I have 3/4 of all my kittens and 3/4 of a kitten. How many kittens do I have?

Answer: x=13, y=12

Step-by-step explanation:

Since AB and DC are parallel, we can use the special angle formed by the transversal AC.

4x is equal to 52. These angles are alternate interior angles and therefore equal in measure.

4x= 52. Divide both sides by 4.

x = 13

m<ADC is 90 degrees. (AD is perpendicular to DC. This forms a right angle measuring 90 degrees.

Use the triangle angle sum theorem to solve for y. (The 3 interior angles of a triangle sum to 180)

52+90+(3y+2) = 180. Combine like terms.

144+3y = 180. Subtract 144 from both sides.

3y= 36. Divide both sides by 3.

y= 12

If events A and B are independent, then they remain independent when conditioned on event C.

To prove that if events A and B are independent, then they are also independent conditioned on event C, we can use the definition of conditional probability.

Recall that two events A and B are independent if and only if P(A and B) = P(A) * P(B). And the conditional probability of A given B can be calculated as P(A | B) = P(A and B) / P(B).

It follows that P(A and B) = P(A) * P(B) if occurrences A and B are independent. Substituting this into the expression for conditional probability, we get:

\(P(A | B) = P(A) * P(B) / P(B) = P(A)\)

Similarly, we can prove that P(B | A) = P(B). This means that the probability of A and B given event C are equal to the probabilities of A and B, respectively, given that A and B are independent. Hence, events A and B are also independent conditioned on event C

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Answer:

-5.

Step-by-step explanation:

5 + -5 = 0, so i's -5.

Answer:157.5

Step-by-step explanation:becuase mutilpy 4.5x35 that equals 157.5

If the value of a in the quadratic function f f(x) = ax² + bx + c is 1/2, the function will; open up and have a minimum

We are told that the value of a in the quadratic function f(x) = ax² + bx + c is 1/2. Thus, the quadratic function is expressed as;

f(x) = ¹/₂x² + bx + c

If the signs of the coefficients of x² and x are equal, then the graph axis of symmetry will be on the left hand side of the y-axis. This is because the axis of symmetry is expressed as; x = -b/2a

Now, if the sign of the constant term is positive, then it means that the y-intercept is positive. This is because the y-intercept is the value at which x = 0 which is f(0)

Now, if the discriminant is negative, then it means that the quadratic graph will not touch the x-axis. This is because the graph touches x-axis when f(x) = 0, but the solution will be imaginary and as such it doesn't touch on the graph.

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Complete question is;

If the value of a in the quadratic function f(x) = ax² + bx + c is 1/2 the function will:

open down and have a minimum

open up and have a maximum

open down and have a maximum

open up and have a minimum

Answer:

I think he should plot the point at (4, 2)

The attachment is a repost showing what I see if Jeff attaches the 3rd point to the listed points.

Using the power reducing formulas the expression \(5cos^4(x) = 5(1 + cos(2x))^{2/4}\).

We can define higher powers of a trigonometric function in terms of lower powers of the same function using the power-reducing formulas, which are trigonometric identities. Higher powers of cosine can be expressed using this formula in terms of sine and cosine's initial powers. For the other trigonometric functions, such as sine and tangent, there are equivalent formulas. These formulas can be used to solve trigonometric equations and to simplify trigonometric expressions.

The given function is 5cos^4(x).

Now, the power reducing formulas are given by:

\(cos(2x) = cos^2(x) - sin^2(x) = 2cos^2(x) - 1\\cos^2(x) = (1 + cos(2x))/2\)

Substituting the value of second equation in 1 we have:

cos(2x) = 2(1 + cos(2x))/4 - 1

\(cos(2x) = (2cos^2(x) - 1) = cos^2(x) - sin^2(x)\)

Now we have:

\(cos^2(x) = (1 + cos(2x))/2\)

Thus,

\(cos^4(x) = (1 + cos(2x))/2)^2\)

Now multiplying by 5:

\(5cos^4(x) = 5(1 + cos(2x))^{2/4}\)

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Answer:

The retail price is $103.6

Step-by-step explanation:

Markdowns are, to be simple, when the price goes DOWN, so the price would be less than the original rather than more. First, you must calculate what one percent of the original is, which is 1.40. As the markdown is 26 percent, you can do 1.40 x 26 to get how much was marked down, which is $36.40. To find the new price now, you must do the original minus the markdown, or 140 - 36.40 in this case. This gives you $103.6 as the retail price.

I hope this helped! :D

Answer:

To find the total number of beads Naina used to complete the ornament, we need to sum the number of beads in each layer.

Total number of beads = 45 + 42 + 39 + ... (continue the pattern until the 10th layer)

Notice that the number of beads in each layer decreases by 3. We can use arithmetic series formula to find the sum of the beads in all 10 layers:

S = (n/2) x (a + l)

where S is the sum, n is the number of terms, a is the first term, and l is the last term.

Here, a = 45, l = 18 (since the 10th layer will have 18 beads), and n = 10 (since there are 10 layers). Thus, we have:

S = (10/2) x (45 + 18) = 5 x 63 = 315

Therefore, Naina used a total of 315 beads to complete the ornament.

Answer:

The answer to your problem is, 1260

Step-by-step explanation:

Well we know she made 10 “ strand ornaments “ for each layers we would need to add;

45 + 42 + 39

= 126

We would actually then need to multiply it by 10. Shown:

126 × 10

= 1260

Thus the answer to your problem is, 1260

Answer: because dna is  game of chance

Step-by-step explanation: hope it helps

Answer:

\(f(x) = 3 \: \: \: \: for \: \: \: \: - 6 < x < 1 \\ f(x) = - x \: \: \: \: for \: \: \: \: 1 < x < 6\)

Answer:

To reduce a fraction: divide the numerator and denominator by their greatest common factor, GCF.

Fraction: 7/18 already reduced to the lowest terms.

The numerator and denominator have no common prime factors.

Their prime factorization:

7 is a prime number;

18 = 2 × 3^2;

gcf (7; 2 × 3^2) = 1;

Fraction: 13/36 already reduced to the lowest terms.

The numerator and denominator have no common prime factors.

Their prime factorization:

13 is a prime number;

36 = 2^2 × 3^2;

gcf (13; 2^2 × 3^2) = 1;

Reduce (simplify) fractions to their simplest form, online calculator

Answer:

a) 0.238 = 23.8% probability that the selected passenger had Phoenix as a final destination.

b) 0.762 = 76.2% probability that the selected passenger did not have Phoenix as a final destination.

c) 0.054 = 5.4% probability that the selected passenger was connecting and missed the connecting flight.

d) 0.709 = 70.9% probability that the selected passenger was a connecting passenger and did not miss the connecting flight.

e) 0.249 = 24.9% probability that the selected passenger either had Phoenix as a initial destination or was delayed overnight in Phoenix.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

(a) Compute the probability that the selected passenger had Phoenix as a final destination.

1900 out of 8000 passengers. So

\(p = \frac{1900}{8000} = 0.238\)

0.238 = 23.8% probability that the selected passenger had Phoenix as a final destination.

(b) Compute the probability that the selected passenger did not have Phoenix as a final destination.

8000 - 1900 = 6100 out of 8000 passengers. So

\(p = \frac{6100}{8000} = 0.762\)

0.762 = 76.2% probability that the selected passenger did not have Phoenix as a final destination.

(c) Compute the probability that the selected passenger was connecting and missed the connecting flight.

430 out of 8000 passengers. So

\(p = \frac{430}{8000} = 0.054\)

0.054 = 5.4% probability that the selected passenger was connecting and missed the connecting flight.

(d) Compute the probability that the selected passenger was a connecting passenger and did not miss the connecting flight.

6100 - 430 = 5670 out of 8000 passengers. So

\(p = \frac{5670}{8000} = 0.709\)

0.709 = 70.9% probability that the selected passenger was a connecting passenger and did not miss the connecting flight.

(e) Compute the probability that the selected passenger either had Phoenix as a initial destination or was delayed overnight in Phoenix.

1900 initial, 95 delayed. So 1995 out of 8000.

\(p = \frac{1995}{8000} = 0.249\)

0.249 = 24.9% probability that the selected passenger either had Phoenix as a initial destination or was delayed overnight in Phoenix.

The translations that would map Figure F onto Figure G are given as follows:

A translation right 4 units and up 3 units.

A translation happens when either a figure or a function are moved horizontally or vertically on the coordinate plane.

The four translation rules for coordinates are defined as follows:

The rule applied to the coordinates of each point on the figure F to obtain Figure G is given as follows:

(x,y) -> (x + 4, y + 3).

Hence the translation is defined as follows:

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Answer:  the number that can be placed in the box to make the statement true is 3.

Step-by-step explanation:

To make the statement true, we need to find a number that, when added to 7, equals 10. From the given options, the number that satisfies this condition is 3.

If we substitute 3 for the box in the statement, it becomes:

If +7=10, then 10-7=3.

Answer:

5y - 9 + 2 -5y =

Step-by-step explanation:

5y - 9 + 2 - 5y

= 5y - 5y - 9 + 2

= -7

(As + 5y and - 5y cancel out)

(a) The sum of the series 1+2+3+4+...+392 is 77,028.

(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).

(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.

To solve the exercise using Polya's four-step problem-solving strategy, we will apply the procedures presented in the lesson.

(a) For the series 1+2+3+4+...+392:

Using the arithmetic series formula Sn = (n/2)(a + l), where n is the number of terms, a is the first term, and l is the last term, we can substitute the values: Sn = (392/2)(1 + 392) = 196(393) = 77,028.

(b) For the series 1+2+3+4...x:

To find the sum of this series, we need to know the number of terms (n) based on the value of x. Since the series follows a consecutive pattern, the number of terms will be equal to x itself. Thus, the sum of the series would be Sn = (x/2)(1 + x).

(c) For the series 546 + 547 + 548 + 549:

Using the arithmetic series formula Sn = (n/2)(a + l), we can determine the number of terms (n) by subtracting 546 from 549 and then adding 1: n = 549 - 546 + 1 = 4. Substituting the values into the formula: Sn = (4/2)(546 + 549) = 2(1095) = 2,190.

The final answer for each part is:

(a) The sum of the series 1+2+3+4+...+392 is 77,028.

(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).

(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.

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It is summer but it is snowing.

The maximum and minimum values of the function is solved

Given data ,

We can find the maximum and minimum values of the function by taking the derivative of y with respect to x and setting it equal to zero.

y = (sin x)³ - (sin x)⁶

y' = 3(sin x)² cos x - 6(sin x)⁵ cos x

Setting y' equal to zero:

0 = 3(sin x)² cos x - 6(sin x)⁵ cos x

0 = 3(sin x)² cos x (1 - 2(sin x)³)

sin x = 0 or (sin x)³ = 1/2

If sin x = 0, then x = kπ for any integer k.

If (sin x)³ = 1/2, then sin x = (1/2)^(1/3) ≈ 0.866. This occurs when x = π/3 + 2kπ/3 or x = 5π/3 + 2kπ/3 for any integer k.

To determine whether these values correspond to a maximum or minimum, we can use the second derivative test.

y'' = 6(sin x)³ cos² x - 15(sin x)⁴ cos² x - 9(sin x)⁴ cos x + 6(sin x)⁵ cos x

y'' = 3(sin x)³ cos x (4(sin x)² - 5(sin x)² - 3cos x + 2)

For x = kπ, y'' = 3(0)(-3cos(kπ) + 2) = 6 or -6, depending on the parity of k. This means that these points correspond to a maximum or minimum, respectively.

For x = π/3 + 2kπ/3 or x = 5π/3 + 2kπ/3, y'' = 3(1/2)^(5/3) cos x (4(1/2)^(2/3) - 5(1/2)^(1/3) - 3cos x + 2). This expression is positive for x = π/3 + 2kπ/3 and negative for x = 5π/3 + 2kπ/3, which means that the former correspond to a minimum and the latter to a maximum.

Hence , the maximum value of the function is y = 27/64, which occurs at x = 5π/3 + 2kπ/3, and the minimum value is y = -1/64, which occurs at x = π/3 + 2kπ/3

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Answer:

Step-by-step explanation:

You want the maximum and minimum values of the function ...

  y = sin³(x) -sin⁶(x)

When we substitute sin³(x) = z, we have the quadratic expression ...

  y = z -z² . . . . . a quadratic function

Adding and subtracting 1/4, we can put this in vertex form:

  y = -(z -1/2)² +1/4

This version of the function describes a parabola that opens downward and has a vertex at (z, y) = (1/2, 1/4). The y-value of the vertex represents the maximum value of the function.

The maximum value of y is 1/4.

The sine function is a continuous function with a range of [-1, 1]. Then z will be a continuous function of x, with a similar range. We already know that y describes a function of z that is a parabola opening downward with a line of symmetry at z = 1/2. This means the most negative value of y will be found at z = -1 (the value of z farthest from the line of symmetry). That value of y is ...

  y = (-1) -(-1)² = -1 -1 = -2

The minimum value of y is -2.

__

Additional comment

The range of y is confirmed by a graphing calculator.

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The magnitude of the vector is 25.5 metres.

The magnitude of a vector is the length of the vector. Therefore, the magnitude of a vector can be found using Pythagoras's theorem as follows:

Hence,

c² = a² + b²

where

Therefore,

| N | = √22.2² + 12.6²

| N | =  √492.84 + 158.76

| N | =  √651.6

| N | = 25.5264568634

| N | = 25.5 metres

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Answer:

107

Step-by-step explanation:

3, 7, 11, 15, 19,

23, 27, 31, 35,

39, 43, 47, 51,

55, 59, 63, 67,

71, 75, 79, 83,

87, 91, 95, 99,

103, 107

32nd term is 107

Answer:

4.

\(x=8\sqrt{3}\)

\(y=16\)

5.

\(x=3\)

\(y=3\sqrt{3}\)

Step-by-step explanation:

The sides of a (30 - 60 - 90) triangle follow the following proportion,

\(a-a\sqrt{3}-2a\)

Where (a) is the side opposite the (30) degree angle, (\(a\sqrt{3}\)) is the side opposite the (60) degree angle, and (2a) is the side opposite the (90) degree angle. Apply this property for the sides to solve the two given problems,

4.

It is given that the side opposite the (30) degree angle has a measure of (8) units. One is asked to find the measure of the other two sides.

The measure of the side opposite the (60) degree side is equal to the measure of the side opposite the (30) degree angle times (\(\sqrt{3}\)). Thus the following statement can be made,

\(x=8\sqrt{3}\)

The measure of the side opposite the (90) degree angle is equal to twice the measure of the side opposite the (30) degree angle. Therefore, one can say the following,

\(y=16\)

5.

In this situation, the side opposite the (90) degree angle has a measure of (6) units. The problem asks one to find the measure of the other two sides,

The measure of the side opposite the (60) degree angle in a (30-60-90) triangle is half the hypotenuse times the square root of (3). Therefore one can state the following,

\(y=3\sqrt{3}\)

The measure of the side opposite the (30) degree angle is half the hypotenuse (the side opposite the (90) degree angle). Hence, the following conclusion can be made,

\(x=3\)

Answer:

330 Minutes

Step-by-step explanation:

A->B is 3 hours

1 hour=60 minutes

3 hours=180 minutes

B->C is 2 1/2 hours

2 hours=120 minutes

1/2 hour=30 minutes

180+120+30=330 minutes

Answer:

The answer is option 1 :)

Step-by-step explanation:

This is the same as writing y = sqrt(4(x+5)) - 1

===============================================

Explanation:

The given graph appears to be a square root function.

The marked points on the curve are:

Reflect those points over the line y = x. This will have us swap the x and y coordinates.

Recall the process of reflecting over y = x means we're looking at the inverse. The inverse of a square root function is a quadratic.

----------

Let's find the quadratic curve that passes through (1,-4), (3,-1) and (5,4).

Plug the coordinates of each point into the template y = ax^2+bx+c.

For instance, plug in x = 1 and y = -4 to get...

y = ax^2+bx+c

-4 = a*1^2+b*1+c

-4 = a+b+c

Do the same for (3,-1) and you should get the equation -1 = 9a+3b+c

Repeat for (5,4) and you should get 4 = 25a+5b+c

We have this system of equations

Use substitution, elimination, or a matrix to solve that system. I'll skip steps, but you should get (a,b,c) = (1/4, 1/2, -19/4) as the solution to that system.

In other words

a = 1/4, b = 1/2, c = -19/4

We go from y = ax^2+bx+c to y = (1/4)x^2+(1/2)x-19/4

----------

Next we complete the square

y = (1/4)x^2+(1/2)x-19/4

y = (1/4)( x^2+2x )-19/4

y = (1/4)( x^2+2x+0 )-19/4

y = (1/4)( x^2+2x+1-1 )-19/4

y = (1/4)( (x^2+2x+1)-1 )-19/4

y = (1/4)( (x+1)^2-1 )-19/4

y = (1/4)(x+1)^2- 1/4 - 19/4

y = (1/4)(x+1)^2 + (-1-19)/4

y = (1/4)(x+1)^2 - 20/4

y = (1/4)(x+1)^2 - 5

The equation is in vertex form with (-1,-5) as the vertex. It's the lowest point on this parabola. Placing it into vertex form allows us to find the inverse fairly quickly.

----------

The last batch of steps is to find the inverse.

Swap x and y. Then solve for y.

y = (1/4)(x+1)^2 - 5

x = (1/4)(y+1)^2 - 5

x+5 = (1/4)(y+1)^2

(1/4)(y+1)^2 = x+5

(y+1)^2 = 4(x+5)

y+1 = sqrt(4(x+5))

y = sqrt(4(x+5)) - 1

I'll let the student check each point to confirm they are on the curve y = sqrt(4(x+5)) - 1.

You can also use a tool like GeoGebra to verify the answer.

Answer:no idea

Step-by-step explanation:

Answer:

90cm2

Step-by-step explanation:

i have worked it in the picture

hope you will understand

Answer:16feet

Step-by-step explanation:

The explanation is in the attached file

Question 24 :

P594.65 : 35 days

P594.65/7 : 35/7 days

P84.95 : 5 days

⇒ A. P84.95

Question 25 :

88.75 + 85.5 + 90.5 + 87.25 / 4

352/4

88

⇒ B. 88

Question 26 :

I = P × r × t

I = 580.00 × 0.065 × 1

I = P37.70

⇒ B. P37.70