What are the period and amplitude of the function?



Question 1 options:

period: 5; amplitude: 3


period: 5; amplitude: 4.5


period: 6; amplitude: 3


period: 6; amplitude: 4.5

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange x + 5y = 10 into this form

Subtract x from both sides

5y = - x + 10 ( divide all terms by 5 )

y = - [tex]\frac{1}{5}[/tex] x +2 ← in slope- intercept form

with slope m = - [tex]\frac{1}{5}[/tex]

• Parallel lines have equal slopes, hence

y = - [tex]\frac{1}{5}[/tex] x + c ← is the partial equation of the parallel line

To find c substitute (1, 3) into the partial equation

3 = - [tex]\frac{1}{5}[/tex] + c ⇒ c = [tex]\frac{16}{5}[/tex]

y = - [tex]\frac{1}{5}[/tex] x + [tex]\frac{16}{5}[/tex] ← equation of parallel line

Answer:

A) y = − 1 /5 x +  16/ 5

Step-by-step explanation:

Answer:

The answer is parabola; (y')² - 8x' = 0 ⇒ answer (b)

Step-by-step explanation:

* At first lets talk about the general form of the conic equation

- Ax² + Bxy + Cy²  + Dx + Ey + F = 0

∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.

∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.

∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.

* Now we will study our equation:

* x² - 8y = 0

∵ A = 1 , B = 0 , C =

∴ B² - 4AC = (0)² - 4(1)(0) = 0

∵ B² - 4AC = 0

∴ it will be a parabola.

∵ Ф = 90°

* The point (x , Y) will be (x' , y')

∵ x = x'cosФ - y'sinФ and y = x'sinФ + y'cosФ

∵ cos(90) = 0 and sin(90) = 1

∴ x = -y' and y = x'

* lets substitute x and y in the first equation

∴ (-y')² - 8(x') = 0

∴ (y')² - 8x' = 0

* We notice that the x' took the place of y and y' took the place of x

∴ The parabola rotated around the origin by 90°

∴ The equation of the parabola is (y')² - 8x' = 0

* The answer is parabola, with angle of rotation 90°

* The equation is (y')² - 8x' = 0

* Look to the graph

- The blue is x² - 8y = 0

- The green is (y')² - 8x' = 0

Answer:

the correct answer is D)

parabola

Answer:

The probability that the sample mean would be greater than 77.21 WPM = 0.9945

Step-by-step explanation:

Mean number of Words per Minute  = u  = 81

Standard Deviation = s = 17

sample size = n = 130

Target value = x = 77.21

we can find the probability by converting x to z-score.

The formula for z-score = [tex]\frac{x-u}{\frac{s}{\sqrt{n} } }[/tex]

using given values, z-score =  [tex]\frac{77.21-81}{\frac{17}{\sqrt{130} } }[/tex]

=> -2.54

using the z table, we can find the find the probability of -2.54, that is 0.9945.

Therefore, the probability that the sample mean would be greater than 77.21 WPM = 0.9945  

The probability that the sample mean would be greater than 77.21 WPM is approximately [tex]\(0.9945\)[/tex] (rounded to four decimal places).

To find the probability that the sample mean is greater than 77.21 WPM, we need to use the Central Limit Theorem.

Here's the step-by-step process:

1. Identify the given information:

Population mean [tex](\(\mu\))[/tex]: 81 WPM

Population standard deviation [tex](\(\sigma\))[/tex]: 17 WPM

Sample size [tex](\(n\))[/tex]: 130

Sample mean [tex](\(\bar{x}\))[/tex]: 77.21 WPM

2. Calculate the standard error of the mean (SEM):

[tex]\[ \text{SEM} = \frac{\sigma}{\sqrt{n}} = \frac{17}{\sqrt{130}} \approx \frac{17}{11.4018} \approx 1.4910 \][/tex]

3. Find the Z-score for the sample mean:

[tex]\[ Z = \frac{\bar{x} - \mu}{\text{SEM}} = \frac{77.21 - 81}{1.4910} \approx \frac{-3.79}{1.4910} \approx -2.543 \][/tex]

4. Use the Z-score to find the probability:

We look up the Z-score of -2.543 in the standard normal distribution table.

[tex]\[ P(Z < -2.543) \approx 0.0055 \][/tex]

This is the probability that the sample mean is less than 77.21 WPM. Since we need the probability that the sample mean is greater than 77.21 WPM, we subtract this value from 1.

[tex]\[ P(\bar{x} > 77.21) = 1 - P(Z < -2.543) = 1 - 0.0055 = 0.9945 \][/tex]

The first answer is correct

Answer:

3 + 9 + 27 + ...

Step-by-step explanation:

3 + 9 + 15 + ... is not a geometric series because it has no common ratio.

[tex]\frac{15}{9}\ne \frac{9}{3}[/tex]

3 + 9 + 27 + ... is a geometric series because there is a common ratio;

[tex]r=\frac{27}{9}=\frac{9}{3}=3[/tex]

3, 9, 27, ... is a geometric sequence and not a series. The sum of all the  terms in a geometric sequence forms a geometric series.

3, 9, 15, ... is a not a geometric series.

The simplest direct ratio of boys to girls in the room is 3:4, which means for every 3 boys, there are 4 girls. This is determined by finding the greatest common divisor of the two quantities. Other possible ratios such as 6:8, 9:12, 12:16, and 15:20 are multiples of this base ratio.

The question is asking for us to form all the possible ratios of boys to girls in the given situation. We are given that there are 42 boys and 56 girls. The simplest ratio of boys to girls can be determined by finding the greatest common divisor (GCD) of both numbers and then dividing both numbers by it. The GCD of 42 and 56 is 14, so if we divide both numbers by the GCD, we get the ratio of 3:4. This implies that for every 3 boys, there are 4 girls. However, other possible ratios could use multiple of these numbers. Therefore, the possible ratios of boys to girls in this scenario also include 6:8, 9:12, 12:16, 15:20, and so on.

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Answer:

g(x) = 2sin(x) + 3

Step-by-step explanation:

f(x) = sin(x)

transformed into a new function, g(x) , by stretching it vertically by a factor of 4 and shifting it 3 units to the right.

so

g(x) = 2sin(x) + 3

Answer:

x=2

Step-by-step explanation:

10=16(x-2)^2+10

Subtract 10 from each side

10-10=16(x-2)^2+10-10

0 =16(x-2)^2

Divide by 16

0/16 = 16/16 (x-2)^2

0 = (x-2)^2

Take the square root of each side

sqrt(0) = sqrt(  (x-2)^2)

0 = x-2

Add 2 to each side

0+2 = x-2+2

2 =x

[tex]Cancel \ 10 \ on \ both \ sides.\\\\0 = 16(x - 2)^2\\\\\\Divide \ both \ sides \ by \ 16.\\0 = (x - 2)\\\\\\Now take the square root of both sides.\\\\0 = x - 2\\\\\\Add 2 to both sides.\\\\2 = x\\\\Switch sides.\\\\\fbox{x = 2}[/tex]

Answer:

Car 1 : 40 gallons

Car 2 : 15 gallons

Step-by-step explanation:

F = Car 1 Fuel Efficiency

S = Car 2 Fuel Efficiency

F + S = 55

40F + 35S = 2125

Using the first equation...

S = 55 - F

Then substitute into the second equation.

40F + 35(55 - F) = 2125

Simplify

40F + 1925 - 35F = 2125

5F + 1925 = 2125

5F = 200

F = 40

Then plug it back into S = 55 - F

S = 15

Plug it back into F + S = 55 to check.

Hope this helps.

Car 1 fuel efficiency is 40 gallons and car 2 fuel efficiency is 15 gallons.

Let car 1 fuel efficiency = x

Let car 2 fuel efficiency = y.

Based on the information given,

x+ y = 55 ...... i

40x + 35y = 2125 ...... ii

Therefore, y = 55 - x ..... iii

Put equation iii into ii

40x + 35(55 - x) = 2125

40x + 1925 - 35x = 2125

Collect like terms

40x - 35x = 2125 - 1925

5x = 200

x = 200/5

x = 40

Since x + y = 55.

y = 55 - 40 = 15

Therefore, Car 1 fuel efficiency is 40 gallons and car 2 fuel efficiency is 15 gallons.

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1. The given curves intersect one another three times:

[tex]x^3=9x\implies x(x^2-9)=0\implies x=0,\pm3[/tex]

The area of the bounded region is

[tex]\displaystyle\int_{-3}^3|x^3-9x|\,\mathrm dx[/tex]

[tex]x^3-9x[/tex] is odd, but the absolute value makes it even. More formally,

[tex]|(-x)^3-9(-x)|=|-x^3+9x|=|x^3-9x|[/tex]

which means the integral is equivalent to

[tex]\displaystyle2\int_0^3|x^3-9x|\,\mathrm dx[/tex]

For [tex]0\le x\le 3[/tex], the definition of absolute value tells us that

[tex]|x^3-9x|=9x-x^3[/tex]

so the integral evaluates to

[tex]\displaystyle2\int_0^3(9x-x^3)\,\mathrm dx=\left(9x^2-\frac{x^4}2\right)\bigg|_{x=0}^{x=3}=\frac{81}2=40.5[/tex]

2. Using the disk method, the volume is given by the integral

[tex]\displaystyle\pi\int_0^\pi\sin^2(\sin x)\,\mathrm dx[/tex]

Use a calculator to get the result 1.219.

x = -21

explanation: a trick i used was just do -3 times 7 and get my answer -21. if you are unsure if the answer is right just check your work with a calculator. -21 divided by 7 is -3 so -21 is the value of x. please mark brainliest !!

Answer:

A) 0.947; B) 0.0392; C) 0.7257; D) 6th

Step-by-step explanation:

For part A,

We find the z-score for both of these values and subtract them; this will give us the area under the curve between the scores, which is the same as the probability between them.

[tex]z=\frac{X-\mu}{\sigma}\\\\z=\frac{1000-1252}{129}\text{ and } z=\frac{1500-1252}{129}\\\\z=\frac{-252}{129}\text{ and } z=\frac{248}{129}\\\\z=-1.95\text{ and }z=1.92[/tex]

Using a z-table, we see that the area to the right of z = -1.95 is 0.0256.  The area to the right of z = 1.92 is 0.9726.  This means the area between them is

0.9726 - 0.0256 = 0.947.

For part B,

To find the probability that fewer than 1025 chips are in the bag, we find the z-score:

[tex]z=\frac{X-\mu}{\sigma}=\frac{1025-1252}{129}=\frac{-227}{129}\\\\=-1.76[/tex]

Looking this number up in the z-table, we find the area under the curve to the left of, or less than, this is 0.0392.

For part C,

Once we find the z-score for the value 1175, the z-table chart will give us the area under the curve less than this.  To find the proportion greater than this, we subtract from 1:

[tex]z=\frac{X-\mu}{\sigma}=\frac{1175-1252}{129}=\frac{-77}{129}=-0.60[/tex]

In the z-table, we see that the area under the curve less than this is 0.2743.  This means that the area greater than this is 1-0.2743 = 0.7257.

For part D,

We again find the area under the curve less than this.  This tells us the proportion of values that will be less than this; this will tell us the percentile value for this.

[tex]z=\frac{1050-1252}{129}=\frac{-202}{129}=-1.57[/tex]

In the z-table, we see the area to the right of this is 0.0582.  This means that 5.82% of values are less than this; this means the value is the 5.82 percentile, which rounds to the 6th percentile.

These questions are solved by converting the specified number of chips to a Z-score and using it to find the corresponding probability in a standard normal distribution table. The various calculated probabilities provide the answers to the different parts of the question.

In order to answer these questions, we need to convert the number of chips to a Z-score, which is a measure of how many standard deviations an element is from the mean, and then find the corresponding probability from a standard normal distribution table.

(a) To calculate the probability of a bag containing between 1000 - 1500 chips, you subtract the mean from each and divide by the standard deviation to get Z-scores. Then one can find the corresponding probabilities in a Z-table and subtracting the smaller probability from the larger. This will give you the probability of number of chips falling between those two amounts.

(b) Similarly, to compute the probability of a bag containing fewer than 1025 chips, find the Z-score for 1025 and look it up in the Z-table. The probability that corresponds to that Z-score is the likelihood of having fewer than 1025 chips.

(c) For the the proportion of bags that contains more than 1175 chips, first compute the Z-score for 1175. The corresponding probability in the Z-table gives the proportion for those with numbers equal or less than 1175. To get the proportion for bags with more than 1175 chips, you need to subtract that value from 1 (since the total probability is always 1).

(d) Finally, for the percentile rank, it's again the same process. You find the Z-score for 1050, look up its corresponding probability and multiply it by 100 to convert it into percentile rank.

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Answer:

On the surface of the sea

Step-by-step explanation:

Six feet below sea level is marked as -6

Go up 6 feet

-6+6 =0 feet below sea level

That would mean we are at 0, which would be sea level

We would be on the surface of the sea

Answer:

x = 12

Solve for x:

Using Pythagorean Theorem

a^2 + b^2 = c^2

a = 9

c = 15

b = x

9^2 + x^2 = 15^2

81 + x^2 = 225

x^2 = 144 | sqrt

x = 12

Answer:

54 times you can fill a cone with the grain that is stored in the container

Step-by-step explanation:

step 1

Find the volume of the paper cone

The volume of the cone is

[tex]V=\frac{1}{3}\pi r^{2} h[/tex]

we have

[tex]r=4\ cm[/tex]

[tex]h=9\ cm[/tex]

[tex]\pi=3.14[/tex]

substitute the values

[tex]V=\frac{1}{3}(3.14)(4)^{2} (9)=150.72\ cm^{3}[/tex]

step 2

Divide the total volume of the container by the volume of one paper cone

[tex]\frac{8,138.88}{150.72}=54[/tex]

Answer:

Its 54

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The function is a quadratic whose graph is a parabola. All parabolas have no limitations on their domain. This means the domain of the function is all real numbers.

This parabola has a minimum value since its leading coefficient is positive. Its vertex is at (0,-2). This means its range is all values greater than -2 or y ≥ -2.

An inverse of a function is its reflection across the y=x line. This results in (x,y) in the function becoming (y,x) in its inverse. The domain of the function becomes the range of the inverse and the range of the function becomes the domain of the inverse. Inverse has x ≥ -2 as its domain and all real numbers for its range.

Answer:

A.

Step-by-step explanation:

I just got 100% on the quiz.

i think the answer is B

The value of x2 is 24.

Two variables are inversely varying if one variable value increases then other variable value decreases. We can represent this relation with an equation

y ∝ 1/x

⇒ y=k/x

where k is a constant.

According to asked problem y is varying inversely with x.

given, x1=6

y1=8

putting these values in the above equation,

8=k/6

⇒k=48

Now we have the value of k.

So the inversely varying equation will become,

y=48/x

By putting the value y2=2

2=48/x

⇒x=48/2

⇒x=24

The value of x2 is 24.

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Answer:

B

Step-by-step explanation:

An equivalent expression is an expression which is equal to 10k + 17 - 7j - 18 - 11k. You can expand or simplify an expression to make an equivalent expression. Combine like terms to form a new equivalent expression. Like terms are terms which have the same base or variable.

10k + 17 - 7j - 18 - 11k

10k -11k + 17 - 18 - 7j                Move to group like terms together.

-k - 1 - 7j

This is the same solution as B written in a different order.

Answer:

BBBBBBBBBBBBBBBBBBBBBBB

Step-by-step explanation:)

Answer:

In the morning, the packing rates per hour was 45. In the afternoon, the packing rates per hour was 40. The difference is 5.

Events A and B are independent events because the product of their probabilities (P(A)P(B)) equals the probability of the intersection of both events (P(A∩B)).

To determine if events A and B are independent events, we need to check if the product of their probabilities equals the probability of their intersection. According to the formula for independent events:

P(A AND B) = P(A)P(B)

Given:

P(A) = 1/4

P(B) = 2/5

P(A∩B) = 1/10

Let's calculate the product of P(A) and P(B):

P(A)P(B) = (1/4) × (2/5) = 1/10

Since P(A∩B) also equals 1/10, which is the same as the product of P(A) and P(B), it is therefore true that:

P(A AND B) = P(A)P(B)

This implies that events A and B are indeed independent because their combined probability equals the product of their probabilities.

➷ cos41 = x/55

x = cos41 x 55

x = 41.50902

The correct option would be 41.51

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Answer:

41.51

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos41° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{55}[/tex]

Multiply both sides by 55

55 × cos41° = x

⇒ x = 41.51 ( to the nearest hundredth )

Answer:

I'm pretty sure the answer is 21.26

I hope thats right if not sorry mark me brainliest

The circumference of the wheel is 21.26 inch

The circumference of a circle refers to the measure of its boundary. If we open a circle and measure the boundary just like we measure a straight line, we get the circumference of the circle in terms of units of length like centimeters, meters, or kilometers.

Now let us learn about the elements that make up circumference. These are the three most important elements of a circle.

Given:

Area of wheel= 36

πr² = 36

r²= 36/ 3.14

r = 3.385

Now,

Circumference of the wheel is

=2πr

=2*3.14*.3.385

=21.264 inches

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Answer:

150 ft

Step-by-step explanation:

triangle area formula= (b*h)/2

25 time 12 is 300. divide 300 by 2 and get 150.

Answer:

A = 150 ft^2

Step-by-step explanation:

The area of a triangle is found by using

A = 1/2 b*h where b is the base and h is the height

A = 1/2 (12)*25

A = 6*25

A = 150 ft^2

Final answer:

Toshi has 1 1/4 hours left before he can leave work, which is found by subtracting the time he has already worked (1 3/4 hours) from his total shift (3 hours).

Explanation:

The student asked how many more hours Toshi has to work before he can leave the car wash, given that he has to work a total of 3 hours and has already worked 1 3/4 hours. To find this out, we subtract the time already worked from the total work time required:

Convert 1 3/4 hours to an improper fraction: 1 3/4 = 7/4 hours.

Convert 3 hours to 4/4 hours increments to have a common denominator: 3 hours = 12/4 hours.

Subtract the time worked from the total time: 12/4 - 7/4 = 5/4 hours.

Convert the answer back to mixed numbers: 5/4 hours = 1 1/4 hours.

Therefore, Toshi has 1 1/4 hours left before he can leave work.

The first one is 4/9 and the second one is 5/9

Final answer:

The probability that the first horse selected is tan and the second horse selected is brown, out of a total of 5 brown horses and 4 tan horses, is 5/18.

Explanation:

The question asks for the probability that the first horse selected is tan, and the second horse selected is brown when there are 5 brown horses and 4 tan horses in a barn. To find this probability, we will multiply the probability of each event happening in sequence.

First, the probability of selecting a tan horse out of the total 9 horses (5 brown + 4 tan) is 4/9. Once a tan horse is selected, there are now 8 horses left, 5 of which are brown. Therefore, the probability of then selecting a brown horse is 5/8.

To find the total probability of both events occurring in sequence (first selecting a tan horse, then a brown horse), we multiply the two probabilities together: 4/9 * 5/8 = 20/72, which simplifies to 5/18.

Answer with step-by-step explanation:

We are given three different expressions and we are to write an equivalent exponential equation for them.

We know that the standard form of a logarithmic expression is given by:

[tex]y = log_a ( x )[/tex] which is equivalent to the exponential form  [tex]x = a ^ y[/tex].

1. [tex] log _ {10} (0.1) = -1 [/tex] ---> [tex]10^{-1}=0.1[/tex]

2. [tex] log _ {3} 9 = 2 [/tex] ---> [tex]3^2=9[/tex]

3. [tex] log _ 5 ( \frac { 1 } { \sqrt { 5 } } ) = -\frac { 1 } { 2 } [/tex] ---> [tex]5^{-\frac{1}{2} }=\frac{1}{\sqrt{5} }[/tex]

Answer:

∠P = 65°

Step-by-step explanation:

The measure of arcs LP and PY are given as 80° and 150°, so their sum is 230°. Arc LY completes the circle of 360°, so is 130°. Inscribed angle P is half that measure, so ...

∠P = 130°/2 = 65°.

Answer: The probability of picking a green token from a box containing 10 red, 6 blue, and 4 green tokens  < the probability of picking a red marble from a bag containing 5 green, 3 red, and 4 blue marbles < the probability of picking a peach from a basket of fruit containing 7 peaches and 3 apples < the probability of picking a golf ball from a box containing 2 tennis balls and 13 golf balls.

i.e.  0.2<0.42<0.7<0.87

Step-by-step explanation:

Since we have given that

1) the probability of picking a red marble from a bag containing 5 green, 3 red, and 4 blue marbles

Probability would be [tex]\dfrac{\text{Red Marble}}{Total\ marble}}=\dfrac{5}{12}=0.42[/tex]

2) the probability of picking a peach from a basket of fruit containing 7 peaches and 3 apples

Probability would be [tex]\dfrac{Peach}{Total}=\dfrac{7}{10}=0.7[/tex]

3) the probability of picking a green token from a box containing 10 red, 6 blue, and 4 green tokens

Probability would be [tex]\dfrac{Green}{Total}=\dfrac{4}{20}=\dfrac{1}{5}=0.2[/tex]

4) the probability of picking a golf ball from a box containing 2 tennis balls and 13 golf balls

Probability would be [tex]\dfrac{Golf\ ball}{Total}=\dfrac{13}{15}=0.87[/tex]

We need to arrange them in order from the event with the lowest probability of occurrence to the event with the highest probability occurrence:

So, 0.2<0.42<0.7<0.87

Hence, it becomes

the probability of picking a green token from a box containing 10 red, 6 blue, and 4 green tokens  < the probability of picking a red marble from a bag containing 5 green, 3 red, and 4 blue marbles < the probability of picking a peach from a basket of fruit containing 7 peaches and 3 apples < the probability of picking a golf ball from a box containing 2 tennis balls and 13 golf balls.

Answer: true :))

Step-by-step explanation:

Public relations is part of business and administrative support as it helps manage a business's image and relationship with the public. Meanwhile, bureaucracy plays a role in not only enforcing policies but also in policy formation.

Public relations is indeed a part of business and administrative support. Businesses use public relations to manage and protect their image and relationship with the public. It's a key component to business administration as it helps businesses improve their brand awareness, manage crises, and strengthen relationships with stakeholders.

The question about bureaucracy is a separate query and in this context, the statement is false. Bureaucracy is not only involved in enforcing policies to ensure people comply, but it is also involved in the process of policy formation. Through different departments and offices, information is gathered, policy proposals are developed and recommendations are made to decision-makers.

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