a rope is wound 50 times around a cylinder of radius 25cm. How long is the rope​

Answer:

[tex]\boxed{\sf 4.41}[/tex]

Step-by-step explanation:

The triangle is a right triangle.

We can solve using trigonometric functions.

[tex]\sf cos(\theta)=\frac{adjacent}{hypotenuse}[/tex]

[tex]\sf cos(25)=\frac{4}{?}[/tex]

[tex]\sf ?=\frac{4}{cos(25)}[/tex]

[tex]\sf ?= 4.41351167...[/tex]

Answer:

The answer is :

Step-by-step explanation:

Axis of symmetry is the equation where it cuts the middle of the quadratic graph.

For quadratic equation in the form of (x+a)² + b, the axis of symmetry will be (x+a) = 0 which is x = -a :

Question 1,

[tex](x + 3) = 0[/tex]

[tex]x = - 3[/tex]

Question 2,

[tex](y - 4 )= 0[/tex]

[tex]y = 4[/tex]

Answer:

[tex]\boxed{x=-3} \\ \boxed{y=4}[/tex]

Step-by-step explanation:

Axis of symmetry is a line that cuts the parabola in half touching the vertex.

Quadratic forms ⇒ y = ax² + bx + c or x = ay² + by + c

Axis of symmetry ⇒ x = [tex]\frac{-b}{2a}[/tex] or y = [tex]\frac{-b}{2a}[/tex]

First problem:

y = -3(x+3)²-2

Write in quadratic form ⇒ y = ax² + bx + c

y = -3(x² + 6x + 9) - 2

y = -3x² -18x - 27 - 2

y = -3x² -18x - 29

a = -3, b = -18

Find axis of symmetry.

[tex]x= \frac{-b}{2a}[/tex]

[tex]x=\frac{--18}{2(-3)}[/tex]

[tex]x=\frac{18}{-6}=-3[/tex]

Second problem:

x = -4(y -4)² +6

Write in quadratic form ⇒ x = ay² + by + c

x = -4(y² - 18y + 16) + 6

x = -4y² + 32y - 64 + 6

x = -4y² + 32y - 58

a = -4, b = 32

Find axis of symmetry.

[tex]y= \frac{-b}{2a}[/tex]

[tex]y=\frac{-32}{2(-4)}[/tex]

[tex]y=\frac{-32}{-8}=4[/tex]

Answer:

Significant figures are any digits that contribute to the number: In 02.400, only 2 and 4 are significant digits.  However, in 2.4001, 2, 4, 0, 0, and 1 are significant digits, because the number would not be the same without them.

Step-by-step explanation:

Hope it helps <3

Answer:

Congruent

Step-by-step explanation:

I am not 100% sure because there are no measurements but it looks like the two shapes are the same size.

If this helped, please consider giving me brainliest, it will help me a lot :)

Have a good day.

Answer:

t

Step-by-step explanation:

Answer:

$41,999

Step-by-step explanation:

Annual income = 45000

monthly income = $45000/12 months = $3750

mandatory expense at 38% rule = $3750 x 0.38 = 1425

other debt = 790

tax and insurance = 340

= 1425 - 790 - 340

= 295

balance left = 295

mortgage payment = (295/8.78) x 1000

= $33,599

purchase price = monthly payment/ 1- % of down payment

= $33599/1 - 0.20

= 33599/0.80

= $41,999

Answer:

1. Debit Petty cash for $400; and Credit Cash for $400.

2. Total petty cash payment = $270.57

3(a) Cash reimbursement is $279.58; and Cash over and short is $9.01.

3(b) Debit Petty cash for $100; and Credit Cash for $100.

Step-by-step explanation:

Note: This question is not complete. The full complete question is therefore provided before answering the question. See the attached pdf file for the full question.

The explanations to the answers are now given as follows:

1. Prepare the journal entry to establish the petty cash fund.

Note: See the journal entry in the attached excel file

2. Prepare a petty cash payments report for February with these categories: delivery expense, mileage expense, postage expense, merchandise inventory (for transportation-in), and office supplies expense. Sort the payments into the appropriate categories and total the expenditures in each category.

Note: See the petty cash payments report in the attached excel file.

3. Prepare the journal entries for required 2 to both (a) reimburse and (b) increase the fund amount.

Note: See the journal entries (a) and (b) in the attached excel file

3(a) Reimburse Workings:

w.1: Calculation of Cash reimbursement

Cash reimbursement = Petty cash fund - Petty cash fund balance = $400 - $120.42 = $279.58

w.2: Calculation of the Cash over and short

Cash over and short = Cash reimbursement – Total expenses = $279.58 - $270.57 - $120.42 = $9.01

Answer:

See below.

Step-by-step explanation:

[tex]2 \ln(x+2)=6[/tex]

[tex]\ln (x+2)=3[/tex]

[tex]e^{\ln(x+2)}=e^3[/tex]

[tex]x+2=e^3[/tex]

[tex]x=e^3-2[/tex]

[tex]x\approx 18. 09[/tex]

Answer: 6 + 4

Step-by-step explanation:

6 is the x

Answer:

if X=6

meaning,when you add X+4 it will give you 6+4 which is equal to 10

Answer:

the null hypothesis would be: p = 70%/0.7

The alternative hypothesis would be: p < 0.7

Step-by-step explanation:

The null hypothesis is most of the time always the default statement while the alternative hypothesis is tested against the null and is its opposite.

In this case study the null hypothesis would be: the proportion of men who own cats is 70%: p = 0.7

The alternative hypothesis would be: the proportion of men who own cats is smaller than 70% : p < 0.7

Answer:

[tex]n = 0.949[/tex]. The waist-to-hip ratio indicates that length of her waist circumference is equal to the 94.9 % of length of her hip circumference.

Step-by-step explanation:

The waist-to-hip ratio of Rachel is:

[tex]n = \frac{37\,in}{39\,in}[/tex]

[tex]n = \frac{37}{39}[/tex]

[tex]n = 0.949[/tex]

The waist-to-hip ratio indicates that length of her waist circumference is equal to the 94.9 % of length of her hip circumference.

The length of her waist circumference is 94.9% the length of her hip circumference.

From the information given, Rachel's waist circumference is 37 inches and her hip circumference is 39 inches.

Therefore, her waist to hip ratio will be calculated thus:

n = 37/39

n = 0.949

This implies that the length of her waist circumference is 94.9% the length of her hip circumference.

Learn more about ratio on:

https://brainly.com/question/13763238

Answer: 16500(.65)^3 =4531.31

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

I suppose this is a trick question.

The answer is equal to the "circular hole" in the numbers. (except 4, which does not contain circular hole).

So by counting the holes,

123456789 = 4

Answer:

4

Step-by-step explanation:

This is a trick/pattern

We have to count the number of holes in each number

1-0

2-0

3-0

4-0

5-0

6-1

7-0

8-2

9- 1

1+2+1 =4

Answer:

2 and 10 are the in and max

Answer:

Min = 2

Max = 10

Step-by-step explanation:

C = 2(x+y)

x ≥1

y ≥0

y ≤5 -x

The smallest y can be is zero

The smallest x can be is 1

The minimum is

C = 2 ( 0+1) = 2 ( 1) = 2

Looking for the max

y ≤5 -x

Add x to each side

x+y ≤5

The max is 5 for x+y

Substituting that into the equation for C

C = 2(5)

C = 10

Min = 2

Max = 10

Answer:

Step-by-step explanation:

Given the functions g(x) = x − 3x  and h(x) = 5x + 2, we are to calculatae for the expression;

a) (g - h)(x)  an (g * h)(x)

(g - h)(x)  = g(x) - h(x)

(g - h)(x)  = x − 3x -(5x+2)

(g-h)(x) = x-3x-5x-2

(g-h)(x) =-7x-2

b)  (g * h)(x) =  g(x) * h(x)

 (g * h)(x)  = (x − 3x )(5x+2)

(g * h)(x) = 5x²+2x-15x²-6x

(g * h)(x) = 5x²-15x²+2x-6x

(g * h)(x) = -10x²-4x

c) To get (g + h)(−2), we need to first calculate (g + h)(x) as shown;

 (g + h)(x)  an (g * h)(x)

(g + h)(x)  = g(x) +h(x)

(g + h)(x)  = x − 3x + (5x+2)

(g+h)(x) = x-3x+5x+2

(g+h)(x) =3x+2

Substituting x = -2 into the resulting function;

(g+h)(-2) = 3(-2)+2

(g+h)(-2) = -6+2

(g+h)(-2) = -4

Answer:

Bob is 15 years old.

Step-by-step explanation:

If Sally is 10 years old and Bob is five years older than Sally then we just need to add 10+5=15.

Hope this helps!!

Answer:

Mixing two concentrations for known amount of mixture

Step-by-step explanation:

Let x = amount (ounces) of 18% solution

then

36-x = amount (ounces) of 9% solution

0.18x + 0.09(36-x) = .16(36)

0.18x + 3.24-.09x = 5.76

0.09x + 3.24 = 5.76

0.09x = 2.52

x = 28 ounces of 18% solution

amount of 9% solution:

36-x = 36-18 = 18 ounces

"prepare 36 ounces", means mass or weight.

Let u = ounces of 16%

Let v = ounces of 18%

(16u + 18v)/36=9

and u + v = 36  

based on the above findings....

Mixing two concentrations for known amount of mixture

Answer:

3 × 7

Step-by-step explanation:

The order of a matrix is the number of rows and columns that it has. Rows are listed first and columns are listed second. The matrix has 3 rows going across horizontally and 7 columns going down vertically.

Therefore, the order of the matrix is 3 × 7.

Hope that helps.

Answer:

x = 18; y = 35

Step-by-step explanation:

This gives us the equation:

1. x+y=53

2. 3x=y+19

3. 3x-y=19

Add the first and last line together: x+y+3x-y=53+19

Simplifies to: 4x=72

Divide by 4 to get: x = 18

Plug your numbers into the first equation to get 18+y=53; y = 35.

Answer:

The numbers are 18 and 35.

Step-by-step explanation:

The smaller number is x.

Let the other number by y.

Three times the smaller number is equal to 19 more than the larger number.

3x = y + 19

The larger number is

y = 3x - 19

the numbers add up to 53

x + y = 53

x + 3x - 19 = 53

4x = 72

x = 18

y = 3x - 19 = 3(18) - 19 = 54 - 19 = 35

The numbers are 18 and 35.

Answer:

5

Step-by-step explanation:

The square Root of 25 in its simplest form means to get the number 25 inside the radical √ as low as possible.

25 is a perfect square, which means that you can simply calculate the square Root of 25 to get the answer. 5 times 5 equals 25. Thus, the square Root of 25 in simplest radical form is = 5

Answer:

x = 60°

Step-by-step explanation:

All the angles in a triangle add up to 180°. So, you have this equation.

87° + 33° + x = 180°

120° + x = 180°

x = 60°

The measure of angle x is 60°.

Hope that helps.

Answer: Local Max = (-1, 0)

              Local Min = (1, -8)

Step-by-step explanation:

f(x) = (x + 1)² (x - 3)

Step 1: Find the zeros

(x + 1)² = 0 --> x = -1   (multiplicity of 2)

(x - 3) = 0  -->  x = 3

Step 2: Find the Vertices

x = -1 --> (multiplicity is even which means this is a vertex)

The midpoint between x = -1 and x = 3 is x = 1

Step 3:  Find the Local Max and Local Min

Use the x-value above to find the y-values

f(-1) = 0        because it is a zero

f(1) = (1 + 1)² (1 - 3)

    =    2²(-2)

    =    4(-2)

    =      -8

Conclusion:

(-1, 0) is the Local Max     bigger y-value

(1, -8) is the Local Min      smaller y-value

Answer:

f ( x ) = ( x – 3) 2 – 4; the minimum value is –4

Step-by-step explanation:

Given the function f ( x ) = x 2 – 6 x + 5, write an equivalent form of the function that reveals the minimum or maximum value of the function and state the minimum or maximum value.

f ( x ) = ( x – 3) 2 – 4; the minimum value is –4

( This The correct question to answer?) can't deleted..

Answer:

760 words for 20 minutes.

Step-by-step explanation:

38 words = 1 minute

1 x 20 = 20

38 x 20 = 760 words

Answer:

Option A

Step-by-step explanation:

If Discriminant < 0 , (Just as -8) the roots are imaginary (Complex) and there are two complex roots.

Answer:

Explained below.

Step-by-step explanation:

X = annual consumption in the United States in 2008 of HFCS

[tex]X\sim N(60, 20^{2})[/tex]

(a)

Find the probability a randomly selected American consumes more than 50 lbs of HFCS per year.

[tex]P(X>50)=P(\frac{X-\mu}{\sigma}>\frac{50-60}{20})=P(Z>-0.50)=P(Z<0.50)=0.6915[/tex]

P (X > 50) = 0.6915.

(b)

Find the probability a randomly selected American consumes between 30 and 90 lbs of HFCS per year.

[tex]P(30<X<90)=P(\frac{30-60}{20}<\frac{X-\mu}{\sigma}<\frac{90-60}{20})\\\\=P(-1.5<Z<1.5)\\\\=0.93319-0.06681\\\\=0.86638\\\\\approx 0.8664[/tex]

P (30 < X < 90) = 0.8664.

(c)

Find the 80th percentile of annual consumption of HFCS.

P (X < x) = 0.80

⇒ P (Z < z) = 0.80

⇒ z = 0.84

[tex]z=\frac{x-\mu}{\sigma}\\\\0.84=\frac{x-60}{20}\\\\x=60+(20\times 0.84}\\\\x=76.8[/tex]

80th percentile = 76.8.

(d)

In a sample of 40 Americans how many would you expect to consume more than 50 pounds of HFCS per year.

P (X > 50) = 0.6915

Number of American who consume more than 50 lbs = 40 × 0.6915

                                                                                          = 27.66

                                                                                          ≈ 28

Expected number = 28.

(e)

Between what two numbers would you expect to contain 95% of Americans HFCS annual consumption?

According to the Empirical rule, 95% of the normally distributed data lies within 2 standard deviations of mean.

[tex]P(\mu-2\sigma<X<\mu+2\sigma)=0.95\\\\P(60-2\cdot20<X<60+2\cdot20)=0.95\\\\P(20<X<100)=0.95[/tex]

Range = 20 < X < 100.

(f)

Find the quartile and Interquartile range for this population.

1st quartile: Q₁

P (X < Q₁) = 0.25

⇒ P (Z < z) = 0.25

⇒ z = -0.67

[tex]z=\frac{Q_{1}-\mu}{\sigma}\\\\-0.67=\frac{Q_{1}-60}{20}\\\\Q_{1}=60-(20\times 0.67)\\\\Q_{1}=46.6[/tex]

3rd quartile: Q₃

P (X < Q₃) = 0.75

⇒ P (Z < z) = 0.75

⇒ z = 0.67

[tex]z=\frac{Q_{3}-\mu}{\sigma}\\\\0.67=\frac{Q_{3}-60}{20}\\\\Q_{3}=60+(20\times 0.67)\\\\Q_{3}=73.4[/tex]

Inter quartile range:

[tex]IQR=Q_{3}-Q_{1}=73.4-46.6=26.8[/tex]

(g)

Compute the z-score for x = 105 lbs as follows:

[tex]z=\frac{Q_{3}-\mu}{\sigma}\\\\z=\frac{105-60}{20}\\\\z=2.25[/tex]

Z-scores greater than +2.00 or less than -2.00 are considered as unusual.

Thus, the result unusual.

Answer:

y = 3 |x − 8| + 1

Step-by-step explanation:

y = 3 |x|

Shift right 8 units:

y = 3 |x − 8|

Shift up 1 unit:

y = 3 |x − 8| + 1

Answer:

absolute minimum = -749 and

absolute maximum = 467

Step-by-step explanation:

To get the absolute maximum and minimum of the function, the following steps must be followed.

First, we need to find the values of the function at the given interval [-4, 5].

Given the function f(x) = 6x³ − 9x² − 216x + 3

at x = -4;

f(-4) = 6(-4)³ − 9(-4)² − 216(-4) + 3

f(-4) = 6(-64) - 9(16)+864+3

f(-4) = -256- 144+864+3

f(-4) = 467

at x = 5;

f(5) = 6(5)³ − 9(5)² − 216(5) + 3

f(5) = 6(125) - 9(25)-1080+3

f(5) = 750- 225-1080+3

f(5) = -552

Then we will get the values of the function at the crirical points.

The critical points are the value of x when df/dx = 0

df/dx = 18x²-18x-216 = 0

18x²-18x-216 = 0

Dividing through by 18 will give;

x²-x-12 = 0

On factorizing the resulting quadratic equation;

(x²-4x)+(3x-12) = 0

x(x-4)+3(x-4) = 0

(x+3)(x-4) = 0

x+3 = 0 and x-4 = 0

x = -3 and x = 4 (critical points)

at x  = -3;

f(-3) = 6(-3)³ − 9(-3)² − 216(-3) + 3

f(-3) = 6(-27) - 9(9)+648+3

f(-3) = -162-81+648+3

f(-3) = 408

at x = 4

f(4) = 6(4)³ − 9(4)² − 216(4) + 3

f(4) = 6(64) - 9(16)-864+3

f(4) = 256- 144-864+3

f(4) = -749

Based on the values gotten, it can be seen that the absolute minimum and maximum are -749 and 467 respectively

Answer:

Option (2)

Step-by-step explanation:

In this question we have to find the values of Sinθ and tanθ where [tex]\frac{3\pi}{2}<x<2\pi[/tex].

Cosθ = [tex]\frac{\sqrt{2}}{2}[/tex] ⇒ θ = [tex]\frac{7\pi }{4}[/tex]

[Since [tex]\text{Cos}\frac{7\pi }{4}=\text{Cos}(2\pi-\frac{\pi}{4})[/tex]

                     [tex]=\text{Cos}\frac{\pi }{4}[/tex]

                     [tex]=\frac{\sqrt{2} }{2}[/tex] ]

Since Cosine of any angle between [tex]\frac{3\pi}{2}[/tex] and 2π is positive and Sine is negative in nature,

[tex]\text{Sin}\frac{7\pi }{4}[/tex] = [tex]-\frac{\sqrt{2}}{2}[/tex]

Since, tanθ = [tex]\frac{\text{Sin}\theta}{\text{Cos}\theta}[/tex]

tanθ = [tex]\frac{\frac{-\sqrt{2} }{2} }{\frac{\sqrt{2} }{2} }[/tex]

       = [tex]-\frac{\sqrt{2}}{2}\times \frac{2}{\sqrt{2}}[/tex]

       = -1

Therefore, Option (2) will be the answer.

Answer:

Step-by-step explanation:

option 2 is the correct answer

Answer:

If the value of our test statistics is less than the critical value of t at 7 degrees of freedom at a 10% level of significance for the right-tailed test (which is 1.415), then we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

If the value of our test statistics is more than the critical value of t at 7 degrees of freedom at a 10% level of significance for the right-tailed test (which is 1.415), then we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Step-by-step explanation:

We are given that the means of two populations using paired observations. Suppose that [tex]\bar D[/tex] = ​3.125, [tex]s_D[/tex] =​ 2.911, and n =​ 8, and that you wish to test the hypothesis below at the​ 10% level of significance.

Let D = difference between the two paired observations.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_D[/tex] = 0    

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_D[/tex] > 0

The test statistics that would be used here is Paired t-test for dependent samples;

                     T.S. =  [tex]\frac{\bar D-\mu_D}{\frac{s_d}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar D[/tex] = ​3.125, [tex]s_D[/tex] =​ 2.911, and n =​ 8

The decision rule for rejecting the null hypothesis in the given hypothesis​ test would be;

Answer:

the temperature reading that separates the bottom​ 4% from the others is -1.75°

Step-by-step explanation:

The summary of the given statistics data set are:

Mean [tex]\mu[/tex] : 0

Standard deviation [tex]\sigma[/tex] = 1

Probability of the thermometer readings = 4% = 0.04

The objective is to determine the temperature reading that separates the bottom​ 4% from the others

From the standard normal table,

Z score for the Probability P(Z < z) = 0.04

P(Z < -1.75) = 0.04

z = -1.75

Now, the z- score formula can be expressed as :

[tex]z = \dfrac{X-\mu}{\sigma}[/tex]

[tex]-1.75 = \dfrac{X-0}{1}[/tex]

-1.75 × 1 = X - 0

X = -1.75 × 1 - 0

X = -1.75

Therefore, the temperature reading that separates the bottom​ 4% from the others is -1.75°