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2 years ago

If x varies directly with y and y is 10 when x is 8, what is x when y is 18?

2 answers:

swat322 years ago

5 0

Knowing that x varies directly with y, we know the basic skeleton of the equation is y = mx.

To find m, plug in the known coordinate (8,10), where the x-coordinate is 8 and the y-coordinate is 10.
$y=mx \\ 10=m8 \\ (10)/8=(8m)/8 \\ m= \frac{10}{8} = \frac{5}{4}$

Then, plug in m to the equation to get y = (5/4)x.

Finally, plug in the y-coordinate 18 to the equation and solve for x!
$y= \frac{5}{4}x \\ 18= \frac{5}{4}x \\ \frac{4}{5}(18)=( \frac{5}{4}x) \frac{4}{5} \\ x= \frac{4*18}{5} \\ x= \frac{72}{5}$

Your exact answer is x = 72/5. However, if your teacher prefers decimals, then x = 14.4

Hope this helps!

Vesnalui [34]2 years ago

3 0

y varies directly with x
y=kx
10=k(15)
k=10/15
y=(10/15)x
when x=6
y=(10/15)(6)=60/15=4
x varies inversely as y
x=k/y
2=k/8
k=16
x=16/y
when y=17

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What is the first step to solve the following system of equations using substitution?

Akimi4 [234]

Answer:

Step 1: Solve one of the equations for one of the variables. Let's solve the first equation for x

Thus, option A) is true.

The solution to the system of equations be:

$x = 4, y = 5$

Step-by-step explanation:

It is important to remember that when we solve the system of equations, the first step we need to do is to solve one of the equations for one of the variables.

Given the system of equations

$x - y = -1$

$2x - y = 3$

Step 1: Solve one of the equations for one of the variables. Let's solve the first equation for x

$x-y=-1$

Add y to both sides

$x-y+y=-1+y$

$x=-1+y$

Thus, option A) is true.

<u>NOW LET US SOLVE THE REMAINING PORTION</u>

$\mathrm{Subsititute\:}x=-1+y$ to solve for y

$\begin{bmatrix}2\left(-1+y\right)-y=3\end{bmatrix}$

$-2+y=3$

$y=5$

For x = -1 + y

substitute y = 5

$x=-1+5$

$x=4$

Thus, the solution to the system of equations be:

$x = 4, y = 5$

3 0

2 years ago

One sixth of fifty four

marissa [1.9K]

1/6 x 54 = 9
Hope this helps ;)

8 0

2 years ago

Worth 12 points and please actually help me

Alekssandra [29.7K]

Answer:

(-3,0)

Step-by-step explanation:

Step 1 identify coordinates of A

The coordinate of A is (-6 , 2)

Step 2 apply translation by adding 3 to the x value and subtracting 2 from the y value

(-6 + 3 , 2 - 2)

Simplify

(-3 , 0)

6 0

2 years ago

According to the World Health Organization (WHO) Child Growth Standards, the head circumference for boys at birth is normally di

Elena L [17]

Answer:

$z = \frac{X -\mu}{\sigma}$

This z score tell to us how many deviations we are below or above the mean for a given normal distribution.

For the case of Eddie we got:

$z= \frac{33.2-34.5}{1.3}= -1$

And for the case of Sue we got:

$z = \frac{32.7-33.9}{1.2}= -1$

So then for both cases we see that Eddie and Sue are 1 deviation below the true mean for each gender so then the best conclusion for this case would be:

C.They are the same size relative to other children of the same sex.

Step-by-step explanation:

We can define the random variable X as the head circumference for boys at birth and we know that the distribution for X is given by:

$X\sim N(\mu = 34.5, \sigma=1.3)$

Similarly we can define the random variable Y as the head circumference for boys at birth and we know that the distribution for Y is given by:

$Y\sim N(\mu = 33.9, \sigma=1.2)$

And we know that Eddie was born with 33.2 cm and Sue with 32.7 cm for the head circumference . Since we are interested to determine which child's head circumference is smaller relative to other children of the same sex, we can use the z score formula given by this formula:

$z = \frac{X -\mu}{\sigma}$

This z score tell to us how many deviations we are below or above the mean for a given normal distribution.

For the case of Eddie we got:

$z= \frac{33.2-34.5}{1.3}= -1$

And for the case of Sue we got:

$z = \frac{32.7-33.9}{1.2}= -1$

So then for both cases we see that Eddie and Sue are 1 deviation below the true mean for each gender so then the best conclusion for this case would be:

C.They are the same size relative to other children of the same sex.

5 0

2 years ago

2. A large fruit-eating bat called the black flying fox, Pteropus alecto, occupies a large mangrove swamp on Indooroopilly Islan

Svetach [21]

Step-by-step explanation:

a. P(mites OR ticks) = P(mites) + P(ticks) − P(mites AND ticks)

P(mites OR ticks) = 0.80 + 0.30 − 0.20

P(mites OR ticks) = 0.90

b. P(no ticks | mites) = P(no ticks AND mites) / P(mites)

P(no ticks | mites) = (0.80 − 0.20) / 0.80

P(no ticks | mites) = 0.75

c. If two events are independent, then P(A and B) = P(A) × P(B).

P(mites AND ticks) = 0.20

P(mites) × P(ticks) = 0.80 × 0.30 = 0.24

They are not independent.

5 0

2 years ago