of cousins (c) are ...

  n -3c = 25 . . . . . 3 each ⇒ 25 left

  n -15c = -71 . . . . . 15 each ⇒ 71 short

Subtracting the second equation from the first, we have ...

  (n -3c) -(n -15c) = (25) -(-71)

  12c = 96

  c = 8 . . . . . . divide by 12

  n = 3c +25 = 24 +25 = 49

(a) James has 8 cousins.

(b) James baked 49 cupcakes.

Answer:

Add all the digits of the number, then check if that sum is divisible by 9. If yes, we know the number is divisible by 9.

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

The additional gas it will take to fill the tank is 16 gallons

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

Capacity = 24 gallons

Current volume = 1/3 full

This means that

Remaning volume = 1 - 1/3

Evaluate

Remaning volume = 2/3

The additional gas it will take to fill the tank is

Additional = 2/3 * 24

Evaluate

Additional = 16

Hence, the additional gas it will take to fill the tank is 16 gallons

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Answer:

Maybe negative or undefined?

Step-by-step explanation:

Miguel uses 300 mL Solution B and 600 mL Solution A.

Let x represent the amount of Solution B used.

2x = the quantity of Solution A used.

Solution A is alcohol = 12%.

Solution B is alcohol = 16%.

Given that 12% = 0.12 and 16% = 0.16, we can calculate the following equation:

2x(0.12) + x(0.16) = 120 (Recall that pure alcohol has a concentration of 100% = 1.00.)

0.24x + 0.16x = 120

0.40x = 120

x = 300 mL

Thus, Miguel  makes use of 300 mL of Solution B and 2(300) = 600 mL of Solution A.

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13.13.13.13.13 in exponential form is 13^5

The expression is given as:

13.13.13.13.13

The factors of the above expression are 13.

And each factor is grouped by product

There are five 13s in the expression.

So, we have:

13.13.13.13.13 = 13^5

Hence, 13.13.13.13.13 in exponential form is 13^5

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Answer:

1.) 1.5972

2.) 11.4688

3.) 4.9725

4.) 1.81

5.) 29.3112

Answer:

2.5%

Step-by-step explanation:

Thorazine is available in the strength of 25mg/mL.

To find out the percentage strength,

W/V = g/mL  (weight in grams of solute/milliliters of solute.)

1mL of Thorazine contains 25mg.

Dissolve Thorazine with the 100mL solution.

Therefore, 25 x 100 = 2500mg

Which is equals to 2.5g

100mL solution contains 2.5g of Thorazine.

Percentage Strength (W/V) = 2.5 / 100 x 100 = 2.5%.

The percentage strength of Thorazine 25mg/mL has 2.5%

1. The trigonometric ratios are given as follows:

2. The equation to solve for x is given as follows: sin(52º) = x/13.

3. Two equations to solve for m are given as follows:

4. The length of the hypotenuse of the triangle is given as follows: 7.9 inches.

5. The lengths are given as follows:

The three trigonometric ratios are given as follows:

In the second problem, we have that the side x is opposite to the angle of 52º, while the hypotenuse is of 13, hence the equation to solve for x is given as follows:

sin(52º) = x/13.

In item 3, the Pythagorean Theorem is used to solve for m, as follows:

n² + m² = l².

m² = l² - n²

m = square root (l² - n²).

In item 4, we have that the angle opposite to the leg of length 7 inches is of 62º, hence the hypotenuse is given as follows:

sin(62º) = 7/h

h = 7/sin(62º)

h = 7.9 inches.

The length BD in item 5 is obtained as follows:

cos(30º) = BD/5

BD = 5 x cos (30º)

BD = 4.3 cm.

Then the length BC is calculated as follows:

sin(22º) = 4.3/BC

BC = 4.3/sin(22º)

BC = 11.5 cm.

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Answer:

15 parts must be shaded

Step-by-step explanation:

3/5 × 25 = 15

15/25 = 3/5

Have a great day.

15 parts must be shaded in order to cover three fifths of the rectangle.

"A rectangle has two pairs of equal opposite parallel sides, four right angles and two diagonals. The diagonals of a rectangle are congruent.

They also bisect each other. Each diagonal divides the rectangle into two congruent right triangles."

Given

A rectangle is divided into 25 equal parts.

Number of parts must be shaded in order to cover three fifths of the rectangle

= \(\frac{3}{5}\) × \(25\)

= 15

Checking whether the 15 parts must be shaded in order to cover three fifths of the rectangle

= \(\frac{15}{25}\)

= \(\frac{3}{5}\)

Hence, 15 parts must be shaded in order to cover three fifths of the rectangle.

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The GCD of 5! and 7! is 2^3 * 3^1 * 5^1 = 120.

the greatest common divisor of 5! and 7! is 120.

To find the greatest common divisor (GCD) of 5! and 7!, we need to factorize both numbers and identify the common factors.

First, let's calculate the values of 5! and 7!:

5! = 5 * 4 * 3 * 2 * 1 = 120

7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040

Now, let's factorize both numbers:

Factorizing 120:

120 = 2^3 * 3 * 5

Factorizing 5,040:

5,040 = 2^4 * 3^2 * 5 * 7

To find the GCD, we need to consider the common factors raised to the lowest power. In this case, the common factors are 2, 3, and 5. The lowest power for 2 is 3 (from 120), the lowest power for 3 is 1 (from 120), and the lowest power for 5 is 1 (from both numbers).

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8.67 as a mixed fraction is

8 and 67/100

you could also say 867/100

P Q P V Q P ^ Q P -> Q -P -Q -P V -Q -P -> Q -P -> -Q P <-> Q

T T T T T F F F F F T    T

F T T F F T T T T T F    F

P F T F F T T T T T F     F

-P T T F F T T T T T F     F

-Q T T T T F T F F F T     T

-P V -Q T T F F T T T T T F

-P -> Q T T F F T T T T T F

-P -> -Q T T F F T T T T T F

P <-> Q T T T T F T T T T F

Here is a more detailed explanation of how I filled out the table:

P | Q : This column is simply the truth value of P and Q. If P and Q are both true, then the entry in this column is T. If P is true and Q is false, then the entry in this column is F. If P is false and Q is true, then the entry in this column is F. And if P and Q are both false, then the entry in this column is T.

P V Q : This column is the truth value of P or Q. If P is true, then the entry in this column is T. If Q is true, then the entry in this column is T. And if P and Q are both false, then the entry in this column is F.

P ^ Q : This column is the truth value of P and Q. If P and Q are both true, then the entry in this column is T. And if P and Q are both false, then the entry in this column is F.

P -> Q : This column is the truth value of P implies Q. If P is true and Q is false, then the entry in this column is F. And if P is false or Q is true, then the entry in this column is T.

-P : This column is the negation of P. If P is true, then the entry in this column is F. And if P is false, then the entry in this column is T.

-Q : This column is the negation of Q. If Q is true, then the entry in this column is F. And if Q is false, then the entry in this column is T.

-P V -Q : This column is the truth value of not P or not Q. If P and Q are both true, then the entry in this column is F. If P and Q are both false, then the entry in this column is T. And if P or Q is true, then the entry in this column is T.

-P -> Q : This column is the truth value of not P implies Q. If P is true and Q is false, then the entry in this column is T. And if P is false or Q is true, then the entry in this column is F.

-P -> -Q : This column is the truth value of not P implies not Q. If P and Q are both true, then the entry in this column is T. If P is false or Q is false, then the entry in this column is T. And if P is true and Q is true, then the entry in this column is F.

P <-> Q : This column is the truth value of P if and only if Q. If P and Q are both true or P and Q are both false, then the entry in this column is T. And if P and Q have different truth values, then the entry in this column is F.

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Answer:

To find the rules for (fg)(x) and (gf)(x), we need to evaluate the composite functions.

(fg)(x) = f(g(x)) = f(sqrt(x - 5)) = (sqrt(x - 5))^2 + 5 = x - 5 + 5 = x

(gf)(x) = g(f(x)) = g(x^2 + 5) = sqrt(x^2 + 5 - 5) = sqrt(x^2) = |x|

Therefore, the rules for (fg)(x) and (gf)(x) are:

(fg)(x) = x

(gf)(x) = |x|

Step-by-step explanation:

Answer:

I have solved it and attached in the explanation.

Step-by-step explanation:

Answer: He must have atleast 98 points on the next exam in order to get an average of 92 points.

Step-by-step explanation: To calculate average, you need to add all the numbers given, and divide the sum by how many numbers there are. 87 + 89 + 94 + 98 (equals 368), and divide 368 by 4. You will get the average of 92 as its result.

Answer:

The cosine function is: adjacent/hypotenuse = cos (40). We know the hypotenuse length is 10, so the equation is now adjacent/10 = cos (40). Solving for adjacent length we get 7.7 inches.

Answer:

the answer is B: 7.7 inches

Step-by-step explanation:

did the test go 100%

"The correct answer is option A." The missing coordinates of point Q are (a, c/2).We are given the coordinates of points P and N as (0, c) and (2a, 0), respectively. We are also given that point Q lies on the same line as points P, Q, and N. We need to find the missing coordinates of point Q.

Since point Q lies on the same line as P, Q, and N, its x-coordinate must be halfway between the x-coordinates of points P and N. That is, the x-coordinate of Q is:

x-coordinate of Q = (x-coordinate of P + x-coordinate of N) / 2

x-coordinate of Q = (0 + 2a) / 2 = a

So, we know that the x-coordinate of point Q is a.

To find the y-coordinate of point Q, we can use the fact that point Q lies on the same line as point P, which has coordinates (0, c). The equation of the line passing through P and N is:

y - c = (0 - c) / (2a - 0) * (x - 0)

Simplifying this equation gives:

y - c = -c/2a * xy = -c/2a * x + c

Substituting x = a in this equation gives:

y = -c/2a * a + cy = -c/2 + cy = c/2

So, we know that the y-coordinate of point Q is c/2.

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The following statements which describes the most likely consequence of the information shown in the graph is the the number of children per classroom which is therefore denoted as option 5.

This is referred to as a pictorial representation or a diagram that represents data or values in an organized manner.

In the graph given above, we were given the trends in the elementary school enrollment in which the the number of schoolchildren enrolled in different years were noted which therefore means that the number of children per classroom as it is the most appropriate choice.

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The slope of a horizontal line is always zero.

What is slope?

The slope of a line is a measure of how steep the line is. It represents the rate at which the y-coordinate of the line changes with respect to the x-coordinate. Symbolically, it is represented by the letter m, and can be calculated using the following formula:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are any two points on the line.

The slope of a horizontal line is always zero. This is because a horizontal line has the same y-coordinate at every point, and therefore, there is no change in the y-coordinate for any change in the x-coordinate.

By definition, the slope of a line is the change in y divided by the change in x. In the case of a horizontal line, the change in y is always zero, since the y-coordinate does not change. So, no matter what value of x you choose, the slope of a horizontal line will always be:

slope = change in y / change in x = 0 / (any non-zero value of x) = 0

So, the slope of a horizontal line is always zero.

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Answer:

x = 12

Step-by-step explanation:

Hello!

x² - 5x + 6

= (x² - 2x) + (-3x + 6)

= x(x - 2) - 3(x - 2)

= (x - 2)(x - 3)

The price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit is 62.13

y = -14x² + 1035x - 10266

-14x² + 1035x - 10266 = 0

x = -b ± √b² - 4ac / 2a

= -1035 ± √1035² -4(-14)(-10266) / 2(-14)

= -1035 ± √1071225 - 574896 / -28

= -1035 ± √496329 / -28

x = 1035 / 28 ± √496329 / 28

x = 11.80 or 62.13

The maximum value of x is 62.13

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Answer:LJ = 18 + 28 = 46

Step-by-step explanation:

Suppose J, K, L, M, N are points on the same line.

MK = MN + (-KN) = MN - KN = 9x - 11 - x - 3 = 8x - 14

Since LK = MK and LK = 7x - 10, then

7x - 10 = 8x - 14

8x - 7x = -10 + 14

x = 4

LJ = MK + KJ

MK = LK = 7x - 10 = 7(4) - 10 = 28 - 10 = 18

LJ = 18 + 28 = 46

X is a positive rational number greater than 1. If the two integers that make up the ratio are both positive, then the numerator must be greater than the denominator for the value of the ratio to be greater than 1.

So now let's look at subtracting the numerator and the denominator. We know that p > q and they are both positive integers.

So, p - q must be a positive integer greater than 1 because it is a positive integer subtracted by a smaller positive integer.

Answer:

8 ft², 21.8ft², and 11.2ft²

Step-by-step explanation: