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What is the value of the expression (54+3³) ?
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Answer:

(1) Therefore, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it is [0.4348, 0.5252].

(2) We can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval

(3) A survey should include at least 3002 people if we wanted the margin of error for the 90% confidence level to be about 1.5%.

Step-by-step explanation:

We are given that a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in school, 48% said they decided not to go to college because they could not afford school.

Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;

                         P.Q.  =  \(\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }\)  ~ N(0,1)

where, \(\hat p\) = sample proportion of Americans who decide to not go to college = 48%

           n = sample of American adults = 331

           p = population proportion of Americans who decide to not go to

                 college because they cannot afford it

Here for constructing a 90% confidence interval we have used a One-sample z-test for proportions.

So, 90% confidence interval for the population proportion, p is ;

P(-1.645 < N(0,1) < 1.645) = 0.90  {As the critical value of z at 5% level

                                                        of significance are -1.645 & 1.645}  

P(-1.645 < \(\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }\) < 1.645) = 0.90

P( \(-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }\) < \(\hat p-p\) < \(1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }\) ) = 0.90

P( \(\hat p-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }\) < p < \(\hat p+1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }\) ) = 0.90

90% confidence interval for p = [ \(\hat p-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }\) , \(\hat p+1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }\) ]

 = [ \(0.48 -1.96 \times {\sqrt{\frac{0.48(1-0.48)}{331} } }\) , \(0.48 +1.96 \times {\sqrt{\frac{0.48(1-0.48)}{331} } }\) ]

 = [0.4348, 0.5252]

(1) Therefore, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it is [0.4348, 0.5252].

(2) The interpretation of the above confidence interval is that we can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval.

3) Now, it is given that we wanted the margin of error for the 90% confidence level to be about 1.5%.

So, the margin of error =  \(Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p(1-\hat p)}{n} }\)

              \(0.015 = 1.645 \times \sqrt{\frac{0.48(1-0.48)}{n} }\)

              \(\sqrt{n} = \frac{1.645 \times \sqrt{0.48 \times 0.52} }{0.015}\)

              \(\sqrt{n}\) = 54.79

               n = \(54.79^{2}\)

               n = 3001.88 ≈ 3002

Hence, a survey should include at least 3002 people if we wanted the margin of error for the 90% confidence level to be about 1.5%.

\(\bold\green{y = -}\)\( \green{\tt \dfrac{5}{9}x + 2} \)

The total amount the man had = 52,200 rupees. Out of this, he gave 21,750 rupees to his son, 13,050 rupees to his daughter, and 17,400 rupees to his wife , the total amount given away by the man = 21,750 + 13,050 + 17,400 = 52,200 rupees.

A man gave 5/12 of his money to his son, 3/7 of the remainder to his daughter, and the remaining to his wife. If his wife gets Rs. 8,700, what is the total amount?

The given problem can be solved using the concept of ratios and fractions. Let us solve the problem step-by-step.Assume the man had x rupees with him.The man gave 5/12 of his money to his son.

The remaining amount left with the man = x - 5x/12= (12x/12) - (5x/12) = (7x/12)The man gave 3/7 of the remainder to his daughter.'

Amount left with the man after giving it to his son = (7x/12)The amount given to the daughter = (3/7) x (7x/12)= (3x/4)The remaining amount left with the man = (7x/12) - (3x/4)= (7x/12) - (9x/12) = - (2x/12) = - (x/6) (As the man has given more money than what he had with him).

Therefore, the daughter's amount is (3x/4) and the remaining amount left with the man is (x/6).The man gave all the remaining amount to his wife.

Therefore, the amount given to the wife is (x/6) = 8700Let us find the value of x.x/6 = 8700 x = 6 x 8700 = 52,200

Therefore, the man had 52,200 rupees with him.He gave 5/12 of his money to his son. Therefore, the amount given to his son is (5/12) x 52,200 = 21,750 rupees.

The remaining amount left with the man = (7/12) x 52,200 = 30,450 rupees.He gave 3/7 of the remainder to his daughter. Therefore, the amount given to his daughter is (3/7) x 30,450 = 13,050 rupees.

The amount left with the man = (4/7) x 30,450 = 17,400 rupees.The man gave 17,400 rupees to his wife.
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Answer:

A) y=9x

B) y=45 when x=5

Step-by-step explanation:

Part A

\(y=kx\\-27=k(-3)\\-27=-3k\\9=k\\y=9x\)

Part B

\(y=9(5)\\y=45\)

Answer:

Round both numbers to 1 significant figure.

400+400=800

800 is the answer.

(6)^2(-2x+1)=(6)³

evaluating the power of both sides as having same base (6)

2-4x=3

2-3=4x

x=-0.25

The solution of the expression for the value of x is -0.25.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is \(36^{(-2x+1)}=216\)

The expression can be written as:-

\((6)^{(2)(-2x+1)}=(6)^3\)

Evaluating the power of both sides as having the same base (6)

2-4x = 3

2-3 = 4x

x = -0.25

Hence, the value of x is -0.25.

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Answer:

The light bulb will consume 600 watts in one day.

Step-by-step explanation:

Let us suppose the light bulb is continuously ON.

As a light bulb consumes 2700 watts an hour in 4 days and 12 hours.

4 days and 12 hours = 96 hours + 12 hours = 108 hours

So, a light bulb consumes 2700 watts in 108 hours.

Hence,

A light bulb consuming the watts per hour will be: 2700/108 = 25 watts

As a light bulb consumes 25 watts in one hour, there are 24 hours in a day.

Light bulb consuming total no of watts in a day = 25 × 24 = 600 watts

Therefore, the light bulb will consume 600 watts in one day.

2ND METHOD

4 days and 12 hours = 4.5 days

Total no of watts cosumed by a light bulb in 4.5 days = 2700 watts

so

Total number watts consumed in a day = 2700 / 4.5 = 600 watts.

Therefore, the light bulb will consume 600 watts in one day

Answer:

x = ±2

Step-by-step explanation:

log 7 (x^2 + 11) = log 7 15

We know that log a ( b) = log a(c)   means b =c

x^2 + 11 = 15

Subtract 11 from each side

x^2 = 15-11

x^2 =4

Take the square root of each side

sqrt(x^2) =±sqrt(4)

x = ±2

The equivalent expression are;

\((\sqrt[7]{x} )^4\)

\((x^4)^1^/^7\)

Option A and B

Index forms are simply described as mathematical forms that are used in the representation of numbers or variables that are too large or too small in more convenient forms.

These index forms are also known as standard forms or scientific notation.

Some rules of index forms are;

From the information given, we have that;

(x)4/7

Find the seventh root of the variable

\((\sqrt[7]{x} )^4\)

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Answer:

Step-by-step explanation:

The triangles are similar.

x/(x+4) = 7.2/12

x/(x+4) = 0.6

x = 0.6(x+4)

0.4x + 2.4

x = 6

Answer:

x = 16

Step-by-step explanation:

subtract 12 from both sides to isolate the variable and its coefficient

4x = 64

divide both sides by 4 to get x

x = 16

Answer:

x = 16

Step-by-step explanation:

4x+12=76

Step 1: Subtract 12 from both sides.

4x + 12 - 12 = 76 - 12

4x = 64

Step 2: Divide both sides by 4.

\(\frac{4x}{4} = \frac{64}{4}\)

x = 16

Answer:

(-2, 3 )

(-1, 2\(\frac{1}{2}\))

(0, 2)

(1, 1\(\frac{1}{2}\))

(2, 1)

Step-by-step explanation:

You just simply substitue the values given into the equation, and the answer worked out will be the value of y.

a = - \(\frac{1}{2}\) × -2 + 2 = 1 + 2 = 3

b = - \(\frac{1}{2}\) × -1 + 2 = \(\frac{1}{2}\)  + 2 = 2\(\frac{1}{2}\)

c =  -\(\frac{1}{2}\) × 0 + 2 = 0 + 2 = 2

d = -\(\frac{1}{2}\) × 1+ 2 =  -\(\frac{1}{2}\)  + 2 = 1\(\frac{1}{2}\)

e = -\(\frac{1}{2}\) × 2+ 2 = -1 +2 = 1

Hope this helps you :)

Answer:

5

Step-by-step explanation:

Step 1:

3x + 4 = 19

Step 2:

3x = 19 - 4

Step 3:

3x = 15

Answer:

x = 5

Hope This Helps :)

well, he has left only 6 oz.

now, if we take the 16(origin amount) to be the 100%, what is 6 off of it in percentage?

\(\begin{array}{ccll} amount&\%\\ \cline{1-2} 16 & 100\\ 6& x \end{array} \implies \cfrac{16}{6}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 8 }{ 3 } ~~=~~ \cfrac{ 100 }{ x }\implies 8x=300\implies x=\cfrac{300}{8}\implies x=\cfrac{75}{2}\implies x=37.5\)

Answer:

a) Equation for Snow Dome Ski Resort:

\(I_s = 65+t\)

Equation for Mt. Winterpark Ski Resort:

\(I_m = 74+\frac{t}{2}\)

b) After 19 hours, Snow dome will have more snow.

Step-by-step explanation:

Given that:

Initial snow at Snow Dome Ski Resort = 65 inches

Snowing rate at Snow Dome Ski Resort = 1 inch per hour

Initial snow at Mt. Winterpark Ski Resort = 74 inches

Initial snow at Mt. Winterpark Ski Resort = \(\frac{1}{2}\) inch per hour

a) To write equations that show amount of snow at each resort.

Let the time in hours be represented by \(t\).

Snow increased in \(t\) hours by snowing at Snow Dome Ski Resort = \(1\times t = t\) inches per hour

Snow increased in \(t\) hours by snowing at Mt. Winterpark Ski Resort = \(\frac{1}{2}\times t = \frac{t}{2}\) inches per hour

Equation for Snow Dome Ski Resort:

\(I_s = 65+t\)

Equation for Mt. Winterpark Ski Resort:

\(I_m = 74+\frac{t}{2}\)

b) Time at which Snow Dome has more snow.

Using the above equations, we can write the following inequality:

\(65+t>74+\dfrac{t}{2}\\\Rightarrow t-\dfrac{t}{2}>74-65\\\Rightarrow \dfrac{t}{2}>9\\\Rightarrow t>18\ hours\)

After 18 hours have passed, they will have equal amount of snow.

After 19 hours, Snow dome will have more snow.

Answer:

D.

Step-by-step explanation:

1) the domain is x∈[0;+∞);

2) the solution is:

\(\sqrt{x}\leq 10; \ => \ x\leq 100;\)

3) finally, the solution with the domain is:

x∈[0;100].

Answer:

-17

Step-by-step explanation:

–3(y + 2)2 – 5 + 6y

(–3y -6)2 – 5 + 6y

-6y -12 - 5 + 6y

-17

Answer:

it is b, 42 units² I'm sure

In the proportion (5x + 1):3 = (2x + 2):7, the value of x is -1/29.

In the proportion (6x):(4x) = 7, there is no value of x that satisfies the proportion.

To find the value of x in the given proportions, let's solve them one by one:

(5x + 1) : 3 = (2x + 2) : 7

To solve this proportion, we can cross-multiply:

7(5x + 1) = 3(2x + 2)

35x + 7 = 6x + 6

Subtracting 6x from both sides and subtracting 7 from both sides:

35x - 6x = 6 - 7

29x = -1

Dividing both sides by 29:

x = -1/29

Therefore, the value of x in the first proportion is -1/29.

(6x) : (4x) = 7

To solve this proportion, we can simplify the left side:

6x / 4x = 7

Dividing both sides by 2x:

3/2 = 7

This equation is not true, as 3/2 is not equal to 7.

Therefore, there is no value of x that satisfies the second proportion.

In summary, the value of x in the proportion (5x + 1) : 3 = (2x + 2) : 7 is -1/29, and there is no value of x that satisfies the proportion (6x) : (4x) = 7.

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Answer:u3

\

Step-by-step explanation:

69

The value of function f (4) is,

⇒ f (4) = 19

We have to given that;

The function is,

⇒ f (x) = x² + 3

Now, WE can find the value of f (4) by substitute x = 4 in above function as,

⇒ f (x) = x² + 3

Plug x = 4;

⇒ f (4) = 4² + 3

⇒ f (4) = 16 + 3

⇒ f (4) = 19

Thus, The value of function f (4) is,

⇒ f (4) = 19

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Answer:

Second option

Step-by-step explanation:

In a case whereby the metal piece has four ridges of equal size on the top. The width of the piece is 3cm the volume of the work is \(450cm^3\)

Based on the provided fiqure, we will need to find te volume of the rectangle, then substract from th volume of the four triangular prism

The volume of the rectangle can be epresed as ;

2*3*10 = \(600cm^3\)

The volume of the four triangular prism can be expressed as

20/4 = 5cm          10-5= 5cm

\(1/2 * 5 * 5*3*4 = 150cm^3\)

\(600- 150 =450 cm^3\)

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-4x^2-28x-68

hope this helped!

Step-by-step explanation:

Hello, there!!!

The answer is: -4x^2-28x-68.

See explanation in picture.

Hope it helps...

The slope of the given lines are representing that these lines are perpendicular.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given, the pair of the equation are parallel, perpendicular, or neither y=-7/8x-1, 32x-28y=-36

Slope intercept form of both equations of a line

1)  y = -7/8x - 1

it is already in a slope intercept form

2) 32x - 28y = -36

-28y = -32x -36

y = 8/7x + 9/7

Since their slope is inverse and had a negative constant.

The slope of a perpendicular line from the slope of a given line is obtained by taking the negative reciprocal of the slope of the given line. If the slope of the given line is m1 and the slope of a perpendicular line is m2 then we have m2 = -1/m1.

Therefore, The slope of the given lines are representing that these lines are perpendicular.

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The quotient of the expressions −48.132 and −0.84 will be 57.30. Then the correct option is C.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Division means the separation of something into different parts, sharing of something among different people, places, etc.

Given −48.132 ÷ −0.84.

Then the value of the expression will be

⇒ −48.132 / −0.84

If in the numerator and the denomination, the negative sign is present, then both will cancel out each other.

⇒ 48.132 / 0.84

⇒ 57.30

The quotient of the expressions −48.132 and −0.84 will be 57.30.

Then the correct option is C.

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The calculated value of the rate of the graph is 0.8

from the question, we have the following parameters that can be used in our computation:

The graph

Where, we have

(0, -16) and (20, 0)

The rate of the graph is calculated as

Rate = Change in y/x

using the above as a guide, we have the following:

Rate = (0 + 16)/(20 - 0)

Evaluate

Rate = 0.8

Hence, the rate is 0.8

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Answer:

83 kilometres per hour =

51.574 miles per hour