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2 years ago

A square has a perimeter of 12x + 52 units. Which expression represents the side length of the square in units?

Mathematics

2 answers:

SVEN [57.7K]2 years ago

8 0

Answer:

3x+13

Step-by-step explanation:

Xelga [282]2 years ago

3 0

Answer:

Option (3) is correct.

side length of square is (3x + 13 ) units.

Step-by-step explanation:

For a square with side 'a'. Perimeter is defined as the sum of length of side. Since, Square has four sides. Thus Perimeter of square = 4 × side

Given square has perimeter = 12x + 52

Comparing both sides,

4 × side = 12 x + 52

⇒ Side = $\frac{12x+52}{4}$

⇒ Side = $\frac{4(3x+13)}{4}$

⇒ Side = 3x + 13

Thus, side length of square is (3x + 13 ) units.

Thus, option (3) is correct.

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Suppose that you want to mix two coffees in order to obtain 100 pounds of a blend. If x represents the number of pounds of coffe

Svetach [21]

Answer: $100-x$

Therefore, the algebraic exp

Step-by-step explanation:

Given : x represents the number of pounds of coffee A.

The total weight of the mix of coffee A and coffee B = 100 pounds.

Then , we have the following expression to represents the number of pounds of coffee B:-

$100-x$

Therefore, the algebraic expression that represents the number of pounds of coffee B. :-

$100-x$

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2 years ago

Among a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in

Hitman42 [59]

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%.

5 0

2 years ago

What number is represented by 4x²+17x+2 if x=10?

Fynjy0 [20]

Answer:

at x = 10, $4x^{2} + 17x + 2 = 572$

Step-by-step explanation:

The given equation is $4x^{2} + 17x + 2$

Here, lets substitute the value of x = 10

So, the equation simplifies to ,

$4 \times (10)^{2} + 17(10) + 2$

= (4 x 100) + 170 + 2 = 400 + 170 + 2

= 572

So, at x = 10, $4x^{2} + 17x + 2 = 572$

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1 year ago

Of the 100 students enrolled at the dance studio, 50 take ballet and 24 take tap dancing. Eight of the students who take ballet

Soloha48 [4]

Answer:

42 over 100

Step-by-step explanation:

8 0

2 years ago

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Which is a zero of the quadratic function f(x) = 16x2 32x − 9?

tankabanditka [31]

A zero of a function is the value of x for which f(x) = 0
f(x) = 16x^2 + 32x - 9 = 0
16x^2 - 4x + 36x - 9 = 0
(16x^2 - 4x) + (36x - 9) = 0
4x(4x - 1) + 9(4x - 1) = 0
(4x + 9)(4x - 1) = 0
4x + 9 = 0 and 4x - 1 = 0
4x = -9 and 4x = 1
x = -9/4 and x = 1/4

8 0

2 years ago

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