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bagirrra123 [75]

2 years ago

9

Which ordered pair is the solution to the system of equations?

1 answer:

r-ruslan [8.4K]2 years ago

8 0

Step-by-step explanation:

y = 2x - 15

4x + 3y = -5

4x + 3(2x - 15) = -5

4x + 6x - 45 = -5

10x = 40

x = 40/10

x = 4

y = 2x - 15

y = 2(4) - 15

y = 8 - 15

y = -7

Solution = (4,-7)

Option → C

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A car travels 2 1/3 miles in 3 1/2 minutes at a constant speed. Write an equation to represent the car travels in miles and minu

Flura [38]

Answer:

The speed of car in miles per minute is $\frac{2}{3}$ miles per minute and

The speed of car in mile per hour is 40 miles per hour,

Step-by-step explanation:

Given as :

The distance cover by car = 2 $\frac{1}{3}$ = $\frac{7}{3}$ miles

The Time taken by car to cover distance = 3 $\frac{1}{2}$ min = $\frac{7}{2}$ min

The speed o car in miles per minute = S miles/min

So, Speed = $\dfrac{\textrm Distance}{\textrm Time}$

Or, S = $\frac{\frac{7}{3}}{\frac{7}{2}}$ mie per min

∴ S = $\frac{2}{3}$ miles per minute

Now, Let The speed of car in miles per hour = x miles/h

So, Time in hour = $\frac{7}{2}$ × $\frac{1}{60}$ = $\frac{7}{120}$ hours

So , Speed = $\dfrac{\textrm Distance}{\textrm Time}$

Or, x = $\frac{\frac{7}{3}}{\frac{7}{120}}$ miles per hours

Or, x = 40 miles per hours

Hence The speed of car in miles per minute is $\frac{2}{3}$ miles per minute and the speed of car in mile per hour is 40 miles per hour, answer

7 0

3 years ago

The amount of money spent on textbooks per year for students is approximately normal.

Ostrovityanka [42]

Answer:a

a

$336.04 < \mu < 443.96$

b

The margin of error will increase

c

The margin of error will decreases

d

The 99% confidence interval is $0.4107 < p < 0.4293$

Step-by-step explanation:

From the question we are told that

The sample size $n = 19$

The sample mean is $\= x = \$\ 390$

The standard deviation is $\sigma = \$ \ 120$

Given that the confidence level is 95% then the level of significance is mathematically represented as

$\alpha = 100 - 95$

$\alpha = 5 \%$

$\alpha = 0.05$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table

So

$Z_{\frac{\alpha }{2} } = 1.96$

The margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }$

=> $E = 1.96 * \frac{120}{\sqrt{19} }$

=> $E = 53.96$

The 95% confidence interval is

$\= x - E < \mu < \= x + E$

=> $390 - 53.96 < \mu < 390 - 53.96$

=> $336.04 < \mu < 443.96$

When the confidence level increases the $Z_{\frac{\alpha }{2} }$ also increases which increases the margin of error hence the confidence level becomes wider

Generally the sample size mathematically varies with margin of error as follows

$n \ \ \alpha \ \ \frac{1}{E^2 }$

So if the sample size increases the margin of error decrease

The sample proportion is mathematically represented as

$\r p = \frac{210}{500}$

$\r p = 0.42$

Given that the confidence level is 0.99 the level of significance is $\alpha = 0.01$

The critical value of $\frac{\alpha }{2}$ from the normal distribution table is

$Z_{\frac{\alpha }{2} } = 2.58$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} }* \sqrt{ \frac{\r p (1- \r p )}{n} }$

=> $E = 0.42 * \sqrt{ \frac{0.42 (1- 0.42 )}{ 500} }$

=> $E = 0.0093$

The 99% confidence interval is

$\r p - E < p < \r p + E$

$0.42 - 0.0093 < p < 0.42 + 0.0093$

$0.4107 < p < 0.4293$

4 0

3 years ago

Name ALL the sets of numbers to which -28 belongs.

miv72 [106K]

A. integers, c. integers rationals, and d. integers rationals reals. it would not be a natural number, because a natural number is a positive number (and sometimes 0)

7 0

3 years ago

Factor -8m^3n^3+2m^5+2m^3

Arada [10]

−

2

m

3

out of

−

8

m

3

n

3

+

2

m

5

+

2

m

3

.

−

2

m

3

(

4

n

3

−

m

2

−

1

)

7 0

3 years ago

A right cone has radius 9cm and slant height 12cm. The radius and slant height are both multiplied by 2/3. Which of the followin

Olegator [25]

Answer:

<em>The surface area is multiplied by 4/9.</em>

Step-by-step explanation:

<u>Surface Area of a Cone</u>

Being r the radius and l the slant height of a cone, then its surface area is

$SA=\pi r^2+\pi r l$

Now let's think both the radius and the slant height are multiplied by the same factor k, i.e.

r'=kr

l'=kl

The new surface area is

$SA'=\pi r'^2+\pi r' l'=\pi (kr)^2+\pi \cdot kr\cdot kl=k^2\pi r^2+k^2\pi rl$

$SA'=k^2(\pi r^2+\pi rl)=k^2\cdot SA$

The new surface area is the $k ^2$ times original SA. Since k=2/3, then

$SA'=4/9\ SA$

The surface area is multiplied by 4/9.

6 0

3 years ago