h
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Answer:

The answer is D. You can confirm this from the graph down below

Step-by-step explanation:

Answer:

[tex]h(t)=-25\cos(\pi t)+29[/tex]

Step-by-step explanation:

First thing to understand is that we will be producing a sine or cosine function to solve this one. I'll use a cosine function for the sake of the problem, since it's most easily represented by a cosine wave flipped over. If you're interested in seeing a visualization of how a circle's height converts to one of these waves, you may find the Better Explained article Intuitive Understanding of Sine Waves helpful.

Now let's get started on the problem. Cosine functions generally take the form

[tex]y=a\cos(b(x-c))+d[/tex]

Where:

[tex]|a|[/tex] is the amplitude

[tex]\frac{2\pi}{b}[/tex] is the period, or the time it takes to go one full rotation around the circle (ferris wheel)

[tex]c[/tex] is the horizontal displacement

[tex]d[/tex] is the vertical shift

Step one, find the period of the function. To do this, we know that it takes six minutes to do three revolutions on the ferris wheel, so it takes 2 minutes to do one full revolution. Now, let's find [tex]b[/tex] to put into our function:

[tex]\frac{2\pi}{b}=2[/tex]

[tex]2\pi=2b[/tex]

[tex]\pi=b[/tex]

I skipped some of the basic algebra to shorten the solution, but we have found our b. Next, we'll get the amplitude of the wave by using the maximum and minimum height of the wheel. Remember, it's 4 meters at its lowest point, meaning its highest point is 54 meters in the air rather than 50. Using the formula for amplitude:

[tex]\frac{\max-\min}{2}[/tex]

[tex]\frac{54-4}{2}[/tex]

[tex]\frac{50}{2}=25=a[/tex]

Our vertical transformation is given by [tex]\min+a[/tex] or [tex]\max-a[/tex], which is the height of the center of the ferris wheel, [tex]4+25=29=d[/tex]

Because cosine starts at the minimum, [tex]c=0[/tex].

The last thing to point out is that a cosine wave starts at its maximum. For that reason, we need to flip the entire function by making the amplitude negative in our final equation. Therefore our equation ends up being:

[tex]h(t)=-25\cos(\pi t)+29[/tex]

Complete Question

If w'(t) is the rate of growth of a child in pounds per year, what does

[tex]\int\limits^{7}_{4} {w'(t)} \, dt[/tex]  represent?

a) The change in the child's weight (in pounds) between the ages of 4 and 7.

b) The change in the child's age (in years) between the ages of 4 and 7.

c) The child's weight at age 7.

d) The child's weight at age 4. The child's initial weight at birth.

Answer:

The correct option is  option a

Step-by-step explanation:

From the question we are told that

       [tex]w'(t)[/tex] represents the rate of growth of a child in   [tex]\frac{pounds}{year}[/tex]

So      [tex]{w'(t)} \, dt[/tex]  will be in  [tex]pounds[/tex]

Which then mean that this  [tex]\int\limits^{7}_{4} {w'(t)} \, dt[/tex]  the change in the weight of the child between the ages of  [tex]4 \to 7[/tex] years

7km/ 4km per hour = 1 3/4 hours

3/4 hour = 45 minutes

Total time = 1 hour and 45 minutes.

Answer:

x<3

Step-by-step explanation:

Answer:

[tex]\boxed{x\leq 3}[/tex]

Step-by-step explanation:

[tex]4x \leq 12[/tex]

[tex]\sf Divide \ both \ parts \ by \ 4.[/tex]

[tex]\displaystyle \frac{4x}{4} \leq \frac{12}{4}[/tex]

[tex]x\leq 3[/tex]

Answer:

$705.30,  $837.67,  $994.89 Respectively

Step-by-step explanation:

Given

P= $500

r= 3.5%= 3.5/100= 0.035

Applying the compound interest formula we have

[tex]A= P(1+r)^t[/tex]

where

A = final amount

P = initial principal balance

r = interest rate

t = number of time periods elapsed

[tex]A= 500(1+0.035)^1^0\\\ A= 500(1.035)^1^0\\\\ A= 500*1.410598\\\ A=705.299[/tex]

A= $705.30

[tex]A= 500(1+0.035)^1^5\\\ A= 500(1.035)^15\\\\ A= 500*1.67534\\\ A=837.67[/tex]

A= $837.67

Answer:

Range { 2,6,8}

Step-by-step explanation:

The domain is the input and the range is the output

Range { 2,6,8}

Answer:

2, 6, 8

Step-by-step explanation:

The range is the possible values of y, (x, y). So in this case, y could be 2, 6, or 8.

Answer:

$17

Step-by-step explanation:

data:

In statistics, the range is the difference between the highest value and the lowest value of the data set.

Highest value = $147

Lowest value = $130

Range = $17

Answer:

not rejecting the null hypothesis when it is false.

Step-by-step explanation:

Significance level or alpha level is the probability of rejecting the null hypothesis when null hypothesis is true. It is considered as a probability of making a wrong decision. It is a statistical test which determines probability of type I error. If the obtained probability is equal of less than critical probability value then reject the null hypothesis.

For making the error, it should not reject the null hypothesis at the time when it should be false.

It is the level where the probability of rejecting the null hypothesis at the time when the null hypothesis should be true. It is relevant for making the incorrect decision. Also, it is the statistical test that measured the probability of type 1 error.

Therefore, For making the error, it should not reject the null hypothesis at the time when it should be false.

Learn more about error here: https://brainly.com/question/18831983

Answer:

3¾

Step-by-step explanation:

Geometric sequence also known as geometric progression, can be said to be a sequence with a constant ratio between the terms.

Formula for geometric sequence:

[tex] a^n = a ( n-1 ) * r [/tex]

Given:

First term, a1 = 30

ratio, r = ½

Required:

Find the fourth term

Where, the first term, a¹ = 30

Second term: a² = 30 * ½ = 15

Third term: a³ = 15 * ½ = 7.5

Fourth term: a⁴ = 7.5 * ½ = 3.75 = 3¾

Therfore the fourth term of the geometric sequence is 3¾

Answer:

[tex]h'(1) = 23[/tex]

Step-by-step explanation:

Let be [tex]h(x) = (x^{2}+8)\cdot g(x)[/tex], where [tex]r(x) = x^{2} + 8[/tex]. If both [tex]r(x)[/tex] and [tex]g(x)[/tex] are differentiable, then both are also continuous for all x. The derivative for the product of functions is obtained:

[tex]h'(x) = r'(x) \cdot g(x) + r(x) \cdot g'(x)[/tex]

[tex]r'(x) = 2\cdot x[/tex]

[tex]h'(x) = 2\cdot x \cdot g(x) + (x^{2}+8)\cdot g'(x)[/tex]

Given that [tex]x = 1[/tex], [tex]g (1) = -2[/tex] and [tex]g'(1) = 3[/tex], the derivative of [tex]h(x)[/tex] evaluated in [tex]x = 1[/tex] is:

[tex]h'(1) = 2\cdot (1) \cdot (-2) + (1^{2}+8)\cdot (3)[/tex]

[tex]h'(1) = 23[/tex]

Answer:

a. 0.04

b. 0.9772

Step-by-step explanation:

Please check attachment for complete solution and step by step explanation

Answer:

x+2y=12-------(1)

x-2y=3---------(2)

Adding equations 1 and 2

we get

2x=18

x=9

Equation 1

9+2y=15

2y=15-9

2y=6

y=3

The solution of the given system is x=9, y=3

Step-by-step explanation

Answer:

X= 3

Y= 18

Each side of the triangle= 10 units

Step-by-step explanation:

LMN is equilateral so

LM = MN

3x+1= 4x-2

3x-4x = -2-1

-x = -3

X= 3

MP is the perpendicular bisector of line LN

so definitely angle lpm =90.

And lpm = 5y = 90

5y = 90

Y= 90/5

Y = 18°

For the side of the triangle

3x+1

But x= 3

3(3)+1

9+1

10

Each side of the triangle= 10 units

Answer:

The answers for:

Step-by-step explanation:

In order to find the value of expression, you have to apply gradient formula :

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

So for Question 1,

[tex]let \: (3,2) \: be \: (x1,y1) \\ let \: (4,j) \: be \: (x2,y2) \\ let \: m = 1[/tex]

[tex] \frac{j - 2}{4 - 3} = 1[/tex]

[tex] \frac{j - 2}{1} = 1[/tex]

[tex]j - 2 = 1[/tex]

[tex]j = 1 + 2 = 3[/tex]

Question 2,

[tex]let \: (5,0) \: be \: (x1,y1) \\ let \: (1,k) \: be \: (x2,y2) \\ let \: m = \frac{1}{2} [/tex]

[tex] \frac{k - 0}{1 - 5} = \frac{1}{2} [/tex]

[tex] \frac{k}{ - 4} = \frac{1}{2} [/tex]

[tex]k = \frac{1}{2} \times - 4 = - 2[/tex]

Question 3,

[tex]let \: (x,2) \: be \: (x1,y1) \\ let \: (3, - 4) \: be \: (x2,y2) \\ let \: m = 2[/tex]

[tex] \frac{ - 4 - 2}{3 - x} = 2[/tex]

[tex] \frac{ - 6}{3 - x } = 2[/tex]

[tex] - 6 = 2(3 - x)[/tex]

[tex] - 6 = 6 - 2x[/tex]

[tex] - 6 - 6 = - 2x[/tex]

[tex] - 2x = - 12[/tex]

[tex]x = - 12 \div - 2 = 6[/tex]

Question 4,

[tex]let \: (12, - 4) \: be \: (x1,y1) \\ let \: (r,2) \: be \: (x2,y2) \\ let \: m = - \frac{1}{2} [/tex]

[tex] \frac{2 - ( - 4)}{r - 12} = - \frac{1}{2} [/tex]

[tex] \frac{6}{r - 12} = - \frac{1}{2} [/tex]

[tex] - 1(r - 12) = 2(6)[/tex]

[tex] - r + 12 = 12[/tex]

[tex]r = (12 - 12) \div - 1 = 0[/tex]

Answer:

Y =4

Step-by-step explanation:

Hope it helps

Answer:

200,000

Step-by-step explanation:

The current population: 50,000

Doubling time:70

Population after 280 years=?

280/70=4

50,000*4=200,000

Hope this helps ;) ❤❤❤

Answer: 800,000

Step-by-step explanation: 50,000x2=100,000. That is after 70 years. 100,000x2=200,000. This is after 140 years. 200,000x2=400,000. This is after 210 years. 400,000x2=800,000. This is after 280 years.

Answer:

1650 yards

Step-by-step explanation:

Here, we have to find the minimal spanning tree required to span the neighborhood.

We start from house 1. The minimum distance from house 1 to house 2 is 250 yards. Now from 2, we can go to house 3,4 or 5 all having the equal distances  of 400 yard from house 2. So we go to from house 2 to house 3. Now from 3, we go to house 5 which is at a minimum  distance of 350 yards. Now from house 5 we go to house 4 with 300 yards and then from house 4 we go to house 6 which is at 350 yards from 4.

Thus the network is complete and the total distance covered is

= 250 + 400 + 350 + 300 + 350

= 1650 yards

This is the minimum distance by which the neighborhood can be wired.

And the tree is

[tex]$1\rightarrow2\rightarrow3\rightarrow5\rightarrow4\rightarrow6$[/tex]    

Answer:

a) Mean = 4.55

   Median = 4.7

   Mode = 1.9

b) S =  2.3952

   CV = 52.64 %

   Range = 6.3

c) Yes, since the average and median values are both over "acceptable" ranges.

Step-by-step explanation:

Explanation is provided in the attached document.

Answer:

x = {9, -3}

Step-by-step explanation:

Or it can be shown as:

Answer:

Step-by-step explanation:

32,256,2048,16384,......,2⁵⁰

32=2⁵

256=2⁸

2048=2¹¹

16384=2¹⁴

2⁵, 2⁸, 2¹¹,2¹⁴, ….,2⁵⁰

[tex]t_{1}[/tex]=2⁵; [tex]t_{2}[/tex]=2⁸

r=2⁸:2⁵=2³

[tex]t_{n}[/tex]=[tex]t_{1}[/tex]*[tex]r^{n-1}[/tex]

2⁵*[tex]2^{3(n-1)}[/tex] =2⁵⁰

5+3(n-1)=50

3n-3=45

3n=48

n=48:3

n=16

So, 16 terms

Answer:

Since we are talking annual interest and, I assume a time period of 1 year:

The interest earned is the sum of the interest earned on the two loans separately

Let x = amount loaned at 14%

18,500-x = amount loaned at 12%

I = prt

p = x and 18500-x

r = 0.14 and 0.12

t = 1

2390 = 0.14x + 0.1(18500-x)

2390 = .14x + 1850 - 0.1x

x = 13500

x = $13,500 loaned at 14%

18500-x = $5,000 loaned at 12%

Answer:

$8,500 was loaned at 14%, and

$10,000 was loaned at 12%.

Step-by-step explanation:

Total loan: $18,500.

Part at 14%

Part at 12%

Let the part at 14% = x.

Let the part at 12% = y.

Equation of amount of loan:

x + y = 18500

x amount at 14% earns 14% of x = 0.14x interest.

y amount at 12% earns 12% of y = 0.12y interest.

Equation of interest charged:

0.14x + 0.12y = 2390

We have a system of equations.

x + y = 18500

0.14x + 0.12y = 2390

Multiply both sides of the first equation by -0.12. Write the second equation below it, and add the equations.

     -0.12x - 0.12y = -2220

(+)    0.14x + 0.12x = 2390

-------------------------------------

      0.02x             = 170

x = 170/0.02

x = 8500

x + y = 18,500

8500 + y = 18,500

y = 10,000

Answer:

$8,500 was loaned at 14%, and

$10,000 was loaned at 12%.

Answer:

1) y=⅚x -2⅓

2) y=8/3x -5

Step-by-step explanation:

Point-slope form:

y=mx+c, where m is the gradient and c is the y-intercept.

Parallel lines have the same gradient.

Gradient of given line= [tex] \frac{5}{6} [/tex]

Thus, m=⅚

Susbt. m=⅚ into the equation,

y= ⅚x +c

Since the line passes through the point (4, 1), (4, 1) must satisfy the equation. Thus, substitute (4, 1) into the equation to find c.

When x=4, y=1,

1= ⅚(4) +c

[tex]1 = \frac{20}{6} + c \\ c = 1 - \frac{20}{6} \\ c = 1 - 3 \frac{1}{3} \\ c = - 2 \frac{1}{3} [/tex]

Thus the equation of the line is [tex]y = \frac{5}{6} x - 2 \frac{1}{3} [/tex].

The gradients of perpendicular lines= -1.

Gradient of given line= -⅜

-⅜(gradient of line)= -1

gradient of line

= -1 ÷ (-⅜)

= -1 ×(-8/3)

= [tex] \frac{8}{3} [/tex]

[tex]y = \frac{8}{3} x + c[/tex]

When x=3, y=3,

[tex]3 = \frac{8}{3} (3) + c \\ 3 = 8 + c \\ c = 3 - 8 \\ c = - 5[/tex]

Thus the equation of the line is [tex]y = \frac{8}{3} x - 5[/tex].

Answer:

6

Step-by-step explanation:

10 - 4 = 6

16 - 10 = 6

22 - 16 = 6

Answer:6

Step-by-step explanation:

1) 10-4=6

2) 16-10=6

3) 22-16=6

Answer:

Step-by-step explanation:

cot (x)=2/3

we know csc^2(x)-cot^2(x)=1

csc^2(x)=1+cot^2(x)=1+4/9=13/9

csc (x)=±√13/3

Answer:

The length is 5.5 inches

Step-by-step explanation:

The area of a rectangle is

A = lw

66 =  l * 12

Divide each side by 12

66/12 = l

5.5 = l

The length is 5.5 inches

Answer:

5.5 inches

Step-by-step explanation:

Length times width is the area so

12*width =66

same as

66/12=5.5 inches

Ask more questions in the comments if you are still confused.

Answer:

1). (0, 1)

2). (1, a)

3). Above

Step-by-step explanation:

This question is not complete; here is the complete question.

The graph of an exponential function of the form y = f(x) = [tex]a^{x}[/tex] passes through the points 1).               and 2).              . The graph lies 3).             x-axis.

1). (0.a), (0,1), (0,2), (0,-1)

2). (1,0), (1,1), (1,a), (1,-2)

3). (above), (below), (on the)

Given exponential function is f(x) = [tex]a^{x}[/tex]

1). For x = 0,

  f(0) = [tex]a^{0}[/tex] = 1

  Therefore, the given exponential function passes through a point (0, 1).

2). For x = 1,

  f(1) = [tex]a^{1}[/tex]

  f(1) = a

  Therefore, graph of the exponential function passes through (1, a)

3).For y = 0

  0 = [tex]a^{x}[/tex]

  But for any value of 'x', f(x) will never be zero. Therefore, there is no x-intercept.

  The graph lies above the x-axis.

Answer: new Q = (-4, 5)

Step-by-step explanation:

Given: Q = (-4, 1)

Reflected across y = -2:    

Q is 3 units above y = -2 so a reflection is 3 units below y = -2 --> Q' = (-4, -5)

Reflected across x-axis:    

Q' is 5 units below x-axis so a reflection is 5 units above x-axis --> Q'' = (-4, 5)

Answer:

Equation: S(W) = 60W + 350

After 19 weeks, total accumulated = S(19) = 1490

Step-by-step explanation:

The interest rate is not indicated, so cannot take that into account.

Each week, he adds 60$, with initial value of 350$

So the equation is

S(W) = 60W + 350

for W = 19,

S = 60*19 + 350

S(19) = 1490

Answer:

$1490

Step-by-step explanation: