All categories

3 years ago

The ratio of the number of Miki's stickers to the number of Ken's

Mathematics

1 answer:

Lera25 [3.4K]3 years ago

7 0

Answer:

Miki had 288 stickers and Ken had 252 stickers.

Step-by-step explanation:

This question is solved using a system of equations.

I am going to say that:

Miki has x stickers.

Ken has y stickers.

The ratio of the number of Miki's stickers to the number of Ken's stickers was 8:7.

This means that $\frac{x}{y} = \frac{8}{7}$ , that is: $7x = 8y$ , or $x = \frac{8y}{7}$

After Miki gave Ken 18 of her stickers, they had the same number of stickers.

This means that:

$x - 18 = y + 18$

$x - y = 36$

Since $x = \frac{8y}{7}$

$\frac{8y}{7} - y = 36$

$\frac{8y}{7} - \frac{7y}{7} = 36$

$\frac{y}{7} = 36$

$y = 36*7 = 252$

And

$x - y = 36$

$x = 36 + y = 36 + 252 = 288$

Miki had 288 stickers and Ken had 252 stickers.

You might be interested in

Z=15+2(x+y) solve for x

horrorfan [7]

<span>Z=15+2(x+y)
Use distributive property
Z= 15 + 2x + 2y
Subtract 2y from both sides
Z - 2y= 15 + 2x
Subtract 15 from both sides
Z - 2y - 15= 2x
Divide 2 on both sides
Final Answer: Z - 2y - 15(All over 2)= x</span>

8 0

3 years ago

Read 2 more answers

Describe in words how you would solve the linear system y = 3x + 1 and y = - 2x + 3.

Sergio [31]

We are using substitution to solve this problem.

y=3x+1
y=-2x+3
Make these equal each other: 3x+1=-2x+3
Add 2x to both sides: 3x+2x+1=-2x+2x+3
= 5x+1=3
Subtract 1 from both sides; 5x+1-1=3-1
= 5x=2
Divide 5 from both sides: 5x/5=2/5
X= 2/5
Plug X into one of the equations: y=3(2/5) +1
y=11/5(2.2)

(2/5,11/5)

5 0

3 years ago

Solve the linear equation x+3+x-8+x=55

babymother [125]

Answer:

X= 20

Step-by-step explanation:

X+X+X+3-8 = 55 (Place Like terms together)

3x - 5 = 55 (Simplifying Like terms by adding and subtracting)

3x = 55+5 ( Move -5 towards Right hand side of equal as there is 55 which is like term of -5 and if we move any number or value from one side of equal towards other the sign of that value would change)

3x = 60

X= 60/3 ( Move 3 toward others side as there is like term of 3 which is 60 but as on Left hand side of equal sign 3 is multiplying with "X" so when we move any number or value toward other side the operation or sign of that value or number would be change, Multiply change into Divide and vice versa and Add change into subtraction and vice versa)

X= 20

4 0

3 years ago

Here are summary statistics for randomly selected weights of newborn girls: nequals=174174, x overbarxequals=30.930.9 hg, seq

MaRussiya [10]

Answer:

The 95% confidence interval would be given by (29.780;32.020)

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=30.9$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=7.5 represent the sample standard deviation

n=174 represent the sample size

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=174-1=173$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,173)".And we see that $t_{\alpha/2}=1.97$ , this value is similar to the obtained with the normal standard distribution since the sample size is large to approximate the t distribution with the normal distribution.