6th grade math. :) help me please

Answer:

y = sin(4(x+π/8)) + 1

Step-by-step explanation:

For a trigonometric equation of form

y = Asin(B(x+C)) + D,

the amplitude is A, the period is 2π/B, the phase shift is C, and the vertical shift is D (shifts are relative to sin(x) = y)

First, the amplitude is the distance from the center to a top/bottom point (also known as a peak/trough respectively). The center of the function given is at y=1, and the top is at y=2, Therefore, 2-1= 1 is our amplitude.

Next, the period is the distance between one peak to the next closest peak, or any matching point to the next matching point. One peak of this function is at x=0 and another is at x= π/2, so the period is (π/2 - 0) = π/2. The period is equal to 2π/B, so

2π/B  = π/2

multiply both sides by b to remove a denominator

2π = π/2 * B

divide both sides by π

2 = 1/2 * B

multiply both sides by 2 to isolate b

4 = B

After that, the phase shift is the horizontal shift from sin(x). In the base function sin(x), one center is at x=0. However, on the graph, the closest centers to x=0 are at x=± π/8. Therefore, π/8 is the phase shift.

Finally, the vertical shift is how far the function is shifted vertically from sin(x). In sin(x), the centers are at y=0. In the function given, the centers are at y=1, symbolizing a vertical shift of 1.

Our function is therefore

y = Asin(B(x+C)) + D

A = 1

B = 4

C = π/8

D = 1

y = sin(4(x+π/8)) + 1

Answer(s):

[tex]\displaystyle y = sin\:(4x + \frac{\pi}{2}) + 1 \\ y = -cos\:(4x \pm \pi) + 1 \\ y = cos\:4x + 1[/tex]

Explanation:

[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{8}} \hookrightarrow \frac{-\frac{\pi}{2}}{4} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{2}} \hookrightarrow \frac{2}{4}\pi \\ Amplitude \hookrightarrow 1[/tex]

OR

[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{2}} \hookrightarrow \frac{2}{4}\pi \\ Amplitude \hookrightarrow 1[/tex]

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = sin\:4x + 1,[/tex] in which you need to replase “cosine” with “sine”, then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{8}\:unit[/tex] to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACK [tex]\displaystyle \frac{\pi}{8}\:unit,[/tex] which means the C-term will be negative, and perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{\pi}{8}} = \frac{-\frac{\pi}{2}}{4}.[/tex] So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = sin\:(4x + \frac{\pi}{2}) + 1.[/tex] Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits [tex]\displaystyle [0, 2],[/tex] from there to [tex]\displaystyle [\frac{\pi}{2}, 2],[/tex] they are obviously [tex]\displaystyle \frac{\pi}{2}\:unit[/tex] apart, telling you that the period of the graph is [tex]\displaystyle \frac{\pi}{2}.[/tex] Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 1,[/tex] in which each crest is extended one unit beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

Answer:

Step-by-step explanation:

Following the cardinal points as regards location of points, the sketch of Musah's movement can be as what is attached to this answer.

Answer:

Mean: 55.9

Median: 55

Mode: None

Step-by-step explanation:

First, find the mean by dividing the sum by the number of elements:

(72 + 58 + 62 + 38 + 44 + 66 + 42 + 49 + 76 + 52) / 10

= 55.9

Next, find the median by putting the numbers in order and finding the middle one:

38, 42, 44, 49, 52, 58, 62, 66, 72, 76

There is no middle number, so we will take the average of 52 and 58, which is 55.

Lastly, to find the mode, we have to find the number that occurs the most.

All of the numbers occur one time, so there is no mode.

Answer:

h(-4) = -2

Step-by-step explanation:

h(x)=-2x-10

Let x = -4

h(-4)=-2*-4-10

       =8-10

       = -2

Answer:

[tex]\huge \boxed{{-2}}[/tex]

Step-by-step explanation:

[tex]\sf The \ function \ is \ given:[/tex]

[tex]h(x)=-2x-10[/tex]

[tex]\sf To \ find \ h(-4), \ put \ x=-4.[/tex]

[tex]h(-4)=-2(-4)-10[/tex]

[tex]h(-4)=8-10[/tex]

[tex]h(-4)=-2[/tex]

Answer:

5 - ? = 4

5- 1 = 4

➪5 - 4 = ?

➪1 = 5-4

➪ 5- 1 = 4

hopes its helps you ..

Answer:

60%

Step-by-step explanation:

9/20 is 45%

Answer:

60 %

Step-by-step explanation: If you divide 9/20, it equals to 0.45, makes it 45% and the number 45 in general is smaller than 60. Thus, 60% is greater than 9/20. I hope this helps.

Answer:

Step-by-step explanation:

3(x + 4) = -12

3x+12 = -12

3x= -12-12

3x= -24

x = -24/3

x= -8

Answer:

x = -8

Step-by-step explanation:

3(x+4) = -12

3*x + 3*4 = -12

3x + 12 = -12

3x = -12 - 12

3x = -24

x = -24/3

x = -8

Check:

3(-8+4) = -12

3*-4 = -12

Answer: The length is 4 centimeters and the width is 6 centimeters.

Step-by-step explanation:

If the length of the  rectangle is eight centimeters less than twice the width then we could represent it by the equation L= 2w - 8 .   And we know that to find the area of a rectangle we multiply the length by the width  and they've already given the area  so we will represent the width by w since it is unknown.

Now we know the length is 2w- 8 and the width is w so we would multiply them and set them equal to 24.

w(2w-8) = 24

2[tex]w^{2}[/tex] - 8w = 24     subtract 24 from both sides to set the whole equation equal zero and solve. solve using any method. I will solve by factoring.

2[tex]w^{2}[/tex] - 8w -24 = 0      divide each term by 2.

[tex]w^{2}[/tex] - 4w - 12 = 0          Five two numbers that multiply to get -12 and to -4

[tex]w^{2}[/tex] +2w - 6w - 12 = 0    Group the left hand side and factor.

w(w+2) -6( w + 2) = 0   factor out w+2

(w+2)(w-6) = 0         Set them both equal zero.

w + 2 =0      or w - 6 = 0  

    -2  -2                + 6   +6

w= -2       or   w=6  

Since we are dealing with distance -2 can't represent a distance so the wide has to 6.  

Now it says that the length is 8 less that twice the width.

So  2(6) - 8 = 12 -8 = 4  So the length in this care is 4.

Check.

6 * 4 = 24

24 = 24

Answer:

The probability that one man sampled from this population has a weight between 72kg and 88kg is 0.6826.

Step-by-step explanation:

The complete question has the data of mean = 80 kg and standard deviation = 8kg

We have to find the probability between 72 kg and 88 kg

Since it is a normal distribution

(x`- u1 / σ/ √n) < Z >( x`- u2 / σ/ √n)

P (72 <x>88) = P ( 72-80/8/√1) <Z > ( 88-80/8/√1)

= P (-1<Z> 1) = 1- P (Z<1) - P (Z<-1)

= 1- 0.8413- (- 0.8413)= 1- 1.6826= 0.6826

So the probability that one man sampled from this population has a weight between 72kg and 88kg is 0.6826.

Answer:

[tex]\sqrt{51}[/tex] units.

Step-by-step explanation:

Point E is inside a rectangle ABCD.

Please refer to the attached image for the given statement and dimensions.

Given that:

Sides AE = 6 units

BE = 7 units and

CE = 8 units

To find:

DE = ?

Solution:

For a point E inside the rectangle the following property hold true:

[tex]AE^2+CE^2=BE^2+DE^2[/tex]

Putting the given values to find the value of DE:

[tex]6^2+8^2=7^2+DE^2\\\Rightarrow 26+64=49+DE^2\\\Rightarrow DE^2=100-49\\\Rightarrow DE^2=51\\\Rightarrow \bold{DE = \sqrt{51}\ units}[/tex]

Answer:

a: 750 ml (three quarters)

b: 750 ml

Step-by-step explanation:

1/4 liter= 250ml

A) 250*3= 750ml

B) the same as A

Answer:

The value of the test statistic is 59.75.

Step-by-step explanation:

The test statistic for the population standard deviation is:

[tex]\chi^2 = \frac{n-1}{\sigma_0^2}s^2[/tex]

In which n is the sample size, [tex]\sigma_0[/tex] is the value tested and s is the sample standard deviation.

A sample of 45 bottles of soft drink showed a variance of 1.1 in their contents.

This means that [tex]n = 45, s^2 = 1.1[/tex]

The process engineer wants to determine whether or not the standard deviation of the population is significantly different from 0.9 ounces.

0.9 is the value tested, so [tex]\sigma_0 = 0.9, \sigma_0^2 = 0.81[/tex]

What is the value of the test statistic

[tex]\chi^2 = \frac{n-1}{\sigma_0^2}s^2[/tex]

[tex]\chi^2 = \frac{44}{0.81}1.1 = 59.75[/tex]

The value of the test statistic is 59.75.

0.012 is the answer!

I hope this helps you out! :D

[tex]\\ \sf\longmapsto \dfrac{12}{1000}[/tex]

[tex]\\ \sf\longmapsto 0.012[/tex]

More:-

[tex]\\ \sf\longmapsto \dfrac{1}{10}=0.1[/tex]

[tex]\\ \sf\longmapsto \dfrac{1}{100}=0.01[/tex]

Answer:

C

Step-by-step explanation:

one line is

y = 3x/7 + 11

its slope is 3/7

the y-intercept is, of course, when x=0. there y=11

the other is

-3x + 7y = 13

7y = 3x + 13

y = 3x/7 + 13/7

its slope is 3/7 (the same as the other line)

the y-intercept (x=0) is y = 13/7 (different to the other line)

Answer:

C. Yes, since the slopes are the same and the y-intercepts are different.

Step-by-step explanation:

[tex]y=\frac{3}{7} x+11[/tex]  and [tex]-3x+7y=13[/tex]

→ Rearrange the second equation to make y the subject

7y = 3x + 13

→ Divide everything by 7

[tex]y=\frac{3}{7} x+\frac{13}{7}[/tex]

Answer:

Hello,

answer C

Step-by-step explanation:

[tex]f(x)=x^2+2x-8\\\\=x^2-4x+2x-8\\\\=x(x-4)+2(x-4)\\\\=(x-4)(x+2)\\\\Answer\ C[/tex]

Answer:

4/3

Step-by-step explanation:

just do the lcm of denomination and after that start solving

9514 1404 393

Answer:

  1 23/24

Step-by-step explanation:

Fractions can be added when they have the same denominator. Then the addition is performed by adding the numerators, and expressing the sum over the common denominator.

Here, your fractions have denominators of 8 and 6. Usually, we want to find a "least common denominator" to use to express the fractions. There are various ways to find that value. One of the easiest is to consult your memory of multiplication tables to find the smallest number that both a multiple of 8 and a multiple of 6. That number is 24.

An equivalent fraction is one that has the same value, but a different denominator than the one it is being compared to. Equivalent fractions can be made by multiplying by "1" in the form of "a/a" where "a" is any non-zero value. Here, it is useful to multiply 9/8 by 3/3 to make the equivalent fraction 27/24, which has a denominator of 24.

Similarly, we can multiply 5/6 by 4/4 to get the equivalent 20/24, which also has a denominator of 24.

These two fractions can now be added:

  [tex]\dfrac{9}{8}+\dfrac{5}{6}=\dfrac{27}{24}+\dfrac{20}{24}=\dfrac{27+20}{24}=\dfrac{47}{24}[/tex]

If you want to turn this into a "mixed number", you need to find how many times 24 goes into 47: 47÷24 = 1 remainder 23. The quotient is the integer part of the mixed number; the remainder is the numerator of the fractional part. Then the mixed number value of the sum is ...

  [tex]\dfrac{47}{24}=1\dfrac{23}{24}[/tex]

_____

Additional comments

The product of the denominators can always serve as a common denominator. That may not be the "least" common denominator. If you use that here, you would have ...

  [tex]\dfrac{9}{8}+\dfrac{5}{6}=\left(\dfrac{9}{8}\cdot\dfrac{6}{6}\right)+\left(\dfrac{5}{6}\cdot\dfrac{8}{8}\right)=\dfrac{54+40}{48}=\dfrac{94}{48}[/tex]

This result can be reduced by removing a factor of 2 from numerator and denominator to give 47/24, the sum we had above.

The "least common denominator" (LCD) is the Least Common Multiple (LCM) of the denominators. It can be found by forming the product of the unique factors of the denominators. Here, we have 8 = 2·2·2 and 6 = 2·3. The LCD is the product 2·2·2·3. We recognize that 2³ and 3 are unique factors that need to contribute to the LCD. 2 is subsumed by 2³.

As you can see from the factoring, 2 is a common factor of both numbers. Another way to find the LCD (or LCM of the denominators) is to form their product (8×6 = 48) and divide that by the greatest common factor (GCF), which is 2. (48/2 = 24, the LCD) Sometimes it is easier to find the GCF and compute (product/GCF) than to find the LCM using factoring.

__

If you don't mind the possibility of having to reduce the resulting fraction, the sum of fractions can always be computed as ...

  [tex]\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad+bc}{bd}[/tex]

This formula computes 94/48 as the sum of these fractions, effectively leaving out the middle step (9/8×6/6 +...) shown in the work above. I find this especially useful for adding rational expressions, not just numerical fractions.

Answer:

See below.

Step-by-step explanation:

Using the right triangle altitude theorem, the correct proportions are:

[tex] \dfrac{AB}{AC} = \dfrac{AC}{AD} [/tex]

[tex] \dfrac{AB}{x} = \dfrac{x}{AD} [/tex]

[tex] \dfrac{25}{x} = \dfrac{x}{16} [/tex]

[tex] x^2 = 25 \times 16 [/tex]

[tex] x = 20 [/tex]

AC = 20 cm

[tex] \dfrac{AB}{CB} = \dfrac{CB}{DB} [/tex]

[tex] \dfrac{AB}{y} = \dfrac{y}{DB} [/tex]

[tex] \dfrac{25}{y} = \dfrac{y}{9} [/tex]

[tex]y^2 = 25 \times 9[/tex]

[tex]y = 15[/tex]

CB = 15 cm

Answer:

9

Step-by-step explanation:

First, find x. Since x is the average of the three number, add the three up and then divided by three. Thus:

[tex]x=\frac{13+-16+6}{3}=3/3=1[/tex]

y is the cube root of 8. Thus:

[tex]y=\sqrt[3]{8}=2[/tex]

So:

[tex]x^2+y^3\\=(1)^2+(2)^3\\=1+8=9[/tex]

Answer:

ljih

Step-by-step explanation:

Answer:

a. 539.54

b. No, the result from part (a) could not be the actual number of adult who said that secondhand smoke are very harmful because a count of people must result into a whole number.

c. 540

d. 25.54%

Step-by-step explanation:

Given that:

A polling company reported that 53​% of 1018 surveyed adults said that secondhand smoke is "very harmful."

Complete parts​ (a) through​ (d) below.

a. What is the exact value that is 53​% of 1018​?

The 53% of 1018 is :

=[tex]\dfrac{53}{100} \times 1018[/tex]

= 0.53 × 1018

= 539.54

b. Could the result from part​ (a) be the actual number of adults who said that secondhand smoke is ''very harmful"? Why or why​ not?

No, the result from part (a) could not be the actual number of adult who said that secondhand smoke are very harmful because a count of people must result into a whole number.

c. What could be the actual number of adults who said that secondhand smoke is secondhand smoke "very harmful"?

Since, a count of people must result into a whole number, the actual number of adults who said that secondhand smoke is secondhand smoke "very harmful" can be determined from the approximation of the exact value into whole number which is 539.54 [tex]\approx[/tex] 540.

d. Among the 1018 ​respondents, 260 said that secondhand smoke is  is "not at all harmful.''  What percentage of respondents said that secondhand smoke is  "not at all harmful"?

Since 260 respondents out of 1018 respondents said that the second hand smoke is not harmful, then the percentage of the 260 respondents is :

= [tex]\dfrac{260}{1018} \times 100 \%[/tex]

= 25.54%

Answer:

1st, keep value of x in 1st equation

Step-by-step explanation:

-6(-2y-1)+2y=48

12y+6+2y=48

14y=48-6

y=42/14

y=3

Now putting value of y in equation ii)

x= - 2y-1

x= - 2×3-1

x= - 6-1

x= - 7

Therefore, x= - 7

y=3

Answer:

Step-by-step explanation:

[tex]\frac{a(b+c)}{bc} ,\frac{b(c+a)}{ca} ,\frac{c(a+b)}{ab} ~are~in~A.P.\\if~\frac{ab+ca}{bc} ,\frac{bc+ab}{ca} ,\frac{ca+bc}{ab} ~are~in~A.P.\\add~1~to~each~term\\if~\frac{ab+ca}{bc} +1,\frac{bc+ab}{ca} +1,\frac{ca+bc}{ab} +1~are~in~A.P.\\if~\frac{ab+ca+bc}{bc} ,\frac{bc+ab+ca}{ca} ,\frac{ca+bc+ab\\}{ab} ~are~in~A.P.\\\\divide~each~by~ab+bc+ca\\if~\frac{1}{bc} ,\frac{1}{ca} ,\frac{1}{ab} ~are ~in~A.P.\\if~\frac{a}{abc} ,\frac{b}{abc} ,\frac{c}{abc} ~are~in~A.P.\\if~a,b,c~are~in~A.P.\\which~is~true.[/tex]

Answer:

C. 1/4

Step-by-step explanation:

Parallel lines always have the same slope.

Answer:

  C.  1/4

Step-by-step explanation:

Parallel lines have the same slope. If line b is parallel to line a, and line a has slope 1/4, then line b has slope 1/4.

Answer:

15

Step-by-step explanation:

15×3=45

15×4=60

15×5=75

Answer:

15

Step-by-step explanation:

45 = 1 × 3^2 × 5

60 =  2^2 × 3 × 5

75 = 3 × 5^2

greatest number than divides 45, 60 and 75 without leaving remainder​ = GCF of 45,60,75 = 3 × 5 = 15

Answer:  see proof below

Step-by-step explanation:

Use the Quotient rule for derivatives:

[tex]\text{If}\ y=\dfrac{a}{b}\quad \text{then}\ y'=\dfrac{a'b-ab'}{b^2}[/tex]

Given: [tex]y=\dfrac{2\sqrtx}{1-x}[/tex]

[tex]\sqrtx[/tex][tex]a=2\sqrt x\qquad \rightarrow \qquad a'=\dfrac{1}{\sqrt x}\\\\b=1-x\qquad \rightarrow \qquad b'=-1[/tex]        

[tex]y'=\dfrac{\dfrac{1-x}{\sqrt x}-(-2\sqrt x)}{(1-x)^2}\\\\\\.\quad =\dfrac{\dfrac{1-x}{\sqrt x}-(-2\sqrt x)\bigg(\dfrac{\sqrt x}{\sqrt x}\bigg)}{(1-x)^2}\\\\\\.\quad =\dfrac{1-x+2x}{\sqrt x(1-x)^2}\\\\\\.\quad =\dfrac{x+1}{\sqrt x(1-x)^2}[/tex]

LHS = RHS:  [tex]\dfrac{x+1}{\sqrt x(1-x)^2}=\dfrac{x+1}{\sqrt x(1-x)^2}\qquad \checkmark[/tex]

Answer:

blue 1

orange 5

green 3

I hope it is helpful and mark me as brainlest and follow me plz

Answer:

The  90% confidence interval is  [tex]\$ \ 30313.9< \mu < \$ \ 33686.13[/tex]

Step-by-step explanation:

From the question we are told that

   The  sample size is  n =  64

     The sample  mean is  [tex]\= x = \$ 32, 000[/tex]

     The  standard deviation is  [tex]\sigma= \$ 8, 200[/tex]

Given that the confidence interval is  90% then the level of significance is mathematically evaluated as

             [tex]\alpha = 100 - 90[/tex]

             [tex]\alpha = 10 \%[/tex]

            [tex]\alpha = 0.10[/tex]

Next we obtain the critical value of  [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table , the value is  

       [tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]

  Generally the margin of error is mathematically represented as

        [tex]E = Z_{\frac{\alpha }{2} } * \frac{ \sigma }{ \sqrt{n} }[/tex]

  =>   [tex]E = 1.645 * \frac{ 8200 }{ \sqrt{64} }[/tex]

  =>   [tex]E = 1686.13[/tex]

The 90% confidence interval is mathematically represented as

      [tex]\= x - E < \mu < \= x + E[/tex]

 =>    [tex]32000 - 1689.13 < \mu < 32000 + 1689.13[/tex]

=>    [tex]\$ \ 30313.9< \mu < \$ \ 33686.13[/tex]

Answer:

The price of bus after 4 yrs is Rs.1652400

Step-by-step explanation:

Present price of car = Rs.3000000

We are given that the price of bus depreciated the first two yrs by 10%

So, The price after first two years =[tex]3000000(1-0.1)^2=2430000[/tex]

Now the price of bus depreciated by 15%

So, The price after third year = 2430000-0.15(2430000)=2065500

Now the price of bus depreciated by 20%

The price after fourth year =2065500-0.2(2065500)=1652400

Hence the price of bus after 4 yrs is Rs.1652400

Answer:

2.25 pounds of raisins

Step-by-step explanation: