Find the solution of the differential equation that satisfies the given initial condition.

Answer:

The p-value of the test is 0.0007 < 0.01, which means that the class demonstrates that the percentage was higher in Owensboro, KY.

The possible proportion of patrons that do borrow books from the Owensboro Library is 0.82.

Step-by-step explanation:

For Americans using library services, the American Library Association claims that at most 67% of patrons borrow books. Test if the proportion is higher in Owensboro, KY.

At the null hypothesis, we test if the proportion is of at most 0.67, that is:

[tex]H_0: p \leq 0.67[/tex]

At the alternative hypothesis, we test if the proportion is of more than 0.67, that is:

[tex]H_1: p > 0.67[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.67 is tested at the null hypothesis:

This means that [tex]\mu = 0.67, \sigma = \sqrt{0.67*0.33}[/tex]

The class randomly selected 100 patrons and found that 82 borrowed books.

This means that [tex]n = 100, X = \frac{82}{100} = 0.82[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.82 - 0.67}{\frac{\sqrt{0.67*0.33}}{\sqrt{100}}}[/tex]

[tex]z = 3.19[/tex]

P-value of the test and decision:

The p-value of the test is the probability of a finding a sample proportion of 0.82 or above, which is 1 subtracted by the p-value of z = 3.19.

Looking at the z-table, z = 3.19 has a p-value of 0.9993.

1 - 0.9993 = 0.0007

The p-value of the test is 0.0007 < 0.01, which means that the class demonstrates that the percentage was higher in Owensboro, KY.

What is the possible proportion of patrons that do borrow books from the Owensboro Library?

The sample proportion of 0.82.

Answer:

cannot understand the language man

but please follow

Answer:

34.5p-2.75

Step-by-step explanation:

First add -0.5p and 12p together which is 11.5p, then add 23p with 11.5p which is 34.5p And -2.75 remains the same

So the answer is 34.5p-2.75

Answer:

34.5p-2.75

Step-by-step explanation:

-0.5p+12p-2.75+23p=34.5p-2.75

Answer:

1320 m^2

Step-by-step explanation:

area of ground = π r ^2

= (22/7) × (137/2)^2

= 14,747.0714286 m^2

area of ground and path

=( 22/7)(143/2)^2

= 16,067.0714286 m^2

area of path

=16,067.0714286 -14,747.0714286

= 1320 m^2

note :

r = radius = diameter /2

area of a circle = π r^2

diameter of circle created with path and ground = 137 + 2 × width of path

= 137 + 2× 3 = 143 m

The best option for Kelsie to create a SMART goal is b) "I will get to work before 9 A.M. every day this month."

Option B captures the essence of a smart goal.  A smart goal has the following characteristics: specific, measurable, achievable or attainable, realistic or relevant, and time-bound.

1. Specific: A smart goal like option B is well-defined, clear, and unambiguous.

2. Measurable: A smart goal sets specific criteria that measure Kelsie's progress toward the accomplishment of her goal.  For example, any day that she does not get to work before 9 a.m. she knows that she does not achieve her work arrival goal for that day.

3. Achievable: Kelsie's goal becomes attainable and possible to achieve because there is a set time for her to arrive at her work.

4. Realistic: Kelsie's goal, which she set for this month, is within her reach.  It is realistic, and relevant to her purpose.

5. Time-bound:  Kelsie has set a clearly defined timeline, which creates the needed urgency for her to realize it.  It includes a starting date and a target date, which will encourage her to realize it.

Thus, option B is the correct option that meets the criteria of a SMART goal unlike options A, C, and D, which are ambiguous, unrealistic, and not time-bound.

Learn more about SMART goals from www.brainly.com/question/4939309

Answer:

196

Step-by-step explanation:

We will use the formula:

Surface Area of A / Surface area of B = (Height of A /Height of B)^2

49/S2 = (4/8)^2

49/S2 = 1/4

S2 = 196

Answred by Gauthmath

Answer:

7x sqrt(2) - 2 sqrt(2)

Step-by-step explanation:

5x sqrt(2) - 2 sqrt(2) + 2x sqrt(2)

Combine like terms

5x sqrt(2) + 2x sqrt(2)    - 2 sqrt(2)

7x sqrt(2) - 2 sqrt(2)

Hi there!

[tex]\large\boxed{(x -3)(x + 2)(x + 1)}[/tex]

We can use long division to find the other roots of p(x).

We know that x + 1 is a factor, so:

Set up:

Find how many times that the first term in the divisor goes into the first of the dividend. Subtract from like terms.

         x² - x - 6

x + 1 | x³ + 0x² - 7x - 6

         x³ + x²

         0 - x²     - 7x

            - x²      - x

             0        - 6x - 6

                        -6x - 6

                          0     0

Therefore, x² - x - 6 is another factor. We can factor this further:

Find two numbers that add up to -1 and multiply into -6. We get:

-3, 2

(x - 3)(x + 2)

The entire polynomial factored is:

(x -3)(x + 2)(x + 1)

Given:

Consider the below figure attached with this question.

The value in the given figure are:

[tex]a=0.2094539899[/tex]

[tex]b=2.507467975[/tex]

[tex]r^2=0.9435996398[/tex]

[tex]r=0.9713905701[/tex]

To find:

The exponential regression equation for the given values (Rounded to three decimal places).

Solution:

The general form of exponential regression equation is:

[tex]y=a\cdot b^x[/tex]          ...(i)

Where, a is the initial value and b is the growth/decay factor.

The given values are:

[tex]a=0.2094539899[/tex]

[tex]b=2.507467975[/tex]

Round these numbers to three decimal places.

[tex]a\approx 0.209[/tex]

[tex]b\approx 2.507[/tex]

Putting [tex]a=0.209, b=2.507[/tex] in (i) to find the exponential regression equation.

[tex]\hat{y}=0.209\cdot 2.507^x[/tex]

Hence, the correct option is C.

d=6ft

According to formula A=πr²

first we need 'r'

Hence,

as, r=d/2

r=6ft/2

r=3ft

A=πr²

A=3.14(3ft)²

A=3.14×9ft²

A=28.26ft²

Answer:

Answer:

Below.

Step-by-step explanation:

IQR is the same

Number of data points is the same.

Mode - can't tell

Range - different

First quartile - same

Median - different.

Answer:

0.81859

Step-by-step explanation:

Given that the length of recovery days for patients with knee surgery is normally distributed with :

Mean, μ = 123 days

Standard deviation, σ = 1 day

The proportion of patients that will recover with 121 and 124 days :

We obtain the Probability of Z score :

Z = (x - μ) / σ

P(Z < (x - μ) / σ) < Z < P(Z < (x - μ) / σ)

P(Z < (121 - 123) / 1) < Z < P(Z < (124 - 123) / 1)

P(Z < - 2) < Z < P(Z < 1)

Using the normal distribution table :

P(Z < 1) - P(Z < - 2)

0.84134 - 0.02275

= 0.81859

Answer:

Step-by-step explanation:

a + ab/100

Answer:

B.) 317

Step-by-step explanation:

100/2 = 50

124/2 = 62

180/2 = 90

634/2 = 317

Answer:

The answer is (B) 1/2=12

Answer:

all answer are in given solution

9.03 divided by 899.8 is closest to a.0.01

Answer: a) 0.01

Step-by-step explanation:

Answer: i) [tex]\frac{1}{3}[/tex]

              ii) [tex]\frac{5}{9}[/tex]

Step-by-step explanation:

Total length of film = 45 mins

Fraction of time left after 15 mins = [tex]\frac{15}{45}[/tex]

                                                       = [tex]\frac{1}{3}[/tex]

Fraction of time left after 25 mins = [tex]\frac{25}{45}[/tex]

                                                        = [tex]\frac{5}{9}[/tex]

Answer:

(-8/7 ; 5/7)

Step-by-step explanation:

5t + 1/2s = 3 - - - (1)

3t - 6s = 9 - - - - - (2)

Multiply (1) by 12 and (2) by 1

Add the result to eliminate s

60t + 6s = 36

3t - 6s = 9

____________

63t = 45

t = 45 / 63

t = 5/7

Put t = 5/7 in either (1) or (2) to obtain the value of s

3(5/7) - 6s = 9

15/7 - 6s = 9

-6s = 9 - 15/7

-6s = (63 - 15)/7

-6s = 48/7

s = 48/7 * - 1/6

s = - 8/7

Answer:

6

Step-by-step explanation:

đạo hàm cấp 2 của f(x) rồi thế 0 vào

Answer:

The correct answer is:

Portfolio A = $107,000

Portfolio B = $36,000

Portfolio C = $32,000

Step-by-step explanation:

According to the question,

[tex]A+B+C=175000[/tex]...(1)

[tex]A+B = 143000[/tex]...(2)

[tex]A+C=139000[/tex]...(3)

Now,

From (1) and (2), we get

⇒ [tex]Portfolio \ C = (1)-(2)[/tex]

                        [tex]=175000-143000[/tex]

                        [tex]=32000[/tex]...(4)

From (1) and (3), we get

⇒ [tex]Portfolio \ B =(1)-(3)[/tex]

                        [tex]=175000-139000[/tex]

                        [tex]=36000[/tex]...(5)

From (1), (4) and (5), we get

⇒ [tex]Portfolio \ A = (1)-(4+5)[/tex]

                        [tex]=175000-(36000+32000)[/tex]

                        [tex]=175000-68000[/tex]

                        [tex]=107000[/tex]  

Thus the above is the correct answer.

Answer:

Pvalue

Step-by-step explanation:

The Pvalue measure which takes up a value in the range 0 - 1 is a statistical measure used on hypothesis testing to measure the likelihood of obtaining result atleast as extreme as the outcome of the statistical hypothesis test, The Pvalue is used in hypothesis testing to make a case for the alternative hypothesis, which involves being compared with the α - value.

Lower p values favors the adoption of alternative depending on how extreme th α-value is. The Pvalue is dependent on the value if the test statistic.

Answer:

b

Step-by-step explanation:

b intercepts the y axis

Multiplying block matrices works just like multiplication between regular matrices, provided that component matrices have the right sizes.

[tex]\begin{bmatrix}\mathbf I&\mathbf 0\\\mathbf K&\mathbf I\end{bmatrix}\begin{bmatrix}\mathbf W&\mathbf X\\\mathbf Y&\mathbf Z\end{bmatrix} = \begin{bmatrix}\mathbf{IW}+\mathbf{0Y}&\mathbf{IX}+\mathbf{0Z}\\\mathbf{KW}+\mathbf{IY}&\mathbf{KX}+\mathbf{IZ}\end{bmatrix}[/tex]

[tex]\begin{bmatrix}\mathbf I&\mathbf 0\\\mathbf K&\mathbf I\end{bmatrix}\begin{bmatrix}\mathbf W&\mathbf X\\\mathbf Y&\mathbf Z\end{bmatrix} = \begin{bmatrix}\mathbf W+\mathbf 0&\mathbf X+\mathbf 0\\\mathbf{KW}+\mathbf Y&\mathbf{KX}+\mathbf Z\end{bmatrix}[/tex]

[tex]\begin{bmatrix}\mathbf I&\mathbf 0\\\mathbf K&\mathbf I\end{bmatrix}\begin{bmatrix}\mathbf W&\mathbf X\\\mathbf Y&\mathbf Z\end{bmatrix} = \begin{bmatrix}\mathbf W&\mathbf X\\\mathbf{KW}+\mathbf Y&\mathbf{KX}+\mathbf Z\end{bmatrix}[/tex]

(I assume I is the identity matrix and 0 is the zero matrix.)

Answer:

f(g(-2)) = 3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Functions

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 4 - x²

g(x) = 2x + 5

Step 2: Find g(-2)

Step 3: Find f(g(-2))

Answer:

64

Step-by-step explanation:

the different sum of money is 64

John can make 6 different sums of money. He can make $0.05 from $2, $0.15 from $1, $0.40 from $0.50, $0.90 from #0.25, $1.90 from $0.10, and $3.90 from $0.05 coins

To discover the different sums of money John can make, we are able to utilize a strategy called "coin alter" or "category" issue.

John has a $2, $1, $0.50, $0.25, $0.10, and $0.05 coin in his pocket

Step 1: Begin with a purge entirety (0).

Step 2: Include each coin group in its entirety, one at a time.

Step 3: Rehash Step 2 for all possible combinations of coins.

Let's go through the method:

With $0.05 coin: total sum = (+ $0.05) = $0.05

With $0.10 coin: total sum = ($0.05 + $0.10) = $0.15

With $0.25 coin: total sum = ($0.15 + $0.25) = $0.40

With $0.50 coin: total sum = ($0.40 + $0.50) = $0.90

With $1 coin: total sum = ($0.90 + $1) = $1.90

With $2 coin: total sum = ($1.90 + $2) = $3.90

Presently, John can make the following different sums of money from the coins:

$0.05

$0.15

$0.40

$0.90

$1.90

$3.90.

There are 6 diverse wholes of cash John can make.

Learn more about sums here:

https://brainly.com/question/30518693

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Answers:

The boxplot is shown below.

=========================================

Explanation:

What your teacher wants is the five number summary.

This consists of:

Given in that exact order.

The given data set is  { 8, 19, 11, 20, 2, 14, 17, 9, 15}

This sorts to  {2, 8, 9, 11, 14, 15, 17, 19, 20}

From this sorted set, we see that 2 is the smallest item. So this is the min value. This is data point 1.

The max is the largest item, which in this case is 20, so this value goes in the box for data point 5.

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

Count out the number of values in the sorted set. You should count out n = 9 items.

Because n is odd, this means the median is in slot n/2 = 9/2 = 4.5 = 5

The value in the 5th slot is 14 which is the median (data point 3).

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

Once you determine the median, break the sorted set up like so

L = {2, 8, 9, 11}

U = {15, 17, 19, 20}

L is the lower set of values smaller than the median

U is the upper set of values larger than the median

The median itself is not part of set L and not part of set U either. It's ignored entirely from this point on.

From here, we find the middle values of L and U

You should find that the middle value of L is (8+9)/2 = 17/2 = 8.5 which is the value of Q1 (data point 2)

And also, the middle value of set U is (17+19)/2 = 36/2 = 18 which is the value of Q3 (data point 4)

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

To wrap everything up, we have this five number summary

These will determine the features of the boxplot as shown below.

In this case, there are no outliers.

Answer:

Kofi earned today = 30 cedis

Step-by-step explanation:

Given:

Kofi earned yesterday = 50 cedis

Kofi earned today = 60% of Kofi earned yesterday

Find:

Kofi earned today

Computation:

Kofi earned today = 60% of Kofi earned yesterday

Kofi earned today = 60% x 50

Kofi earned today = 0.60 x 50

Kofi earned today = 30

Kofi earned today = 30 cedis