X
38°
750
x= -
degrees

The amount of money in the account at the end of the period would be $1345.58.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

Given is that an initial investment of $480 is appreciated for 7 years in an account that earns 15% interest, compounded quarterly.

We can write the compound interest as -

[tex]$A = P(1 + \frac{r}{n})^{nt}[/tex]

A = 480(1 + 0.15/4)^(4 x 1)

A = 480 + 865.58

A = 1345.58

Therefore, the amount of money in the account at the end of the period would be $1345.58.

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Part (a)

Answers:  

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Work Shown:

Refer to figure 1 in the screenshot attached below.

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Part (b)

Answers:  

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Work Shown:

Refer to figure 2 in the screenshot attached below.

Correction:

The derivative for h should be

[tex]h(x) = f(x)*(x-1)^{-1}\\\\h'(x) = \frac{d}{dx}[f(x)*(x-1)^{-1}]\\\\h'(x) = \frac{d}{dx}[f(x)]*(x-1)^{-1}+f(x)*\frac{d}{dx}[(x-1)^{-1}]\\\\h'(x) = f'(x)*(x-1)^{-1}+f(x)*(-1(x-1)^{-2})\\\\[/tex]

I had a -2 in there instead of -1 as the coefficient.

You should find that h ' (2) = -2

That would then lead to y = -2x+9

The steps shown in figure 2 are effectively the same, just with different numbers of course.

Answer:

a. Sample  = 1664 adults

b. Parameter= % of poll based on telephone interview

c. Statistic = 66%

d. Population = American adult population

e. Confidence level= 95%

f. Margin of error = +/- 3%

g. Sampling Error

Step-by-step explanation:

The missing part of the question is

The quotation below describes an opinion poll conducted by CBS News and the New York Times. Oneof the questions asked was "Do you favor an amendment to the Constitution that would permitorganized prayer in public schools?" Sixty-six percent answered, "Yes."

a. Sample  = 1664 adults

The number included in the sample

b. Parameter= % of poll based on telephone interviews

The sample chosen on the bases

c. Statistic = 66%

The statistic obtained after applying the formula etc.

d. Population = American adult population

The sample is chosen from the population

e. Confidence level= 95%

f. Margin of error = +/- 3%

g. Sampling Error

It is a sampling error because the areas omitted had a very large religious population and the results were biased.

The sample was not chosen from the areas omitted.

Answer:

Lisa's percentage of error regarding the weight of the dog was 57.14%.

Step-by-step explanation:

Given that the German Shepard actually weighs 28 pounds, but Lisa thought the dog weighed 44 pounds, to determine what is the percent error the following calculation must be performed:

28 = 100

44 = X

(44 x 100) / 28 = X

4,400 / 28 = X

157.14 = X

157.14 - 100 = 57.14

Thus, Lisa's percentage of error regarding the weight of the dog was 57.14%.

Answer:

180 minutes to cook 9lb turkey.

Step-by-step explanation:

Let the time taken to cook a 9lb turkey be x.

Using proportions,

6/120 = 9/x

6x = 120 x 9

6x = 1080

x = 1080/6

x = 180

Question

If a 6 lb turkey takes 120 minutes to cook, how long would a 9 lb. Turkey take to cook?

Solution

time taken by 6 lb. Turkey to cook = 120 minutes

time taken by 1 lb. Turkey to cook = (120/6 = 20) minutes

time taken by 9 lb. Turkey to cook = ( 20×9= 180 ) minutes

Answer:

Step-by-step explanation:

making all terms have a common denominator of 12

(3(2x-3)+2(2x-5))/12=6(1)/12 now the 12s cancel out

3(2x-3)+2(2x-5)=6

6x-9+4x-10=6

10x-19=6

10x=25

x=2.5

Answer:

depends on the ammount

Step-by-step explanation:

Answer:

The Binomial model is inappropriate because the Trials are independent of each other

Step-by-step explanation:

Given data :

probability of a company started by a person  failing with 2 years = 0.3

14 start-ups ( 98 people ) are followed for 2 years

The probability that at least 42 of these 98 people will fail in 2 years

Reason why the Binomial model is inappropriate for finding the probability that at least 42 of these 98 people will fail

The Binomial model is inappropriate because the Trials are independent of each other

Step-by-step explanation:

Given

GPA = NO + B1Study + B2work + B3leisure + B4sleep + u

1. No it makes no sense. There is an intercorellation between these explanatory variables. Changing study while holding the rest variables constant or fixed would not make sense. If study us changed then one or more of the other predictors should be changed so that they can still be equal to 168

2. Study is a perfect linear function of work, leisure and sleep. There is the problem of multicollinearity among these independent variables. One assumption of the MLR is no multicollinearity.

3. To reformulate model, you have to drop the variable that is having the issue. Let's say that leisure is dropped from the model. After this the assumption is satisfied.

GPA = b0 + B1Study + b2sleep + b3work + u

[tex](2^{\frac{1}{2}})^n=\frac{2^x}{2^{3y}}\\2^{\frac{1}{2}n}=2^{x-3y}\\\frac{n}{2}=x-3y\\n=2x-6y[/tex]

Answer:

8 liters

Step-by-step explanation:

3x+2x+4x=9x

36/9=x

x=4

2x= smallest bucket= 8

Answer:

10, 8, -5. Pls tell me if wrong i will retry. Im doing this mentally to be fast.

Step-by-step explanation:

A. 12 - |1 + -3 | = 12 - 2 = 10

B. 6 - -2 = 8

C. 18 -3/-3 = 15/-3 = -5

Answer:

14,8,-5

Step-by-step explanation:

1. 12-{1+(-3)}

12-{1(-3)} 1-3=-2

12-(-2) -×-=+

12+2

14

2. 6-{1+(-3)}

6-(1-3)

6-(-2)

6+2

8

3. 3×6+(-3)

________

-3

18-3

______

-3

15

_____

-3

=-5

Answer:

y = (1/2)x + 2

Step-by-step explanation:

it is a straight line so it will be in the form of y = mx + c

m = gradient, c = y intercept

Reading from graph it cuts the y-axis at 2,

so c = 2

to find gradient we can pick any 2 points on the line,

e.g (0,2) and (10,7)

gradient = (y1 - y2) / (x1 - x2) = (7 - 2) / (10 - 0)

= 1/2

so the equation is y = (1/2)x + 2

Using slope intercept formula, the equation of the blue line

y = (1/2)x + 2.

The slope intercept form is one of the form to represent" equation of the straight iine".

According to the question,

The graph intercept the y-axis at 2.

Slope intercept formula, y = mx + c where m = slope of the line, c = y- intercept of the line,  x, y as variable.

From given, y-intercept, c = 2.

To find slope of the line take any two points on the line (0,2) and (10,7).

Formula to find slope of the line m = (y₁ -y₂)/(x₁ - x₂).

m = (2-7)/(0-10)=  [tex]\frac{1}{2}[/tex]

Hence, the equation of the blue line  y = (1/2)x + 2.

Learn more about Slope intercept form here

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Answer:

Z= -2.83

Brainliest please if you dont mind

Answer:

36c2-81

Step-by-step explanation:

It's a difference of squares so you Florida it (FL) do first and last to get 36c2-81

Step-by-step explanation:

step 1. a diagram is important and can be uploaded. you will get a quicker answer with a diagram

step 2. triangle RST is a right triangle so we can use trigonometry to find <S

step 3. the adjacent side of <S is ST and the hypotenuse is RS so we will use cos

step 4. cosS = adj/hyp = ST/RS = 2.7/4.9

step 5. <S = 56.6° using inverse cos.

Answer:

42.43

Step-by-step explanation:

This is because you had to divbide by 3

Answer:

24

Step-by-step explanation:

Answer:

ur lame asl

Step-by-step explanation:

Answer:

5). x = 11.9°

6). x = 27.2°

Step-by-step explanation:

5). By applying cosine rule in the given triangle,

   cos(32)° = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

   cos(32)° = [tex]\frac{x}{14}[/tex]

    x = 14cos(32)°  

    x = 11.87

    x ≈ 11.9°

6). By applying sine rule in the given triangle,

    sin(54°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

    sin(54°) = [tex]\frac{22}{x}[/tex]

     x = [tex]\frac{22}{\text{sin(54)}}[/tex]

     x = 27.19°

     x ≈ 27.2°

Answer:

(a) See attachment for table

(b) [tex]Atmost\ 6 = 21.667\%[/tex]

(c) [tex]Less\ than\ 6 = 21.667\%[/tex]

(d) [tex]At\ least\ 6 = 78.333\%[/tex]

Step-by-step explanation:

Given

The data (in the question)

Solving (a): Frequency and Relative frequencies of each data

The range of the data is 0 to 8. So the frequency of each is the number of times each of 0 - 8 occurs.

This is tabulated below:

[tex]\begin{array}{ccc}x & {Frequency} & {Relative\ Frequency} & {0} & {7} & {11.667\%} &{1}& {13} & {21.667\%} & {2} & {13} & {21.667\%} & {3} & {14} &{23.333\%} & {4} & {5} & {8.333\%} & {5} &{3} &{5.000\%} &{6} &{2} & {3.333\%} & {7} & {2} & {3.333\%} & {8} & {1} & {1.667\%} \ \end{array}[/tex]

[tex]Total\ \ \ 60[/tex]

The relative frequency is calculated as:

[tex]Relative\ Frequency = \frac{Frequency}{Total\ Frequency} * 100\%[/tex]

For instance: When x = 0:

[tex]Relative\ Frequency = \frac{7}{60} * 100\%[/tex]

[tex]Relative\ Frequency = \frac{700}{60} * \%[/tex]

[tex]Relative\ Frequency = 11.667 \%[/tex]

Solving (b): Proportion that have at most 6.

Here, we consider frequencies of 0 to 6.

This is represented as thus:

[tex]\begin{array}{ccc}x & {Frequency} & {Relative\ Frequency} & {4} & {5} & {8.333\%} & {5} &{3} &{5.000\%} &{6} &{2} & {3.333\%} & {7} & {2} & {3.333\%} & {8} & {1} & {1.667\%} \ \end{array}[/tex]

Add up the relative frequencies to get the proportion

[tex]Atmost\ 6 = 8.333\% + 5.000\% + 3.333\% + 3.333\% + 1.667\%[/tex]

[tex]Atmost\ 6 = 21.667\%[/tex]

Solving (c): Proportion that have at fewer than 6.

Here, we consider frequencies of 0 to 5.

This is represented as thus:

[tex]\begin{array}{ccc}x & {Frequency} & {Relative\ Frequency} & {4} & {5} & {8.333\%} & {5} &{3} &{5.000\%} &{6} &{2} & {3.333\%} & {7} & {2} & {3.333\%} & {8} & {1} & {1.667\%} \ \end{array}[/tex]

Add up the relative frequencies to get the proportion

[tex]Less\ than\ 6 = 8.333\% + 5.000\% + 3.333\% + 3.333\% + 1.667\%[/tex]

[tex]Less\ than\ 6 = 21.667\%[/tex]

Solving (d): Proportion that have at least 6.

Here, we make use of the complement rule:

[tex]At\ least\ 6 = 100\% - Less\ than\ 6[/tex]

[tex]At\ least\ 6 = 100\% - 21.667\%[/tex]

[tex]At\ least\ 6 = 78.333\%[/tex]

-9-(-7)

-9--7

-9+7

7-9

-2

---

hope it helps

Answer:

The given data does not support the submission that there has been a change in the mean arrival times on Southwest

Step-by-step explanation:

The known mean late arrival time, μ = 72.3

The known standard deviation in late arrival time, σ = 9.8 minutes

The number of flights in the sample, n = 47

The sample mean late arrival time, [tex]\overline x[/tex] = 70.7

The sample standard deviation  late arrival time, s = 7.1

Using a significance level of 0.01

The null hypothesis is, H₀ ; μ = 70.7

The alternative hypothesis is, Hₐ ; μ ≠ 70.7

The test statistic is given as follows;

[tex]z=\dfrac{\bar{x}-\mu }{\dfrac{\sigma }{\sqrt{n}}}[/tex]

[tex]z=\dfrac{70.7-72.3 }{\dfrac{9.8 }{\sqrt{47}}} \approx -1.119290547[/tex]

∴ z ≈ -1.12

p-value = 2 × P(z < -1.12)  = 2 × 0.13136 = 0.26272

Given that the p-value of 0.26272 is larger than the significance level, 0.05, we fail to reject the null hypothesis

Therefore, there is not enough statistical evidence to show that there has been a change in the mean arrival times on Southwest

Answer:

Factors of 16: 1, 2, 4, 8, 16

Factors of 56: 1, 2 , 4, 7, 8, 14, 28, 56

GCF: 8

Step-by-step explanation:

Answer:

[tex]\theta=41.18^{\circ}[/tex]

Step-by-step explanation:

Given that,

The height of the tree, h = 14 ft

The height of the shadow, b = 16 ft

We need to find the angle of elevation of the sun from the ground. Let the angle be θ. We can use trigonometry to find it. So,

[tex]\tan\theta=\dfrac{P}{B}\\\\\tan\theta=\dfrac{14}{16}\\\\\theta=41.18^{\circ}[/tex]

So, the required angle of elevation of the sun is equal to [tex]41.18^{\circ}[/tex].

Answer:

N=433.31

Step-by-step explanation:

720(cos(53))=(n/720)720

n=720cos(53)

n=433.306

n=433.31

Hope this helps i aced this unit

Answer:

is two more than the row before

Step-by-step explanation:

i hope i help\

Answer:

Profit, increase, and income are all examples of words that mean positive. A negative number is a number that is less than zero. It is always written with a - symbol in front of it. A loss is written with a negative number

Hope this helps

Answer:

[tex]1. \to B:5...\\ 2.. \to C:10.\\3. \to D:785[/tex]

y

Answer:

it's less than

Step-by-step explanation:

12/8 simplified is 3/2

11/6 cannot be further simplified

3/2<11/6

Answer:

This is your answer ☺️☺️☺️