What does the transformation f(x)↦ 1 4 f(x) do to the graph of f(x)

Answer:

Therefore, 1 + 2cos a can be expressed as the product of 2 and (cos a/2 + 1).

1 + 2cos a = 2(cos a/2 + 1)

Step-by-step explanation:

We can use the trigonometric identity:

cos 2a = 1 - 2 sin^2 a

to rewrite 1 + 2cos a as:

1 + 2cos a = 1 + 2(1 - sin^2 a/2)

= 1 + 2 - 2(sin^2 a/2)

= 3 - 2(sin^2 a/2)

Now, using another trigonometric identity:

sin a = 2 sin(a/2) cos(a/2)

we can rewrite sin^2 a/2 as:

sin^2 a/2 = (1 - cos a)/2

Substituting this into the expression for 1 + 2cos a, we get:

1 + 2cos a = 3 - 2((1 - cos a)/2)

= 3 - (1 - cos a)

= 2 + cos a

Therefore, 1 + 2cos a can be expressed as the product of 2 and (cos a/2 + 1).

1 + 2cos a = 2(cos a/2 + 1)

Answer:

13

Step-by-step explanation:

2(13 - 8) + 3

26 - 16 + 3

10 + 3

13

Least number of packages of plates Shaniya needs to buy=24

Based on the given problem above, it is mentioned that in one pack of cups has 6 and one pack of plates has 8. Therefore, the least number of packages of plates that Shaniya needs to buy is 3 packages and for the cups, it would be 4 packages. 4 x 6 is 24 cups, and 3 x 8 would be 24 plates.

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Answer:

It would be C.

Step-by-step explanation:

This is because they allow it to be 50 dollars and less, making it C.

Answer:

see explanation

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

a hexagon has 6 sides , then

sum = 180° × (6 - 2) = 180° × 4 = 720°

12

the polygon has 5 sides , so

sum = 180° × (5 - 2) = 180° × 3 = 540°

sum the interior angles and equate to 540

y + 90 + 120 + 90 + 110 = 540

y + 410 = 540 ( subtract 410 from both sides )

y = 130

13

the polygon has 7 sides , so

sum = 180° × (7 - 2) = 180° × 5 = 900°

sum the interior angles and equate to 900

p + 90 + 141 + 130 + 136 + 123 + 140 = 900

p + 760 = 900 ( subtract 760 from both sides )

p = 140

Answer:

the answer is the second choice

Step-by-step explanation:

Answer:

C: .75

Step-by-step explanation:

I really just subtracted

Answer:

7 + 2 = 9, so AC = 7/9 and CD = 2/9

1 + 2 = 3, so AB = 1/3 = 3/9 and

BD = 2/3 = 6/9

AB + BC = AC

3/9 + BC = 7/9, so BC = 4/9

AB:BC:CD = (3/9):(4/9):(2/9) = 3:4:2

Therefore, the probability that a senior boy does both wrestling and football is approximately 0.063 or 6.3%.

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that the event is impossible, and 1 indicating that the event is certain. The probability of an event can be determined by calculating the ratio of the number of favorable outcomes to the total number of possible outcomes.

Here,

Let A be the event that a senior boy wrestles, and B be the event that a senior boy plays football. Then, we want to find P(A and B), the probability that a senior boy does both wrestling and football. We know that there are 143 senior boys in total, 104 of whom do not do either wrestling or football. Therefore, the number of boys who do at least one of the two sports is:

N(A or B) = N(A) + N(B) - N(A and B)

= 21 + 27 - N(A and B) (since we don't know N(A and B))

= 48 - N(A and B)

We also know that N(A or B) = 143 - 104 = 39.

Therefore, we can solve for N(A and B):

N(A and B) = 48 - N(A or B)

= 48 - 39

= 9

So there are 9 senior boys who do both wrestling and football.

Finally, we can find the probability that a senior boy does both sports by dividing N(A and B) by the total number of senior boys:

P(A and B) = N(A and B) / N(total)

= 9 / 143

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Answer:

Together they equal 180 l so you need to do 180-128 which equals 52. The answer is <D measures 52

Step-by-step explanation:

Answer:

80%

Step-by-step explanation:

out of 20, 1 would be 5%  

4 = 20%

100% -  20% = 80%

She needs to paints the 15% of the total toys.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

Total toys= 20

Toys to be paint= 7

She paints 4 toys and 3 toys are remaining .

so, percent of the 20 toys does she still have to paint

= 3/ 20 x 100

= 3 x 5

= 15%

Hence, she needs to paints the 15% of the total toys.

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1. B.

2. C.

3. A.

4. C.

Answer: 0.4337

Step-by-step explanation:

Let X represents the test results for a class that follow a normal distribution .

Given: Mean \(\mu=78\), Standard deviation  \(\sigma=36\)

Then, the probability that it is greater than 84 will be

\(P(X>84)=P(\dfrac{X-\mu}{\sigma}>\dfrac{84-78}{36})\\\\=P(Z>0.167)\ \ \ [Z=\dfrac{X-\mu}{\sigma}]\\\\=1-P(Z<0.167)\\\\=1-0.5663=0.4337\ [\text{By p-value table}]\)

Hence, the required probability = 0.4337

Answer:

Below

Step-by-step explanation:

A parbola with zeroes at 0 and 598 would look like this:

  f(x) = a ( x-0)(x-598)      at the midpoint 299   the value is 625

   625 = a (299) (299-598)      shows a = - 625/89401

-625/89401 (x)(x-598)   <======expand as necessary

Answer:

105 cm ^ 2 / s

Step-by-step explanation:

We have that the area of a rectangle is given by the following equation:

A = l * w

being the length and w the width, if we derive with respect to time we have:

dA / dt = dl / dt * w + dw / dt * l

We all know these data, l = 15; w = 12; dl / dt = 5; dw / dt = 3, replacing we have:

dA / dt = 5 * 12 + 3 * 15

dA / dt = 105

Which means that the area of the rectangle increases by 105 cm ^ 2 / s

Answer:

32.965°

Explanation:

To solve the expression we need to use the calculator, so:

Therefore, the answer is 32.965°

The Commutative Propery of Addition states that rearranging the order of the numbers upon adding does not change the sum. For example, 2 + 1 and 1 + 2 are both equal to 3 or 2 + 5 and 5 + 2 are both equal to 7.

So, rewriting 15y + 4x using the Commutative Property of Addition is 4x + 15y. (Second Option)

All that apply are:

The slope is 0.

The y-intercept is -2

The line is horizontal.

The equation of the line is Y = -2.

Given points:

(1,-2) and (4,-2)

slope m = -2-(-2) / 4 - 1

= -2+2/3

= 0

so slope is 0

y = mx + c

(1,-2) passes

-2 = 0*1 + c

c = -2

y = 0*x + -2

y = -2

so the line is horizontal and equation of the line is y = -2.

The y-intercept is -2.

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Answer:

Step-by-step explanation:

The weighted average of the student's scores is ...

  0.20×63 +0.05×97 +0.35×85 +0.40×77 = 78

The student's overall final score is 78.

__

The letter grade earned is between 70 and 80, so is a C.

The statement is AB=CD,BC=AD due to definition of parallelogram. The statement is AC=AC due to Reflexive property of equality.

A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size. A quadrilateral with the opposing sides parallel is called a parallelogram. A parallelogram with all right angles is known as a rectangle, and a quadrilateral with equal sides is known as a rhombus.

Here,

1. Statement: AB=CD,BC=AD

Reason: By definition of parallelogram.

2. Statement: AC=AC

Reason: Reflexive property of equality.

The definition of a parallelogram causes the sentence to be AB=CD,BC=AD. Due to the reflexive feature of equality, the assertion is AC=AC.

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The following table shows the number of hours 45 hospital patients slept for one night. Use the table to answer the questions:Hours of Sleep | Patients0-2 | 53-5 | 96-8 | 179-11 | 2212-14 | 10a) How many patients slept between 6 and 11 hours?A total of 22 patients slept between 6 and 11 hours.

To find out, we need to add the number of patients who slept for 6-8 hours (17) and those who slept for 9-11 hours (5). Therefore, 17+5=22.b)

The mode is the value that occurs most frequently in the data set. In this case, the mode is the number of hours that the highest number of patients slept.

From the table, we can see that 9-11 hours is the mode because 22 patients slept for that number of hours, which is more than any other number of hours.c)

The median is the middle value in the data set when the data are arranged in numerical order. In this case, we have 45 patients, so we need to find the middle value between the 22nd and 23rd patients. These patients slept for 9-11 hours, so the median is 9-11 hours.

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The electrical resistance varies directly as the square of the voltage and inversely as the electric power, and the equation that relates them isR ∝ V²/PR = kV²/PR = V²/P. This relationship can be used to calculate the electrical resistance of the wire or component for any given voltage and power.

The electrical resistance is the measure of the difficulty in passing electric current through a wire or an electrical component. It depends on various factors, such as the material, dimensions, and temperature of the wire.The given statement says that the electrical resistance varies directly as the square of the voltage and inversely as the electric power.

In mathematical terms, this relationship can be expressed as R ∝ V²/PR = kV²/P where R is the electrical resistance, V is the voltage, P is the electric power, and k is the constant of proportionality. The constant k depends on the material, dimensions, and temperature of the wire or component.

The given statement implies that the constant k is the same for the given wire or component, and it is not affected by the voltage or the power.To find the value of k, we can use the given values of V, P, and R.

According to the statement, if the voltage is 20 volts and the electric power is 5 watts, then the electrical resistance is 80 ohms. Therefore,R = kV²/PR = k(20²)/5R = 400k/5R = 80 ohms

Substituting the value of R in the equation, we get80 = 400k/5k = (80 x 5)/400k = 1. Therefore, the equation that relates the electrical resistance, voltage, and power isR = V²/PThe constant of proportionality k is 1 for the given wire or component.

Therefore, the electrical resistance varies directly as the square of the voltage and inversely as the electric power, and the equation that relates them isR ∝ V²/PR = kV²/PR = V²/P. This relationship can be used to calculate the electrical resistance of the wire or component for any given voltage and power.

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From the given information, Therefore, the function \(= > y = 4(\frac{5}{6} )^x\) is an exponential decay.

The process of decreasing a sum at a constant percentage rate over time is referred to in mathematics as exponential decay. It may be written as the formula y=a(1-b)x, where y represents the final amount and a, b, and x, respectively, represent the initial amount and the decay factor.

The formula for an exponential function is where b is a positive integer that is not equal to 1.

Whether a function is an exponential growth or a decay depends on the value of b. If b > 1 or if b<  1, an exponential function exhibits exponential growth and exponential decline, respectively.

given,

\(= > y = 4(\frac{5}{6} )^x\)

\(= > b = \frac{5}{6} < 1\)

Therefore, the function \(= > y = 4(\frac{5}{6} )^x\) is an exponential decay.

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Answer:

6.9 feet

Step-by-step explanation:

You can get this by dividing 27.6 by 4

then can check your answer by multiplying 4 by 6.9

Answer:

Step-by-step explanation:

4x² - 0x - 9 = 4x² - 9 = (2x)² - 3² = (2x - 3)(2x + 3)

used: (a - b)(a + b) = a² - b²

Answer:

The 72nd term is -708

Step-by-step explanation:

Area of Sector.

The area of a sector is given by the formula below:

Substituting these values into the formula above, we get

Thus, the correct answer is 46.5 square meters.