Find the indicated derivative.
Find y(⁴) if y = 6 sin x.
a y(⁴) = 6 sin x
b y(⁴) = - 6 sin x
c y(⁴) = - 6 cos x
d y(⁴) = 6 cos x

may not know the answer that well but try this called symbolab. Hope that could help you

Answer:

p = - \(\frac{1}{2}\)

Step-by-step explanation:

Given

p = \(\frac{x^2-y^2}{x^2+xy}\) ( factorise numerator and denominator )

x² - y² ← is a difference of squares and factors as (x - y)(x + y)

x² + xy ← factor out x from each term

= x(x + y) , thus

p = \(\frac{(x-y)(x+y)}{x(x+y)}\) ← cancel (x + y) on numerator/ denominator

   = \(\frac{x-y}{x}\) ← substitute x = - 4, y = - 6

   = \(\frac{-4-(-6)}{-4}\)

   = \(\frac{-4+6}{-4}\)

    = \(\frac{2}{-4}\) = - \(\frac{1}{2}\)

To sketch the region enclosed by the curves y = cos(x) and y = sin(2x) for the interval 0 ≤ x ≤ 2, we can follow these steps:

1. Plot the graphs of the two functions separately on the given interval.

For y = cos(x):

- Start by marking key points on the graph: (0, 1), (π/2, 0), (π, -1), (3π/2, 0), (2π, 1).

- Connect the points smoothly to create a curve that oscillates between 1 and -1.

For y = sin(2x):

- Start by marking key points on the graph: (0, 0), (π/4, 1), (π/2, 0), (3π/4, -1), (π, 0), (5π/4, 1), (3π/2, 0), (7π/4, -1), (2π, 0).

- Connect the points smoothly to create a curve that oscillates between 1 and -1, but with twice the frequency of the cosine curve.

2. Identify the region enclosed by the curves.

- The region enclosed by the curves is the area between the two curves from x = 0 to x = 2.

3. Shade the region enclosed by the curves.

- Shade the area between the two curves on the interval 0 ≤ x ≤ 2.

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Answer:  y = 5

using pythagoras theorem

Step-by-step explanation:

If y = 5  there is sufficient information to show that triangle ABC = triangle DEF using the Pythagoras theorem.

Answer:

are you really struggling well just go to sleep

Step-by-step explanation:

hahahahaha

The simplified and rationalized expression is: (4√3)/x.

To simplify the expression and rationalize the denominator, we need to rewrite the expression with a rational denominator.

First, let's simplify the expression: √3 4/0.5x.

To simplify the square root term, we can write it as: √(3 * 4)/(0.5x).

Simplifying the numerator: √12/(0.5x).

Next, let's rationalize the denominator by multiplying both the numerator and the denominator by 2:

(√12 * 2)/((0.5x) * 2).

Simplifying further: (2√12)/(1x).

Finally, simplifying the square root term: (2√(4 * 3))/x.

Simplifying the square root: (2 * 2√3)/x.

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Answer:

1785

Step-by-step explanation:

16+19+22+25+28+31+34+37+40+43+46+49+52+55+58+61+64+67+70+73+76+79+82+85+88+91+94+97+100+103=1785

Answer:

Step-by-step explanation:

The above sequence is an arithmetic sequence

The sum of an nth term of an arithmetic sequence is written as

\( \frac{n}{2} (2a + (n - 1)d)\)

Where n is the number of terms

a is the first term

d is the common difference

From the question

n is 30

a is 16

d = 19 - 16 = 3

So the first 30 terms of the series is

\( \frac{30}{2} (2(16) + (30 - 1) \times 3) \\ = 15(32 + 29 \times 3) \\ = 15(32 + 87) \\ = 15(119) \\ = 1785\)

Hope this helps you.

Answer:

.........

it is -7

Given parameters:

Real area = 9000sq yards

Map area = 6sq yards

Unknown:

Scale of the map = ?

Solution:

A scale is the ratio of the map unit to the real world expression. Maps use scales to present the real world in a smaller sample space:

   For this problem;

              6sq yards on map = 9000sq yards on ground

              1sq yards on map = xsq yards on ground

                     6x  = 9000

                         x = \(\frac{9000}{6}\)  = 1500sq yards

So,

            1sq yards on map is 1500sq yards on ground

Answer: Yes it is

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

The z-scores, we see that Roberto's z-score is -0.69 and Zandra's z-score is -0.73. Both z-scores are relatively close, but Roberto's z-score is slightly higher. Roberto performed better in relation to his gender compared to Zandra.

To determine who did better in relation to their gender, we can compare the finishing times of Roberto and Zandra to the mean finishing times of their respective genders.

For Roberto:

- Mean finishing time for men: 69.4 minutes

- Standard deviation for men: 8.9 minutes

To compare Roberto's performance, we can calculate his z-score, which tells us how many standard deviations his finishing time is away from the mean for men:

z-score = (Roberto's finishing time - Mean finishing time for men) / Standard deviation for men

        = (63.2 - 69.4) / 8.9

        = -0.69

For Zandra:

- Mean finishing time for women: 84.7 minutes

- Standard deviation for women: 7.4 minutes

Similarly, we calculate Zandra's z-score:

z-score = (Zandra's finishing time - Mean finishing time for women) / Standard deviation for women

        = (79.3 - 84.7) / 7.4

        = -0.73

The z-score indicates how many standard deviations each individual's finishing time is away from the mean of their respective gender. A negative z-score indicates that their finishing time is below the mean.

Comparing the z-scores, we see that Roberto's z-score is -0.69 and Zandra's z-score is -0.73. Both z-scores are relatively close, but Roberto's z-score is slightly higher. Therefore, Roberto performed better in relation to his gender compared to Zandra.

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In the given situation (D) randomized block design was used to experiment with incorporating randomization into this study.

An experimental design known as a randomized block design divides the experimental units into units known as blocks.

The experimental units inside each block are assigned the treatments at random.

We have a fully randomized block design when each block has at least one instance of each treatment.

By ensuring that a crucial predictor of the outcome is fairly distributed amongst research groups to require them to be balanced, something that a completely randomized design cannot guarantee, a randomized block design differs from a completely randomized design.

Therefore, in the given situation (D) randomized block design was used to experiment with incorporating randomization into this study.

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Complete question:

R.A. Fisher, a famous statistician, describes a well-known design in his book, Design of Experiments. Five varieties of wheat were compared to determine which gave the highest yield in bushels per acre. Eight farms were available for planting. Each farm was divided into five plots. For each farm, the five varieties were randomly assigned to the five plots with one variety per plot. The varieties were planted on their assigned plots and their yields were measured and compared.

How was randomization incorporated into this study?

A. All five varieties were randomly assigned to the five plots at each farm.

B. The five varieties were randomly assigned to the eight farms - three varieties were planted twice and two varieties only once.

C. It was not incorporated. The wheat seeds were not randomly selected from the population of wheat seeds.

D. Experiment - randomized block design

Answer:

6 : 5

Step-by-step explanation:

Volume of a cube = s^3

5^3 = 125

Surface area of a cube = 6s^2

6(5^2) = 6(25) = 150

150 : 125

30 : 25

6 : 5

Answer:

x=-1

Step-by-step explanation:

if h(x)-4x+4 and h(x)=0,

0=4x+4

0-4=4x

-4=4x

-4/4=x

-1=x

Answer:

99 TVs

Step-by-step explanation:

5 and a half hours is about 330 minutes.

9:30 = x:330

If 30 * 11 = 330, then 9 * 11 will equal x.

Judy should inspect 99 TVs.

Answer:

y = 110 degree

x = 70 degree

z = 70 degree

Step-by-step explanation:

Vertical angles are always congruent.

so, the angle with the 110 degree is equal to the angle y.

now we have the measure of y.

as you can see angle y and angle z form a straight light wich means the sum of angle y and angle x is 180 degree

now, to get the measure of angle z,

180 - 110 = angle z

70 = angle z

now we have the measure of angle z

as angle z and angle x are vertical angle, they are congruent.

so angle x = 70

x = 70

z= 70

y = 110

hope this helps:)

Answer:

1. ∠YZX = 37°

2. ∠YXZ = 53°

3. XZ = 30 meters

Step-by-step explanation:

1. To solve for an unknown angle, we need to utilize the inverse of a trigonometric function.

⭐What are the inverses of the trigonometric functions?

To know which inverse of the trigonometric functions we use, we have to see the type of side lengths we are given (opposite, adjacent, or hypotenuse)

We are given side length XY, which is opposite of ∠YZX, and we are given side length YZ, which is adjacent to ∠YZX. Therefore, we will use \(tan^-1 (opposite/adjacent) =\)

Substitute the values we are given into the function:

\(tan^-1 (18/24) =\)

Compute this equation using a scientific calculator. I recommend using the Desmos Scientific Calculator:

\(= 37\)

∴ ∠YZX = 37°

2. We already know 2 angles (∠YZX = 37°, and ∠ZYX = 90°) Therefore, to find ∠YXZ, we have to utilize the triangle sum theorem.

⭐ What is the triangle sum theorem?

Substitute the angles we know already (∠YZX and ∠ZYX), and solve for ∠YXZ.

\(< YZX + < ZYX + < YXZ = 180\)

\(37 + 90 + YXZ = 180\)

\(127 + YXZ = 180\)

\(< YXZ = 53\)

∴ ∠YXZ = 53°

3. We already know 2 side lengths (ZY = 24 meters, and XY = 18). Therefore, to find XZ, we have to utilize the Pythagoras' theorem.

⭐ What is the Pythagoras' theorem?

Substitute the values of the side lengths into the formula:

\((XZ)^2 = (XY)^2 + (ZY)^2\)

\((XZ)^2 = 18^2 + 24^2\)

Solve for XZ:

\((XZ)^2 = 324 + 576\)

\((XZ)^2 = 900\)

\(\sqrt{(XZ)^2} = \sqrt{900}\)

\(XZ = 30\)

∴ XZ = 30 meters

We are given v = ds/dt, v = 9.8t + 9, s(0) = 17. We need to find the position of a body moving along a coordinate line at time t.

Using the formula of velocity, we can integrate it with respect to t to find the position of the body at any time t. The formula for velocity is:v = ds/dt... (1) Integrating equation (1) with respect to t, we get's = ∫vdt + C ...(2)

Here, C is the constant of integration, and it is found using the given initial position. Given, s(0) = 17Substitute s = 17 and t = 0 in equation (2).17 = ∫(9.8t + 9)dt + C [∵ s(0) = 17]17 = 4.9t² + 9t + C

Therefore, C = 17 - 4.9t² - 9tOn substituting the value of C in equation (2), we get:s = ∫vdt + 17 - 4.9t² - 9t ...(3)Now, we can substitute the given velocity, v = 9.8t + 9, in equation (3).s = ∫(9.8t + 9)dt + 17 - 4.9t² - 9ts = 4.9t² + 9t + 17 - 4.9t² - 9ts = 9t + 17

Hence, the position of the body at time t is 9t + 17 units.

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The crude oil is likely to be paraffinic. Paraffinic crude oils are characterized by having a high API°, low Watson characterization factor, and low refractive index. They also tend to have a high surface tension.

Specific gravity at 60 °F: 0.88

API° at 60 °F: 28

Watson characterization factor: 1.014

Refractive index: 1.44

Surface tension: 20 dyne/cm

Paraffinic, naphthenic, or aromatic: Paraffinic

Specific gravity at 60 °F the specific gravity of a liquid is its density relative to the density of water. The specific gravity of crude oil is typically between 0.8 and 1.0. A specific gravity of 0.88 means that the crude oil is 88% as dense as water.

API° at 60 °F: The API°, or American Petroleum Institute gravity, is a measure of the lightness or darkness of crude oil. A higher API° indicates a lighter crude oil. A crude oil with an API° of 28 is considered to be a medium-heavy crude oil.

Watson characterization factor the Watson characterization factor is a measure of the aromaticity of crude oil. A higher Watson characterization factor indicates a more aromatic crude oil. A crude oil with a Watson characterization factor of 1.014 is considered to be a paraffinic crude oil.

Refractive index the refractive index of a liquid is a measure of how much light is bent when it passes through the liquid. The refractive index of crude oil is typically between 1.4 and 1.5. A refractive index of 1.44 indicates that the crude oil is slightly more refractive than water.

Surface tension the surface tension of a liquid is a measure of the force that acts at the surface of the liquid, tending to minimize the surface area. The surface tension of crude oil is typically between 20 and 30 dyne/cm. A surface tension of 20 dyne/cm indicates that the crude oil has a relatively high surface tension.

Based on the estimated values, the crude oil is likely to be paraffinic. Paraffinic crude oils are characterized by having a high API°, low Watson characterization factor, and low refractive index. They also tend to have a high surface tension.

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The mean of the sampling distribution is μₘ = 72 and the standard deviation of the sampling distribution is σₘ = 3.

To find the mean and standard deviation of the sampling distribution of sample means, we can use the following formulas:

Mean of the sampling distribution (also known as the expected value):

μₘ = μ

Standard deviation of the sampling distribution (also known as the standard error):

σₘ = σ / √n

Given:

Population mean (μ) = 72

Population standard deviation (σ) = 18

Sample size (n) = 36

Plugging the values into the formulas, we can calculate the mean and standard deviation of the sampling distribution as follows:

Mean of the sampling distribution:

μₘ = μ = 72

Standard deviation of the sampling distribution:

σₘ = σ / √n

σₘ = 18 / √36

σₘ = 18 / 6

σₘ = 3

Therefore, the mean of the sampling distribution is μₘ = 72 and the standard deviation of the sampling distribution is σₘ = 3.

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Complete question =

A population has a mean μ=72 and a standard deviation σ=18. Find the mean and standard deviation of a sampling distribution of sample means with sample size n=36.

Using the cosine double-angle identity. The cosine double angle formula tells us that cos(2θ) is always equal to cos²θ-sin²θ.

Answer:

74.9

Step-by-step explanation:

a) Given preferences are not monotonic.

b) The budget constraint is binding and the consumer cannot afford that bundle.
c) The interpretation of these choices is that the consumer maximizes their utility.

(a) These preferences are not monotonic. Monotonicity means that if one bundle is preferred to another, any bundle with more of both goods should also be preferred. In this case, if x1'+x2' < x1''+x2'', it does not necessarily mean that x1'+x2' < x1''+x2'' for all bundles with more of both goods.

(b) To determine which bundle would be chosen by the consumer, we need to compare the total expenditure on each bundle to the consumer's income. If the total expenditure on a bundle is less than or equal to the consumer's income, then that bundle would be chosen.

If the total expenditure exceeds the consumer's income, then the budget constraint is binding and the consumer cannot afford that bundle.

(c) When prices are strictly negative (p1 = -ω, p2 = -e), the budget set can be represented graphically as a set of bundles that the consumer can afford.

The initial endowment P represents the amount of good 2 that the consumer already possesses without having to spend any money. It is a starting point for the consumer's choices.

(d) To characterize the optimal selection of the consumer, we need to consider whether ω > e or e > ω.

If ω > e, the consumer's optimal choice would lie on the highest attainable indifference curve that is tangent to the budget set.

If e > ω, the optimal choice would lie on the indifference curve that is tangent to the budget set at a point where the consumer exhausts their initial endowment P.

The interpretation of these choices is that the consumer maximizes their utility by selecting the bundle that provides the most satisfaction given their budget constraints and initial endowment.

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The money the carnival committee expects to pay for prizes for that booth is $447.5

In previous years, they've discovered that 28% of students win a stuffed toy ($3.65).

14% of students win a jump rope ($1.20).

8% of students win a t-shirt ($7.50) at a booth at the school carnival.

There is no award for the remaining students. How much money should the carnival committee anticipate spending on prizes for that booth if 250 kids participate in the game at the booth.

percentage of students win a stuffed toy ( $3.65 ) = 28%

percentage of students win a jump rope ( $1.20 ) = 14%

percentage of students win a t-shirt ( $7.50 ) = 8%

Given 250 students playing the game.

Out of 250, 28% win a stuffed toy;

                        = 250 * (28/100)

                        = 70

                    14% win a jump rope;

                        = 250 * (14/100)

                        = 35

                    8% win a t-shirt;

                        = 250 * (8/100)

                        = 20

According to the total number of products sold for each quantity;

Amount of money the carnival committee expects to pay for prizes for that booth;

= ($3.65 * 70) + ($1.20 * 35) + ($7.50 * 20)

= 255.5 + 42 + 150

= $447.5

The money the carnival committee expects to pay for prizes for that booth is $447.5.

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Answer:

1≤f(x)≤5

Step-by-step explanation:

-1≤x≤1

-2≤2x≤2 (Multiplied by 2 both side)

-2+3≤2x+3≤2+3 (Adding three both sides)

1≤f(x)≤5

The probability that a woman tests positive given that she has breast cancer is 7/8 and the probability that a woman tests negative for breast cancer given that her test result is negative is 923/1000.

Probability is the possibility of happening an event.

Since 14 of 16 have breast cancer test positive, the probability is:

p = 14/16

p = 7/8

Therefore, the probability that a woman tests positive given that she has breast cancer is 7/8.

The number of women who test negative is:

2000 - 154

= 1846

Therefore, 1846 out of 2000 women test negative.

The probability of a woman testing negative is:

p = 1846/2000

p = 923/1000

Therefore, The probability that a woman tests negative for breast cancer given that her test result is negative is 923/1000.

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