Simplifying an Expression with the Numerator and the Denominator Raised to a Power

Answer:

From the sample of n= 200 people,

The proportion of people with kids is:

p'= 110/200= 0.55

The confidence interval for population proportion is given by:

[tex]p' - Z_{\alpha /2} \sqrt[]{\frac{p'(1-p')}{n} } } \leq P\leq p' + Z_{\alpha /2}\sqrt[]{\frac{p'(1-p')}{n} } }[/tex]

[tex]= p' - Z_{\alpha /2} \sqrt[]{\frac{0.55(0.45)}{200} } } \leq P \le p' + Z_{\alpha /2} \sqrt[]{\frac{0.55(0.45)}{200} } }[/tex]

[tex]= p' - Z_{\alpha /2} 0.0352} } } \leq P\le p' + Z_{\alpha /2} 0.0352} }[/tex]

Where P is the population proportion and Z is the critical value at a given level of significance α.

Question is not proper, Proper question is given below;

Consuelo's living room is in the shape of a rectangle and has an area of 360 square feet. The width of the living room is  [tex]\frac{5}{8}\ ft[/tex] its length. What is the length of the living room?

Answer:

Length of the living room is 24 feet.

Step-by-step explanation:

Given:

Area of the living room = [tex]360 \ ft^2[/tex]

We need to find the length of the living room.

Solution:

the length of the living room be 'l'.

Given:

Width of the living room [tex]\frac{5}{8}\ ft[/tex] of it length.

width [tex]w= \frac{5}{8}l[/tex]

It has been given that living room is in rectangular format.

So we can say that;

Area of living room is equal to length of the living room times width of the living room.

framing in equation form we get;

[tex]l\times w=360\\\\l\times\frac{5}{8}l=360\\\\\frac{5}{8}l^2=360[/tex]

Now Multiplying both side by [tex]\frac{8}{5}[/tex] we get;

[tex]\frac{5}{8}l^2\times\frac{8}{5}=360\times\frac{8}{5}\\\\l^2= 576[/tex]

Taking square root on both side we get;

[tex]\sqrt{l^2} =\sqrt{576} \\\\l=24 \ ft[/tex]

Hence Length of the living room is 24 feet.

Answer:

Metaphysics

Step-by-step explanation:

Metaphysics is a system of reasoning or process that is often employed to find answers through examining fundamental nature of reality, the relationship between minds and also knowledge.

The systematic use of critical reasoning to try to find answers to fundamental questions about reality, morality, and knowledge is called philosophy.

The systematic use of critical reasoning to try to find answers to fundamental questions about reality, morality, and knowledge is called philosophy.

Philosophy is the discipline that seeks to explore and understand the fundamental aspects of existence, including the nature of reality, the principles of ethics and morality, and the limits of human knowledge. It involves the rigorous examination of concepts, arguments, and ideas to gain deeper insights into the nature of the world and our place in it.

Philosophers engage in critical thinking and analysis to address questions related to the meaning of life, the nature of truth, the basis of ethics, and the foundations of human understanding. Through philosophical inquiry, individuals seek to develop a deeper and more comprehensive understanding of the complex issues that shape our lives and society.

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Answer:

Bianca's height = 42 inches

Step-by-step explanation:

Let x be the Bianca height.

Given:

Meredith height = 60 inches

We need to find the Bianca height.

Solution:

From the given statement the Meredith's height is [tex]\frac{2}{3}[/tex] of Bianca's height plus 32 inches, so the equation is.

Meredith's height = [tex]\frac{2}{3}(Bianca\ height)+32[/tex]

Substitute Meredith's height in above equation.

[tex]60=\frac{2}{3}x+32[/tex]

Now we solve the above equation for x.

[tex]\frac{2}{3}x=60-32[/tex]

[tex]\frac{2}{3}x=28[/tex]

By cross multiplication.

[tex]x=\frac{3\times 28}{2}[/tex]

28 divided by 2.

[tex]x= 3\times 14[/tex]

[tex]x=42\ in[/tex]

Therefore, the height of the Bianca is 42 inches.

Answer:

4 cups of lemon juice is required for 12 cups of water to make lemonade.

Step-by-step explanation:

Given:

To make lemonade 1 cup of lemon juice is required with 3 cups of water.

To find how many cups of lemon juice is required with 12 cups of water.

Solution:

We will construct a double number line of which one represents the cups of lemon juice and the other represents the cups of water.

From the number lines we can see that with 1 cup of lemon juice there are 3 cups of water.

So, ratio of cups of lemon juice to cups of water = 1 : 3

If we require [tex]x[/tex] cups of lemon juice with 12 cups of water then ratio = x : 12

Since ratio will always be equivalent, so we can write it as:

[tex]\frac{x}{12}=\frac{1}{3}[/tex]

Multiplying both sides by 12.

[tex]12.\frac{x}{12}=12\times\frac{1}{3}[/tex]

∴ [tex]x=4[/tex]

Thus, 4 cups of lemon juice is required for 12 cups of water to make lemonade.

Answer:

100 blueberries and 40 blackberries

Step-by-step explanation:

Multiply each by 20 and you have 5 x 20 = 100 and 2 x 20 = 40

Answer:

SR = (6,4)

Step-by-step explanation:

The ship position is (1,0)

The rocks position is (7,4)

SR is the vector line joining ship and rock

Using triangle law of addition

OS + SR = OR

SR = OR - OS

= ( 7 - 1 , 4 - 0)

= (6,4)

The vector line joining Ship and rock is (6,4)

Answer:

The answer is B)7.4%

Step-by-step explanation:

Pure cost of the car is 11595$. It is stated that taxes costs 860$ for the car. To find the overall tax rate we need to simply divide tax value to car original cost.

[tex]860/11595=0.074[/tex]

Answer:

option (c) 4:15 a.m. Thursday

Step-by-step explanation:

Time difference in  New York City and Athens = 7 hours

Now,

The flight leaves at 7:30 a.m on Wednesday i.e 7:30 hrs

Therefore,

the time in Athens at the time of leaving of flight =  7:30 hrs + 7 hours

= 14 : 30 hrs i.e 2 : 30 pm on Wednesday

now,

after the 13 hours and 45 minutes of flight time in Athens i.e

= 14 : 30 + 13 : 45

= 28 : 15   i.e 1 day and 4 : 15 hrs

This means Flight will land at 4 : 15 a.m on Thursday

Hence,

option (c) 4:15 a.m. Thursday

Answer:

C

Step-by-step explanation:

4:15am Thursday

Answer:

I=\frac{t^2}{2}

Step-by-step explanation:

From exercise we have that x=t, t>0. Because A(t) be the area of the region in the first quadrant, we get that x started at 0. The limits for y are the following e-x and e. We get the integral :

I=\int\limits^0_t \int\limits^{e}_{e-x} 1 dy dx

I=\int\limits^0_t [y]_{e-x}^{e} dx

I=\int\limits^0_t (e-e+x) dx

I=\int\limits^0_t {x} \, dx

I=[\frac{x^2}{2} ]_{0}^{t}

I=\frac{t^2}{2}

Answer:

cosecant

Step-by-step explanation:

Inverse Cosine

cos-1

Cos-1

arccos

Arccos

The inverse function of cosine.

Basic idea: To find cos-1 (½), we ask "what angle has cosine equal to ½?" The answer is 60°. As a result we say cos-1 (½) = 60°. In radians this is cos-1 (½) = π/3.

More: There are actually many angles that have cosine equal to ½. We are really asking "what is the simplest, most basic angle that has cosine equal to ½?" As before, the answer is 60°. Thus cos-1 (½) = 60° or cos-1 (½) = π/3.

Details: What is cos-1 (–½)? Do we choose 120°, –120°, 240°, or some other angle? The answer is 120°. With inverse cosine, we select the angle on the top half of the unit circle. Thus cos-1 (–½) = 120° or cos-1 (–½) = 2π/3.

In other words, the range of cos-1 is restricted to [0, 180°] or [0, π].

Note: arccos refers to "arc cosine", or the radian measure of the arc on a circle corresponding to a given value of cosine.

Technical note: Since none of the six trig functions sine, cosine, tangent, cosecant, secant, and cotangent are one-to-one, their inverses are not functions. Each trig function can have its domain restricted, however, in order to make its inverse a function. Some mathematicians write these restricted trig functions and their inverses with an initial capital letter (e.g. Cos or Cos-1). However, most mathematicians do not follow this practice. This website does not distinguish between capitalized and uncapitalized trig functions.



See also

Inverse trigonometry, inverse trig functions, interval notation

Answer:

a) P = 2/7

b) P = 4/7

c) P = 1/7

Step-by-step explanation:

In the range of [2,8], we have the following integers which are: 2, 3, 4, 5, 6, 7, 8. So this is a total of 7 integers.

a) We look for the probability that the numbers are less than 4, so we conclude that there are possible numbers 2 and 3 out of possible 7, so the required probability is equal to P = 2/7.

b) We look for the probability that the numbers are greater than 4, so we conclude that there are possible numbers 5, 6, 7, 8 out of possible 7, so the required probability is equal to P = 4/7.

c) Based on the previous two examples, we conclude that the required probability is P = 2/7· 1/2=1/7.

Answer:

she should beat a speed of  v₂ = 6.04 m/s in order to win the competition

Step-by-step explanation:

Since the momentum p is defined as

p = m*v

where

m= mass of the ball

v= velocity of the ball

denoting 1 and 2 as the first and second bowler , then to reach the momentum of the first bowler

p₂=p₁

therefore

m₁*v₁ = m₂*v₂

v₂ = v₁ * (m₁/m₂)

replacing values

v₂ = v₁ * (m₁/m₂) =8.6 m/s * (4.5 kg/6.4 kg ball) = 6.04 m/s

then since the momentum p = m*v increases with increasing v (at constant m)  , she should beat a speed of  v₂ = 6.04 m/s in order to win the competition

Answer:

The answer is the last one

Step-by-step explanation:

Answer:

Step-by-step explanation:

X= 11/tan17

Where tan17= 3.494

Therefore, X = 3.148

Since obtuse angles are greater than 90 degrees and acute angles are less than 90 degrees, then obtuse angles have greater measures than acute angles.

Happy to help

Answer:

Step-by-step explanation:

obtuse angles >90

acute angles <90

Answer:

The correct option is c.

can be very confident; it will be close, but it probably won’t be exact.

Step-by-step explanation:

Correlation coefficient r lies between -1 and +1 , if r is close to +1 the variables compared are highly positively correlated. If r is close to -1 then the variables compared are highly negatively correlated. If r is close to zero then the correlation between the variables compared is low. If r=0 then the variables compared do not correlate at all.

The closer the correlation coefficient is to +1, the better the prediction.

Therefore since r=0.793 , the correlation coefficient is close to +1 , it means there is a highly positive correlation between variables. Therefore the correct option is c. If r is exactly +1 then we can say without any shadow of doubt that the prediction will be perfect.

Answer: Nominal

Step-by-step explanation:

A categorical variable whose values are purely qualitative and unordered is called a Nominal variable. Nominal variables are qualitative variables that does not have a particular rank, order or value. An example of nominal variables are colour (red,blue etc), gender (male, female), skin and hair colour etc.

Answer:

The answer to your question is letter C

Step-by-step explanation:

Equations

                             x  +  4y  =  10

                           5x + 10y  = 20

Process

1.- Substitute all the options in both equations and evaluate them

a) x = 3, y = 2              This option is incorrect

           (3) +  4(2)  =  10             3 + 8 = 10         11 ≠ 10

         5(3) + 10(2)  = 20           15 + 20 = 20      35 ≠ 20    

b) x = 2, y = -3       This option is incorrect

  (2)  +  4(-3)  =  10                  2 -12 = 10            -10 ≠ 10

  (2) + 10(-3)  = 20                   2 - 30 = 20        -28 ≠ 20

c)  x = -2, y = 3    This is the right answer

  (-2)  +  4(3)  =  10                -2 + 12 = 10            10 = 10

 5(-2) + 10(3)  = 20               -10 + 30 = 20          20 = 20

d) x = 3, y = -2               This option is incorrect

  (3)  +  4(-2) =  10                 3 - 6 = 10                 - 3 ≠ 10

 5(3) + 10(-2)  = 20              15 - 20 = 20              -10 ≠ 10

Answer:the coastline is 20000 miles.

The land boundaries are 12000 miles.

Step-by-step explanation:

The length of the entire border of the Unites States is approximately 32,000 miles.

5/8 of the entire length is the coastline. It means that the length of the coastline of the U.S would be

5/8 × 32000 = 20000 miles.

Therefore, the length of the boundaries of the US would be

32000 - 20000 = 12000 miles.

Answer: the speed with which the car strikes the tree is 27.025 m/s

Step-by-step explanation:

We would apply Newton's equation of motion. It is expressed as

S = ut + 1/2at²

Where

S represents the distance covered by the car

u represents the initial velocity of the car( the speed with which the car strikes the tree)

t represents the time taken to cover the distance

a represents the deceleration of the car.

From the information given,

S = 62.9 meters

a = - 5.65 m/s2

t = 4 seconds

Therefore

62.9 = u × 4 + 1/2 × - 5.65 × 4²

62.9 = 4u - 45.2

4u = 62.9 + 45.2

4u = 108.1

u = 108.1/4 = 27.025 m/s

Final answer:

The car's speed at the moment it strikes the tree, after decelerating with an acceleration of -5.65 m/s² for 4.00 seconds over a distance of 62.9 m, is calculated to be 22.6 m/s.

Explanation:

The question relates to the final speed of a car after it has been decelerating over a certain distance due to the driver applying the brakes. With an acceleration of −5.65 m/s² over a time period of 4.00 seconds, and the car making skid marks 62.9 m long, we are tasked with determining the speed at which the car eventually hits the tree.

To solve this problem, we first calculate the initial speed of the car before it started to decelerate. We use the kinematic equation: v = u + at, where 'v' is the final velocity (0 m/s, since the car eventually stops), 'u' is the initial velocity, 'a' is the acceleration, and 't' is the time. Rearranging this equation to solve for 'u', we get u = v - at. Substituting the given values, we find that the initial velocity 'u' was 22.6 m/s.

However, to find the speed at which the car hits the tree implies we need to know the speed at a specific point before it comes to a complete stop, specifically at the end of the 62.9 m distance. For this, considering the constant deceleration, the car's speed when it strikes the tree can be considered to be the same as its speed just before deceleration, which is calculated to be 22.6 m/s.

Answer:

d. An additional month of buying and selling is associated with an additional $417 in profits.

Step-by-step explanation:

We have general form of intercept form of equation:

y = m*x + c ----- (A)

Given equation is : y = 2502 + 417*x

Rewrite equation: y = 417*x + 2502 ------(B)

comparing equation (B) with equation (A), we get

m = 417 (additional benefits per month) because multiplied factor x is the month.

Final answer:

The slope in Rick's linear model represents an additional profit of $417 for each additional month of buying and selling antiques, making option d correct.

Explanation:

Rick's linear model for his profits from buying and selling antiques is given by the equation y = 2,502 + 417x, where x represents time in months and y represents his total profits in dollars. The coefficient of x in this equation, which is 417, represents the slope of the line.

In this context, the slope indicates that for each additional month of buying and selling antiques, Rick's profits are expected to increase by $417. Therefore, the correct interpretation of the slope is that an additional month of buying and selling is associated with an additional $417 in profits, making option d the correct answer.

Answer:

b. 0.027

Step-by-step explanation:

We have been given that the Masterfoods Company says that before the introduction of purple, yellow candies made up 20% of their plain candies, red another 20%, and orange, blue and green each made up 10%.

Probability of a yellow candy would be 0.20 and probability of a red candy would be 0.20.

Probability of orange candy would be 0.10, probability of blue candy would be 0.10 and probability of green candy would be 0.10.

The probability of brown candy would be [tex]1-0.20-0.20-0.10-0.10-0.10=0.30[/tex]

To find the probability that three candies are all Brown, we will use multiplication rule of independent events as:

[tex]0.30\times 0.30\times 0.30=0.027[/tex]

Therefore, the probability that that three candies are Brown would be 0.027 and option 'b' is the correct choice.

The probability that they are all Brown is option b. 0.027.

The probability of brown candy should be

= 1-0.20 -0.20 -0.10 - 0.10-0.10

= 0.30

Now

the probability should be

[tex]= 0.3^3[/tex]

= 0.027

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Answer:

The rate the swimming pool is filled is 9 gallons of water per minute

Step-by-step explanation:

Let's review the information provided by Ronald to us to help him to find the answer to the question:

Time it takes to fill the swimming pool = 8 minutes

Amount of water the swimming pool can hold = 72 gallons

2. At what rate does the swimming pool fill, in gallons per minute?

Rate the swimming pool is filled = Amount of water the swimming pool can hold /Time it takes to fill the swimming pool

Replacing with the real values, we have:

Rate the swimming pool is filled = 72/8 = 9 gallons of water per minute

Answer:a) {(a,b)[a is required to read book b or has read book b]}

b) {(a,b)[a has read book b that he was required to read)]

c) {(a,b)[a is either required to read book b or has read it but he has not read both)]

d) {(a,b)[a is required to read book b and he is yet to read book b)]

e) {(a,b)[a has read book b that was not required)]

Step-by-step explanation: The answers is a description of the explanation

The question asks about various operations with the sets R₁ and R₂, which represent the students and the books they are required to read and have read respectively. It looks at the union, intersection, symmetric difference, and difference of these two sets in relation to each other, where variables 'A' and 'B' represent a student and a book respectively.

This is a question in set theory. We will be defining the different operations performed on the ordered pairs of two relations R₁ and R₂. Let's consider 'A' as a student studying in your school and 'B' be a book in the library, the ordered pairs (A, B) indicate the relationship between the student and the book.

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Answer: 15/16

Step-by-step explanation:

There will be 16 outcomes for 4 coins=2^4

Probability of only head is : P(C)=1/16

P(C) + P(C') = 1

P(C') = 1 - P(C)

P(C') = 1 - 1/16

Take the l.c.m

P(C') = (16-1) / 16

P(C') = 15/16

So the probability of getting at least 1 tail is 15/16

Answer:

D 0.94

Step-by-step explanation:

when solved the answer is 15/16. This equals 0.9375 which rounded to the second decimal  = 0.94

Answer:

There are 8 nickels, and 20 dimes.

Brian has 20 dimes and 8 nickels in his coin box.

Let's make a system of equations to solve this problem. Let's assume the number of dimes is 'x', then the number of nickels would be 'x - 12' since Brian has 12 fewer nickels than dimes.

The value of dimes in cents is 'x * 10', and the value of nickels in cents is '(x - 12) * 5'. We can write the equation: '10x + 5(x - 12) = 240' since the total value is $2.40 or 240 cents.

Simplifying the equation, we get '10x + 5x - 60 = 240'. Combining like terms, we have '15x - 60 = 240'. Adding 60 to both sides, we get '15x = 300'. Dividing both sides by 15, we get 'x = 20'.

Therefore, Brian has 20 dimes and 20 - 12 = 8 nickels.

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Answer:

Step-by-step explanation:

1) The equation of a line is given by y = mx + c, where m = slope or gradient and c is intercept on y - axis. Given in this question, m = -5 and c = 3. Subtituting this in the equation y = mx + c, we have y = -5x + 3, therefore, the equation of the line is y = -5x + 3 or y + 5x = 3

2) The equation of a line is given as y-y1 = m(x-x1), where x1 = 6, y1 = -4 and m = -1/3. The equation of the line is y - -4 = -1/3(x - 6)

   y+4 =-1/3(x-6)

  3(y+4)= -1(x-6)

  3y + 12 = -x+6

  x+3y=6-12

   x+3y= -6, therefore the equation of the line is x+3y = -6

3) The equation is y-y1=m(x-x1), where m=(y2-y1)/(x2-x1)=

(2- -4)/(-2-0)=6/-2=-3

     y- -4= -3(x-0)= -3x

    y+4= -3x

     y+3x= -4

4) y-y1=m(x-x1)    

  m=(2-1) /(-4- -6)=1/2

  y-1=1/2(x- -6)

  y-1=1/2(x+6)

 2(y-1) = x+6

 2y-2=x+6

2y-x =6+2=8     2y-x=8

5) The equation is with undefined slope passing through (2, 5) is

       x-2=0

       x=2

Answer:

[tex]sin ( u +\frac{\pi}{2} ) = cos (u)[/tex]

Step-by-step explanation:

Let us use the identity

sin(A+B)=  cos(A) sin(B)+cos (B) sin(A) to simplify the given expression

Then

[tex]sin(u + \frac{\pi}{2})= \cos \left(u\right)\sin \left(\frac{\pi }{2}\right)+\cos \left(\frac{\pi }{2}\right)\sin \left(u\right)[/tex]--------------------(1)

Here

[tex]cos (\frac{\pi}{2}) = 0\\[/tex]---------------------(2)

[tex]sin(\frac{\pi}{2})= 1[/tex]---------------------(3)

Substituting the values  in (1)

[tex]sin(u + \frac{\pi}{2})= \cos \left(u\right)(1)+(0)\sin \left(u\right)[/tex]

[tex]sin(u + \frac{\pi}{2})= \cos \left(u\right) + 0[/tex]

[tex]sin(u + \frac{\pi}{2})= \cos \left(u\right)[/tex]

Answer:

[tex]x^{\frac{1}{5} } = \sqrt[5]{x}[/tex]

Step-by-step explanation:

A radical expression is an expression with a variable, number, or combination of both of them under a root symbol.

A radical expression has a general form of [tex]\sqrt[n]{x}[/tex]

For the given expression [tex]x^{\frac{1}{5} }[/tex]

So, [tex]x^{\frac{1}{5} } = \sqrt[5]{x}[/tex]

[tex]x^{1/5}[/tex] in radical form is √5x.

To write the expression [tex]x^{1/5}[/tex] in radical form, we use the property of exponents where a fractional exponent represents a root. Specifically, the exponent 1/5 indicates the fifth root of the base.

Here are the steps:

Therefore, the radical form of [tex]x^{1/5}[/tex] is √5x.

The area of one trapezoidal face of the figure is 2 square inches

The dimensions of the trapezoid are given as:

The area of one trapezoidal face of the figure is the calculated using:

Area = 0.5 * (base + top side) * height

So, we have:

Area = 0.5 * (3 + 1) * 1

Evaluate

Area = 2

Hence, the area of one trapezoidal face of the figure is 2 square inches

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Answer: 2

Step-by-step explanation: