In a study of government financial aid for college​ students, it becomes necessary to estimate the percentage of​ full-time college students who earn a​ bachelor's degree in four years or less. Find the sample size needed to estimate that percentage. Use a .03 margin of error and use a confidence level of 90​%. Complete parts​ (a) through​ (c) below.
a. Assume that nothing is known about the percentage to be estimated.
n=
b. Assume prior studies have shown that about 60​% of​ full-time students earn​ bachelor's degrees in four years or less.
n=
c. Does the added knowledge in part​ (b) have much of an effect on the sample​ size?

The missing part of the triangle are x = 7.5 units, y = (7.5√3)/2 units, y = (7.5√3)/2 units, z = (15√3)/2 units, a = 3.75 units and b = 11.25 units

Given: c = a+b = 15, X = 30°, Z = 60°, C = 90° for the triangles

Using the sine rule

x/sin X = z/sin Z = c/sin C

x/sin X =  c/sin C

x/sin30 = 15/sin90

x/0.5 = 15/1

x = 0.5 × 15 = 7.5 units

Using trigonometrical ratio:

sin 60 = y/x

(√3)/2 = y/7.5

y = (7.5√3)/2 units

sin 30 = y/z

1/2 = (7.5√3)/2/z

z = [(7.5√3)/2] / (1/2)

z = (15√3)/2 units

cos 30 =  b/z

(√3)/2 = b/(15√3)/2

b = [(√3)/2] × [(15√3)/2]

b = 45/4 = 11.25 units

a+b = 15

11.25 + b = 15

a = 15 - 11.25

a = 3.75 units

b = 45/4 = 11.25 units

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As per the 98% confidence interval for the proportion of all American adults who would report having earned money by selling something online in the previous year is (0.1859,0.2133).

Confidence interval:

In statistics, confidence interval is an estimate of an interval in statistics that may contain a population parameter.

Given,

According to a recent pew research center report, many American adults have made money by selling something online. in a random sample of 4579 American adults, 914 reported that they earned money by selling something online in the previous year. assume the conditions for inference are met.

Here we need to construct a 98% confidence interval for the proportion of all American adults who would report having earned money by selling something online in the previous year.

As per the given question, the value of

Confidence interval = 98%

Number of samples = 4579

Reported numbers = 914

Therefore, the number of failure is calculated as,

=> 4579 - 914

=> 3665

Here the sample proportion is the number of successes divided by the sample size:

=> 941/4579

=> 0.1996

Here for confidence level 1 − α = 0.98,

We have to determine zα / 2 ​= z0.01​ using the normal probability table in the appendix, we get

zα/2 ​= 2.33

Then the margin of error is calculated as,

E = 2.33 x √[0.1996 x (1 - 0.1996)]/4579

E = 0.0137

Then the boundaries of the confidence interval are then:

p⁻ˣ = 0.1996−0.0137 = 0.1859

p⁺ˣ = 0.1996+0.0137 = 0.2133

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Answer:

1

Step-by-step explanation:

Therefore the  the time todd needed to complete one full rotation around the Ferris wheel is 0.785min

There are numerous ways to define an equation in mathematics. In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. In the equation 2x + 4 = 14, for example, the two expressions 2x + 4 and 14 are separated by the symbol "equal." Mathematical variables are used in even the simplest and most basic mathematical equations.

Here,

the ferris wheel  radius = 10 meters

and he is 14 meters above the ground.

So we can build an equation with given data to find the time todd needed to complete one full rotation around the Ferris wheel

thus time is represented as t

Therefore ,the Ferris wheel rotates at a constant rate so that the angle sweeps out & radians per minute

so speed =8 rad/min

t=distance/speed

t=2[tex]\pi[/tex]/8 min

t=0.785min

Therefore the  the time todd needed to complete one full rotation around the Ferris wheel is 0.785min

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As Company will not invest in both cases, decision to invest is not sensitive over this annual revenue range.

In the given question, Decker scientific is considering an investment of $850,000 in a new product line.

The company will make the investment only if it will result in a rate of return of 20% per year or higher.

If the revenue is expected to be between $290,000 and $325,000 per year for each of 5 years, we have to determine if the decision to invest is sensitive to the projected range of income using an annual worth analysis.

AW of investment when expected revenue is

290000 = -1080000*(A/P,20%,4) + 290000

A/P = -1080000*0.386289 + 290000

A/P = -127192.12

A/P = -127192

AW of investment when expected revenue is

369000 = -1080000*(A/P,20%,4) + 369000

A/P = -1080000*0.386289 + 369000

A/P = -48192.12

A/P = -48192

As Company will not invest in both cases, decision to invest is not sensitive over this annual revenue range.

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The force exerted by her biceps to allow her hold the tray is 282 N.

Force is the product of mass and acceleration.

To calculate the force the biceps must exert to allow her hold the tray, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1 and solve for F'

Hence, the force exerted by her biceps is 282 N.

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Congruent triangles are triangles having corresponding sides and angles to be equal.

Congruent triangles are triangles that have both the same size and the same shape and they have the same perimeter and the same area. Congruence is denoted by “≅”.  For example, we can write ABC ≅ DEF. They have the same area and the same perimeter.

Congruent triangles have the same angle measures and the same side lengths.

On the other hand, the similar triangle is the term used for triangles that have the same shape, but not necessarily the same size.

Two triangles are considered to be congruent if they meet one of the following criteria.

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[tex]\stackrel{\textit{\LARGE P~E~M~D~A~S}}{3^2 + 3[ ~~ 2^3 (\sqrt{49}-2^2)(3^2-2^3) -2^2 ~~ ]}\implies 3^2 + 3[ ~~ 2^3 (\sqrt{49}-4)(9-8) -2^2 ~~ ] \\\\\\ 3^2 + 3[ ~~ 2^3 (7-4)(9-8) -2^2 ~~ ]\implies 3^2 + 3[ ~~ 2^3 (3)(1) -2^2 ~~ ] \\\\\\ 3^2 + 3[ ~~ 8 (3)(1) -4 ~~ ]\implies 3^2 + 3[ ~~ 24 -4 ~~ ]\implies 3^2 + 3[ ~~ 20 ~~ ] \\\\\\ 9+3[20]\implies 9+60\implies \text{\LARGE 69}[/tex]

Answer:

C) y=1/2x-2

Step-by-step explanation:

In the graph we have to identify the slope and y-intercept.

Y-intercept = -2 (In the graph it goes down two units)

To find the slope I identified the next nearest point, which was (2,-1).

From my y-intercept, -2, I had to go up one unit and two units to the right.

That makes my slope = 1/2

You need to remember slope intercept form is: y=mx+b

When plugging in the numbers you get:

y=1/2x-2

The entry to record this payment when the company’s estimated taxes for the first quarter total $50,000 will be:

Debit Income taxes payable $50000

Credit Cash $50000.

A journal is a book in which all of a company's transactions are recorded for the first time. Journaling is the process of recording transactions in a journal. Every transaction has two effects: one is debited and the other is credited.

The act of keeping or making records of any transaction, economic or non-economic, is referred to as journal entry. An accounting journal, which shows a company's debit and credit balances, records transactions. The journal entry may include multiple recordings, each of which is either a debit or a credit. A journal entry's purpose is to physically or digitally record every business transaction properly and accurately.

The journal entry based on the information is illustrated.

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A game that has an equal probability of winning or losing is said to be fair.

The foundational elements of fair play can be observed and learned both on and off the field, and include honesty, solidarity, tolerance, care, excellence, and joy. Fair competition, respect, camaraderie, team spirit, equality, and sport without doping are also examples.

A simple game of chance is deemed fair if there is an equal chance of winning for each player. If there is an equal chance of selecting each alternative, the decision is fair. Your understanding of probability can help you evaluate the fairness of games and make just decisions.

Children love playing together more when everyone is being fair. Additionally, it plays a significant role in getting along with people.

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Answer: A

Step-by-step explanation: when 18/20 is turned into a decimal it comes out as even and is the best one you can choose from

Answer:

yes

Step-by-step explanation:

Answer:

94%

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

The equation of the line passing through the point (6,-2) that is parallel to the line y=4x-11 is y = 4x - 26

The equation of the linear passes through the point (6, -2) and is parallel to the line y = 4x - 11

Parallel lines have the same slope.

Therefore,

y = 4x - 11

using

y = mx + b

where

m = slope

b= y-intercept

Therefore, the slope of y = 4x - 11 is 4.

And the slope of the other line will be 4 because they are parallel.

Therefore,

y = mx + b

y = 4x + b

it passes through (6, -2)

-2 = 6(4) + b

-2 - 24 = b

b = -26

The equation will be y = 4x - 26

Simple linear regression is a model that assesses the relationship between a dependent variable and an independent variable. The simple linear model is expressed using the following equation:

Where:

1. Y– Dependent variable

2. X– Independent (explanatory) variable

3. a– Intercept

4. b– Slope

Statistical Analysis Regression uses the statistics methods such as mean, median, normal distributions to figure out the relationships between the dependent and independent variables, to access the relationship strength between the variables and for modelling the new relationship among them, as it involves various variations such as simple linear, multilinear and non-linear where the non-linear regression is mainly used for complicated datasets in which the independent and dependent variables shows the nonlinear relationship.

The maximum number of automobile registrations that the police may have to check is 72 license.

Concept Introduction:-

Mathematics defines time as an ongoing and continuous series of events that take place in order, from the past to the present to the future.

Given Information:-

We have been given that a witness to a hit-and-run accident told the police that the license number contained the letters RLH followed by  3 digits, the first of which was a 5 . If the witness cannot recall the last  2 digits, but is certain that all 3 digits are different.

We have to find that the maximum number of automobile registrations that the police may have to check

According to the problem

Since digits are different, available digits are 0,1,2,3,4,6,7,8,9  ( as 5 is already used)

Number of available digits = 9

2nd digit can be any of the above 9 digits

3rd digit can be any of the remaining 8 digits

Police have to check 9*8 = 72 registrations.

Hence , The maximum number of automobile registrations that the police may have to check is 72 license.

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Answer: $1,184,537.217

Step-by-step explanation:

You just multiply the number by 1.22 every year.

For example: year 1 (60,000 * 1.22)= 73,200

Year 2: (73,200 *1.22) =89,304

and so on until year 15 is reached.

The volume of the rind is growing at the rate 681.097 cubic centimeters per week at the end of the fifth week.

In the given question, the radius of a spherical watermelon is growing at a constant rate of 2 centimeters per week.

The thickness of the rind is always one tenth of the radius.

We have to find the volume of the rind is growing at the rate cubic centimeters per week at the end of the fifth week.

Assume that the radius is initially zero.

Let r be the radius of watermelon.

dr/dt = 2 cm/week

Radius after 5 week = 10 cm

Thickness of the rind = r/10 cm = 0.1r cm

Now the volume of rind

V = 4/3 π[r^3-(0.9r)^3]

dV/dt = 4/3 π[3r^2-3r^2(0.9)^3]dr/dt

dV/dt = 4/3 π[1-(0.9)^3](3r^3)(2)

dV/dt = 8(3.14)(0.271)(10)^3

dV/dt = 8(3.14)(0.271)(1000)

dV/dt = 681.097 cm^3/ week.

Hence, the volume of the rind is growing at the rate 681.097 cubic centimeters per week at the end of the fifth week.

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Answer:

angle A = 124 degrees, angle D = 124 degrees, angle C = 56 degrees

Step-by-step explanation:

1. apply that opposite angles in a parallelogram are congruent

measure of angle A = measure of angle C

measure of angle B = measure of angle D

2. given the measure of angle A = 56 degrees, angle C is also 56 degrees

angle A = angle C = 56 degrees

3. calculate the measure of angle A

measure of angle A + 56 degrees = 180 degrees

4. subtract 56 from both sides

measure of angle A = 124 degrees

5. measure of angle A = measure of angle D

angle A = angle D = 124 degrees

answer:

angle A = 124 degrees

angle D = 124 degrees

angle C = 56 degrees

5) The equation with a negative slope (- m) and a positive y - intercept (b) will be;

⇒ y = - mx + b

6) The value of slopes are,

a) Slope = 4

b) Slope = 3

c) Slope = 1

The equation of line passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;

y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

In question 5;

The value of slope = - m

And, The y - intercept = b

In question 6;

The points are,

a) (3, 13) and (5, 21)

b) (- 2, - 7) and (1, 2)

c) (4, 9) and (10-, 15)

Now,

Since We know that;

The equation of line in slope - intercept form is,

⇒ y = mx + b

Where, 'm' is slope and 'b' is y - intercept.

Here, In question 5;

The value of slope = - m

And, The y - intercept = b

Hence, The equation of line is,

⇒ y = - mx + b

And, We know that;

The slope of the line passing through the points (x₁ , y₁) and (x₂, y₂) is,

⇒ m = (y₂ - y₁) / (x₂ - x₁)

Here, In question 6;

The points are,

a) (3, 13) and (5, 21)

b) (- 2, - 7) and (1, 2)

c) (4, 9) and (10, 15)

So, The slopes are find as;

a) (3, 13) and (5, 21)

⇒ m = (21 - 13) / (5 - 3)

⇒ m = 8/2

⇒ m = 4

b) (- 2, - 7) and (1, 2)

⇒ m = (2 - (-7)) / (1 - (-2))

⇒ m = 9/3

⇒ m = 3

c) (4, 9) and (10, 15)

⇒ m = (15 - 9) / (10 - 4)

⇒ m = 6/6

⇒ m = 1

Thus, We get;

5) The equation with a negative slope (- m) and a positive y - intercept (b) is,

⇒ y = - mx + b

6) The value of slopes are,

a) Slope = 4

b) Slope = 3

c) Slope = 1

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As per the given matrix, the stable age distribution vector is 25 and 25

Matrix:

In algebra, matrix means a set of numbers arranged in rows and columns so as to form a rectangular array.

Given,

Here we have the age transition matrix L and the age distribution vector x1 to find the age distribution vectors x2 and X3.

In order to find a stable age distribution vector we need to find an eigenvalue λ and a corresponding eigenvector x such that 

=> Lx=λx.

Here the characteristics polynomial of L is x2−41​ which implies the eigenvalues are 21​ and −21​.

Now, we have to choose the +ve eigenvalue, λ=21​, we need to find the corresponding eigenvector i.e. to find a basis of the solution space (L−21​I2​)x=0.

Then the augmented matrix is

[tex]\begin{bmatrix}200 & 0 \\ 0& 200\end{bmatrix}[/tex]

Then the age transmission is written as 25 and 25.

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Fraction which are equivalent to the given fractions are as follow:

a. 4 /6 is equivalent to 2/3, 8/12, 12/18 ,...

b. 4/8 is equivalent to 1/2 , 8/16, 12/24,.....

c. 2/6 is equivalent to 1/3 , 4/12, 6/18,....

d. 2/4 is equivalent to 1/2, 4/8, 6/12,...

e. 3/4 is equivalent to 6/8, 9/12, 12/16,...

As given in the question,

Equivalent fraction are the fractions which when reduced have the same numerator and denominator.

Multiply or divide by 2/2, 3/3, 4/4, 5/5,...so on to all numerator and denominators of the given fractions to get equivalent fraction.

a. 4/6 divide by 2 both numerator and denominator we get

4/6 = 2/3

Now multiply by both numerator and denominator by 2/2, 3/3,...so on.

4/6 is equivalent to 2/3 , 8/12, 12/18,...

Multiply and divide by same numbers in the numerator and denominator of all the fractions to get equivalent

b. b. 4/8 is equivalent to 1/2 , 8/16, 12/24,.....

c. 2/6 is equivalent to 1/3 , 4/12, 6/18,....

d. 2/4 is equivalent to 1/2, 4/8, 6/12,...

e. 3/4 is equivalent to 6/8, 9/12, 12/16,...

Therefore, equivalent fractions of the given fractions are :

a. 4 /6 is equivalent to 2/3, 8/12, 12/18 ,...

b. b. 4/8 is equivalent to 1/2 , 8/16, 12/24,.....

c. 2/6 is equivalent to 1/3 , 4/12, 6/18,....

d. 2/4 is equivalent to 1/2, 4/8, 6/12,...

e. 3/4 is equivalent to 6/8, 9/12, 12/16,...

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Answer:

The function is going up

Step-by-step explanation:

the arrow is going up

Answer: y=2^{x}

Step-by-step explanation:

The given trigonometric equations have the value tan x, -cot x.

Since the given trigonometric equations  are: cos2x-cos4x/sin2x+sin4x   and  cos2x+cos4x/sin2x-sin4x. The problem is related to trigonometric Ratios, which are the ratios of the side of a right-angled triangle.Now for the equation (cos 2x - cos 4x )/(sin2x +sin4x)

since we know the formulas  :

cos A + cos B = - sin (A+B)/2 sin(A-B)/2

sin A - sin B = sin( A+B)/2 cos (A-B)/2

so for the equation, we can

= (-sin 3x) sin ( -2x)/2)/( cos 3x cos x)

= sin 3x sin x/ (sin 3x) cos x

= tan x

for the second equation    cos2x+cos4x/sin2x-sin4x

= cos 3x cosx/ cos3x sin(- x)

= - cot x

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Answer: 44.55

Step-by-step explanation:

The velocity at which the diver hits the water is 45.96 feet/s.

The velocity of an object is in feet per sec after it has fallen a distance of d feet is approximated by the function v(d) = √64.4d

Given that, height of olympic diving platform d = 10 m = 32.8 feet

We know that, v(d) = √64.4d and d = 32.8

So, substituting in the above function, we have

v(d) = √64.4d

⇒ √64.4 * 32.8

⇒ √ 2112.32

⇒ 45.96 feet/s

Thus, the velocity at which the diver hits the water is 45.96 feet/s.

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The sections of the function that are decreasing, defined by the ordered pairs are;

Section 2; (-1, 4) to (1, 0)

Section 4; (3, 2), to (5, -2)

The part of the second function that is decreasing is; (2, -2) to (3, -5)

A function is a definition of the mapping of the set of input variables unto the set of the output variables.

The points in the specified functions are;

Section 1 line ; (-3, 4) to (-1, 4)

Section 2 line ; (-1, 4) to (1, 0)

Section 3 line ; (1, 0) to (3, 2)

Section 4 line ; (3, 2) to (5, -2)

The points through which the function goes through are; (-4, -2.5), (3, -5), (-2, -2), (0, 5), (2, -2), (3, -5), (4, 2.5) and (5, -2)

A function is decreasing when the positive increase in the x-value of the function is accompanied by a decrease in the y-value.

The sections of the functions that are decreasing are;

Section 2 line ; (-1, 4) to (1, 0),

Section 4; (3, 2) to (5, -2)

Parts of the function that is decreasing is; (2, -2), (3, -5)

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