A boat traveled is 30 miles up a river in 5 hours. What was the average rate of travel, in miles per hour, of the boat

The Apple, Inc. sales manager for the Chicago West Suburban region is disturbed about the large number of complaints her office

ankoles [38]

Answer:

0.6856

Step-by-step explanation:

$\text{The missing part of the question states that we should Note: that N(108,20) model to } \\ \\ \text{ } \text{approximate the distribution of weekly complaints).]}$

Now; assuming X = no of complaints received in a week

Required:

To find P(77 < X < 120)

Using a Gaussian Normal Distribution ( $\mu =$ 108, $\sigma$ = 20)

Using Z scores:

$Z = \dfrac{77-108}{20} \\\\ Z = -\dfrac{35}{20} \\ \\ Z -1.75$

As a result X = 77 for N(108,20) is approximately equal to to Z = -1.75 for N(0,1)

SO;

$Z = \dfrac{120-108}{20} \\ \\ Z = \dfrac{12}{20}\\ \\ Z = 0.6$

Here; X = 77 for a N(108,20) is same to Z = 0.6 for N(0,1)

Now, to determine:

P(-1.75 < Z < 0.6) = P(Z < 0.6) - P( Z < - 1.75)

From the standard normal Z-table:

P(-1.75 < Z < 0.6) = 0.7257 - 0.0401

P(-1.75 < Z < 0.6) = 0.6856

3 0

3 years ago

1. Consider this dilation in this question for A and B

Readme [11.4K]

Answer:

a) enlargement

b) scale factor is 2

Step-by-step explanation:

As we can see, we went from the block to the red figure

a) Since the red figure is bigger, then what we have is an enlargement of the original figure

b) As we can see, the coordinates of the red is two times the value of the coordinates of the black

So, we can conclude that what we have as a scale factor is 2

3 0

3 years ago

Let f(x) = 4x+3 and g(x) = -2x+5

brilliants [131]

f(x) = 4x + 3
g(x) = -2x + 5

(f · g)(5) = (4(5) + 3)(-2(5) + 5)
(f · g)(5) = (20 + 3)(-10 + 5)
(f · g)(5) = (23)(-5)
(f · g)(5) = -115

3 0

3 years ago

Lauren invests money in an accout paying simple interest.She invests $50 and no money is added or removed from investments.After

xxMikexx [17]

Answer:

1%

Step-by-step explanation:

\text{\color{blue}{100\%} represents the \color{blue}{starting balance}: \color{blue}{\$50}.}

100% represents the starting balance: $50.

Method 1

Express the ending balance as a percentage of the starting balance:

\frac{\color{darkviolet}{\$50.50}}{\color{blue}{\$50}}=

$50

$50.50

=

\,\,1.01

1.01

1.01\times100=

1.01×100=

\,\,\color{darkviolet}{101\%}

101%

\text{Subtract the starting \color{blue}{100\%} to get the \color{green}{percent interest}:}

Subtract the starting 100% to get the percent interest:

\color{darkviolet}{101\%}-\color{blue}{100\%}=

101%−100%=

\,\,\boxed{\color{green}{1\%}}

1%

8 0

3 years ago

The price of products may increase due to inflation and decrease due to depreciation. Marco is studying the change in the price

likoan [24]

Answer:

A) 3%

B) Product A

Step-by-step explanation:

Exponential Function

General form of an exponential function: $y=ab^x$

where:

a is the initial value (y-intercept)
b is the base (growth/decay factor) in decimal form
x is the independent variable
y is the dependent variable

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

Part A

Product A

Assuming the function for Product A is exponential:

$f(x) = 0.69(1.03)^x$

The base (b) is 1.03. As b > 1 then it is an increasing function.

To calculate the percentage increase/decrease, subtract 1 from the base:

⇒ 1.03 - 1 = 0.03 = 3%

Therefore, product A is increasing by 3% each year.

Part B

$\sf percentage\:change=\dfrac{final\:value-initial\:value}{initial\:value} \times 100$

To calculate the percentage change in Product B, use the percentage change formula with two consecutive values of f(t) from the given table:

$\implies \sf percentage\:change=\dfrac{10201-10100}{10100}\times 100=1\%$

Check using different two consecutive values of f(t):

$\implies \sf percentage\:change=\dfrac{10303.01-10201}{10201}\times 100=1\%$

Therefore, as 3% > 1%, Product A recorded a greater percentage change in price over the previous year.

Although the question has not asked, we can use the given information to easily create an exponential function for Product B.

Given:

a = 10,100
b = 1.01
n = t - 1 (as the initial value is for t = 1 not t = 0)

$\implies f(t) = 10100(1.01)^{t-1}$

To check this, substitute the values of t for 1 through 4 into the found function:

$\implies f(1) = 10100(1.01)^{1-1}=10100$

$\implies f(2) = 10100(1.01)^{2-1}=10201$

$\implies f(3) = 10100(1.01)^{3-1}=10303.01$

$\implies f(4) = 10100(1.01)^{4-1}=10406.04$

As these values match the values in the given table, this confirms that the found function for Product B is correct and that Product B increases by 1% per year.

4 0

2 years ago