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3 years ago

what is the equation of a line in slope-intercept form for a line with slope = 1/4 and y-intercept at (0,-1)

Mathematics

1 answer:

Nadya [2.5K]3 years ago

3 0

Answer:

y = (1/4)x - 1

Step-by-step explanation:

Start with the general slope-intercept form: y = mx + b. Subst. -1 for b and (1/4) for m. Then,

y = (1/4)x - 1

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the length of a rectangle is 5 times as long as its breadth and its area is 1620 m² find area of square whose perimeter is equal

Rus_ich [418]

Answer:

Area of the square is 2916 $m^{2}$ .

Step-by-step explanation:

Let the breadth of the rectangle be represented by w. So that;

length of rectangle = 5w

Area of rectangle = length x breadth

= 5w x w

1620 = 5 $w^{2}$

divide through by 5 to have,

$w^{2}$ = 324

w = $\sqrt{324}$

= 18

Thus, the breadth of the rectangle is 18 m.

length = 5 w = 5 x 18

= 90 m

The length of the rectangle is 90 m.

Perimeter of the rectangle = 2(l + w)

= 2( 90 + 18)

= 216 m

Perimeter of a square = 4l

where l is the length of its side.

Given that the perimeters of the rectangle and square are equal, then;

4l = 216

l = $\frac{216}{4}$

= 54

length of the side of square is 54 m.

Therefore,

Area of square = $l^{2}$

= $54^{2}$

= 2916

Area of the square whose perimeter is equal to that of the rectangle is 2916 $m^{2}$ .

6 0

3 years ago

The intelligence quotient (iq) test scores for adults are normally distributed with a mean of 100 and a standard deviation of 15

Mrrafil [7]

<span>0.9818 is the answer </span>

3 0

3 years ago

I understand some of this but this ones got me stumped i tried pemdas but im still lost

Mandarinka [93]

Just replace $x$ with its given value:

$9x^{2}-4x-3~~~~\text{where }x=-2\\ \\ \\ 9\cdot (-2)^{2}-4\cdot (-2)-3\\ \\ =9\cdot 4+8-3\\ \\ =36+8-3\\ \\ =41$

6 0

3 years ago

A researcher wishes to estimate the proportion of adults who have high-speed Internet access. What size sample should be obtain

Kamila [148]

Answer:

Step-by-step explanation:

Solution:-

- The sample size = n

- The Error of estimation, E = 0.04

- The confidence level, CI = 99%

What size sample should be obtained when she uses previous estimate of p = 0.52?

- We are given the sample proportion p = 0.52, the required sample size is a function of confidence value and error of estimation (E):

$n = p*( 1 - p ) * (\frac{Z-critical}{E})^2$

Where,

- The critical value of the confidence level = 99% would be:

significance level ( α ) = 1 - CI = 1 - 0.99 = 0.01

Z-critical = Z_α/2 = Z_0.005 = 2.575

- The required sample size (n) can be calculated:

$n = 0.52*( 1 - 0.52 ) * (\frac{2.575}{0.04})^2\\\\n = 0.2304*(51.5)^2 = 611.0784$

- Hence, the minimum required sample size (n) should be = 612 adults.

- If the preliminary estimate of proportion is missing or not given, we are to assume the proportion p = 0.5.

- Similarly, repeat the calculations for sample size (n) when p = 0.5

$n = 0.5*( 1 - 0.5 ) * (\frac{2.575}{0.04})^2\\\\n = 0.25*(51.5)^2 = 663.0625$

- Hence, the minimum required sample size (n) should be = 664 adults.

5 0

3 years ago

Please help.........................

Snezhnost [94]

Answer:

y = 114

Step-by-step explanation:

n + x = y

n - 20 = 85

n = 105

x=9

105 + 9 = 114

3 0

3 years ago

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