Twice a number plus eight times a second number is 19. Five times the first number plus seven times the

1000 tickets were bought at a concert. the amount needed to buy a children’s ticket was $4.50 and the amount needed for an adult

Sholpan [36]

Answer:

The number of children's tickets bought was 300 and the number of adult tickets bought was 700

Step-by-step explanation:

Let

x ----> the number of children's tickets bought

y ----> the number of adult tickets bought

we know that

$x+y=1,000$

$x=1,000-y$ -----> equation A

$4.50x+8.50y=7,300$ -----> equation B

Solve the system by substitution

substitute equation A in equation B

$4.50(1,000-y)+8.50y=7,300$

solve for x

$4,500-4.50y+8.50y=7,300$

$4y=7,300-4,500$

$4y=2,800$

$y=700$

<em>Find the value of x</em>

$x=1,000-700=300$

therefore

The number of children's tickets bought was 300 and the number of adult tickets bought was 700

6 0

3 years ago

What is the answer to <br> 3/2x - 5 = y

77julia77 [94]

Answer:

$x = \frac{2y + 10}{3}$

$y = \frac{3}{2}x -5$

Step-by-step explanation:

Hope this helps!

6 0

3 years ago

In a primary school class, the ratio of boys to girls is 3:4. If there are 12 girls in the class, what is the total number of st

AfilCa [17]

Answer:

21

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Find the lateral and surface area of each cone

Sophie [7]

Answer:

$\large\boxed{L.A.=153\pi\ mm^2}\\\boxed{S.A.234\pi\ mm^2}$

Step-by-step explanation:

The formula of a lateral area of a cone:

$L.A.=\pi rl$

r - radius

l - slant height

The formula of a surface area of a cone:

$S.A.=\pi r^2+\pi rl$

We have r= 9mm and l = 17mm. Substitute:

$L.A.=\pi(9)(17)=153\pi\ mm^2$

$S.A.=\pi(9^2)+153\pi=81\pi+153\pi=234\pi\ mm^2$

7 0

3 years ago

A regression was run to determine if there is a relationship between the happiness index (y) and life expectancy in years of a g

Natasha2012 [34]

Answer:

(A) $y=-0.762+0.119x$

(B) If a country increases its life expectancy, the happiness index will increase.

(C) If the life expectancy is increased by 3.5 years in a certain country, the happiness index will increase by 0.4165.

(D) If the life expectancy is 67 years in a certain country, the happiness index will be 7.21.

Step-by-step explanation:

A regression analysis was performed to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x).

The output of the regression analysis are as follows:

a = -0.762

b = 0.119

r² = 0.8649

r = 0.93

(A)

The equation of the Least Squares Regression line of the form y = _ + _ x is:

$y=-0.762+0.119x$

(B)

The correction between the variables happiness index (y) and life expectancy in years of a given country (x) is, 0.93.

The correlation coefficient is positive. This implies that there is a positive relation between the two variables, i.e. as the value of life expectancy in years increases the happiness index also increases.

Thus, if a country increases its life expectancy, the happiness index will increase.

(C)

Compute the value of y for x = x + 3.5 as follows:

$y=-0.762+0.119x$

$=-0.762+0.119\times (x+3.5)\\\\=(-0.762+0.119x)+0.4165\\\\=y+0.4165$

Thus, if the life expectancy is increased by 3.5 years in a certain country, the happiness index will increase by 0.4165.

(D)

Compute the value of y for x = 67 as follows:

$y=-0.762+0.119x$

$=-0.762+0.119\times 67\\\\=-0.762+7.973\\\\=7.211\\\\\approx 7.21$

Thus, if the life expectancy is 67 years in a certain country, the happiness index will be 7.21.

6 0

4 years ago