Mike has a collection of baseball cards and baseball figurines. If the ratio of cards to figurines is 5:7 and there are 25 cards in his collection, how many figurines does he have

Answer:

Approximately [tex]0.012[/tex] (that's approximately [tex]1.2\%[/tex].)

Step-by-step explanation:

The question did not specify the exact distribution of the size of those images. However, the sample size [tex]n = 80[/tex] is a rather large number. Assume that:

If both assumptions are met, the central limit theorem would apply. This theorem would suggest that the sum of the sizes of these [tex]80[/tex] image (a random variable) will approximately follow a normal distribution. The mean of that sum would be approximately [tex]n\cdot \mu= 80 \times 0.5[/tex]. The standard deviation of that sum would be approximately [tex]\sigma\, \sqrt{n} = 0.2\times \sqrt{80}[/tex].

Let [tex]\displaystyle \Sigma X[/tex] denote the sum of these eighty sizes.

Under these assumption, [tex]\displaystyle \Sigma X \stackrel{\text{app.}}{\sim} \mathrm{N}\left(n\, \mu,\, \sigma\,\sqrt{n}\right)[/tex].

That is: [tex]\displaystyle \Sigma X \stackrel{\text{app.}}{\sim} \mathrm{N}\left({80\times 0.5},\, \left(0.2\times \sqrt{80}\right)^2}\right)[/tex].

The question is asking for the probability [tex]P(49 \le \Sigma X \le 53)[/tex]. Therefore, calculate the [tex]z[/tex]-score that corresponding to [tex]\Sigma X = 49[/tex] and [tex]\Sigma X = 53[/tex]:

Make use of a [tex]z[/tex]-table to find these two probabilities:

Calculate the probability that this question is asking for:

[tex]\begin{aligned}& P(49 \le \Sigma X \le 53) \\ &= P(\Sigma X < 53) - P(\Sigma X < 49) \\ & \approx 0.99942 - 0.98778 \approx 0.012 = 1.2\%\end{aligned}[/tex].

Answer:

Option (a) [tex]\sum_{k=1}^{\infty} \dfrac{3}{k(k+1)}[/tex]

Step-by-step explanation:

The given expression is :

[tex]\dfrac{3}{1{\cdot} 2}+\dfrac{3}{2{\cdot} 3}+\dfrac{3}{3{\cdot} 4}+\dfrac{3}{4{\cdot} 5}+....[/tex]

We need to rewrite the sum using sigma notation.

The numerator is 3 in all terms.

At denominator, in first term (1)(2), in second term (2)(3) and so on.

A general term for the denominator is k(k+1).

Sigma notation is :

[tex]\sum_{k=1}^{\infty} \dfrac{3}{k(k+1)}[/tex]

Hence, the correct option is (A).

Answer:

Step-by-step explanation:

Let s be the surface area and r be the radius

Then according to given statement

s∝r²

Removing the proportionality symbol introduces k, the constant of proportionality

[tex]s = kr^2[/tex]

Now

A soap bubble with a  0.75 in. radius has a surface area of approximately 7.07 square inches.

Putting in the equation

[tex]7.07 = k (0.75)^2\\7.07 = k * 0.5625\\k = \frac{7.07}{0.5625}\\k = 12.5688..\\k = 12.57[/tex]

The euqation beomes

[tex]s = 12.57r^2[/tex]

Putting s = 113.1 in the equation

[tex]113.1 = 12.57r^2\\r^2 = \frac{113.1}{12.57}\\r^2 = 8.99761...\\\sqrt{r^2} = \sqrt{8.9976..}\\r = 2.9996..[/tex]

Hence,

Answer: 32

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

Inside the parentheses, we see 5+3, which equals 8. Now, do 8x4, which equals 32!

Method 1: A pure algebraic approach

The unknown in this problem is the percent of decrease. A percent of decrease is the percentage of the original price that was deducted from the original price to obtain the sale price. We could write a "word equation" for this process like this:

original price - (percent of decrease)(original price) = sale price

Since the percent of decrease is the unknown in this problem, we'll call the percent of decrease x%.

Here's what we know so far:

The original price was $200

The sale price was $170

The percent of increase was x%

Putting this information in our word equation gives us an algebraic equation:

200 - (x%)(200) = 170

What do we do with the percent sign in this equation? "Percent" means "out of 100", so x% means x out of 100, or . Now we have this:

200 - (200) = 170

Now we'll solve our equation:

200 - (200) = 170

200 - 2x = 170

-2x = -30

x = 15

So the percent of decrease is 15%

Method 2: A method involving pure arithmetic.

If we know the original price and the sale price, we can find the percent of decrease in two steps:

Find the amount of decrease

Divide the amount of decrease by the original amount

This will give us the percent of decrease (written as a decimal number). We can then write the decimal as an equivalent percent to find our final answer.

Let's use method 2 on the same problem:

Frank bought a new television set on sale. If the TV's original price was $200 and Frank paid $170 for the TV, what was the percent of decrease?

First, let's find the amount of decrease:

Amount of decrease = 200 - 170 = 30

So the price decreased by $30.

Next, we'll find the percent of decrease, and rewrite the decimal answer as a percent:

Percent of decrease =  = = .15 = 15%

So the percent of decrease is 15%

Before we leave the problem, let's check our answer:

Original price = $200

Price reduced by 15% of original price = 200(.15) = $30

Sale price would then be = $200 - $30 = $170

Our answer checks. We're done!    Me not know if correct.

here's the answer.....I hope it would work

Answer:

3/17

Step-by-step explanation:

Substitute the given values for the variables.

[tex]\frac{12}{5+9(7)}[/tex]

Simplify

[tex]\frac{12}{5+63}[/tex]

[tex]\frac{12}{68}[/tex]

[tex]\frac{3}{17}[/tex]

Answer:

the 3rd one im pretty sure

Step-by-step explanation:

Answer:

the 3rd one <3

Step-by-step explanation:

Answer:

Step-by-step explanation:

The slope of the line is 2 and the y-intercept is -6. y-intercept is the point where x is zero. Hence, the point is (0,-6) When we graph a linear function by slope-intercept method, first of all we plot the y-intercept. Hence, first of all we plot the point (0,-6) Now, slope is given by if rise is positive then we move up from the y -intercept and if negative then move down. We keep run always positive and hence we move right from the rise point. rise = 2 run = 1 Rise is positive hence, we move 2 units up from the point (0,-6) and then move 1 unit right to get the next point. Then we draw a line passing through these points. A is the correct option.

Answer:

yes

Step-by-step explanation:

if they do not have x intercepts, the answer will have an imaginary number (i)

Answer:

The answer is D. the gas mileage after the additive is used

Step-by-step explanation:

I got 100% on edg!

Answer:

d

Step-by-step explanation:

edge2o2o

Answer:

189

Step-by-step explanation:

Also can you make me brainliest please

Step-by-step explanation:

Use the slope-intercept form

y=mx+b

to find the slope m and y-intercept b

Slope: 5/4

y-intercept: (0,-4)

Answer:

Step-by-step explanation:

4• (7 • y) is equivalent to all of the following:

28 • y

4 · 7y or (4 · 7) · y

(7 · 4) · y

Note that 4 • 7 + 4 • Y is absolutely wrong, since the original expression has no " + " sign

twenty thousandddd

20k

Answer:

twenty thousand

Step-by-step explanation:

Because you just have to spell it out spell twenty and then thousand.

Answer:

the second to last one

Step-by-step explanation:

Sorry if it is incorrect!

Answer:

angle 5 will be 55 °

Step-by-step explanation:

Answer:

2388.16 in³

Step-by-step explanation:

1) find volume of cylinder

formula: πr²h

given:

π = 3.14

r = 8/2 = 4 in

h = 9 in

[tex]\pi \: r {}^{2} h[/tex]

[tex](3.14) \times (4 {}^{2} ) \times 9[/tex]

[tex]3.14 \times 16 \times 9[/tex]

[tex]452.16 \: {in}^{3} [/tex]

2) find volume of cuboid

formula: length × width × height

given:

length = 16 in

width = 11 in

height = 11 in

[tex]l \: \times w \: \times h[/tex]

[tex]16 \times 11 \times 11[/tex]

[tex]1936 \: in {}^{3} [/tex]

total volume of figure

= volume of cylinder + volume of cuboid

= 452.16 in³ + 1936 in³

= 2388.16 in³

Answer:

4

Step-by-step explanation:

I am pretty sure its that one

Answer:10

Step-by-step explanation:

Answer:

x = 1.25

y = 1.75

Step-by-step explanation:

Since, the line that is 8 units long is parallel to the line that is ten units long.

Therefore, both the triangles are similar by AA postulate.

Corresponding sides of of the similar triangles are in proportion.

Therefore,

[tex] \frac{5}{x + 5} = \frac{7}{y + 7} = \frac{8}{10} \\ \\ \implies \frac{5}{x + 5} = \frac{8}{10} \\ \\ 5 \times 10 = 8(x + 5) \\ \\ 50 = 8x + 40 \\ \\ 50 - 40 = 8x \\ \\ 10 = 8x \\ \\ \frac{10}{8} = x \\ \\ x = 1.25 \\ \\ \\ \frac{7}{y + 7} = \frac{8}{10} \\ \\ 7 \times 10 = 8(y + 7) \\ \\ 70 = 8y + 56 \\ \\ 70 - 56 = 8y \\ \\ 14 = 8y \\ \\ \frac{14}{8} = y \\ \\ y = 1.75[/tex]

Answer:

Step-by-step explanation:

A. 40:80

B: 80/40

C; 40: 120

D: 80:120 ;)

Answer:

-24

hope this helped! :3

Step-by-step explanation:

3 x -4 = -12

-12 x 2 = -24

Answer:

3× -4 = -12

-12 × 2=-24

Step-by-step explanation:

follow your sign discriptively take notice in change of ur sign.

+× - = -

- × - = +

+ × + = +

- × + = -

Answer:

24

Step-by-step explanation:

[tex]\sqrt{25^2-7^2}\\\\=\sqrt{(25-7)(25+7)}\\\\=\sqrt{18(32)}\\\\=\sqrt{9*2*2^5}\\\\=\sqrt{3^2\cdot 2^6}\\\\=\sqrt{(3\cdot2^3)^2}\\\\=3\cdot2^3\\\\=3\cdot8\\\\=24[/tex]

Answer:

24

Step-by-step explanation:

First we compute the number under the radical.

We have 25² = 625 and 7² = 49, so 25² - 7² = 625 - 49 = 576.

Thus, √25² - 7² = √576 = √24², which is 24.

Answer:

4

Step-by-step explanation:

Answer:

The thief stole 36 apples originally.

Step-by-step explanation:

The thief left the orchard with 1 apple.

which means:

​∴  before meeting the 3rd watchman, he must have had ​=6 apples.

​∴  before meeting the 2nd watchman, he must have had ​=16 apples.

​∴  before meeting the 1st watchman, he must have had ​=36 apples.

​(1+2)×2

​(6+2)×2

​(16+2)×2

​​

So, the thief stole 36 apples originally.

Answer:

The thief took 36 apples.

Step-by-step explanation:

This problem can be solved from end to beginning.

The thief ends up with a single apple. This happed after he gave half of the apples he had and two extra apples.

Thus, adding two apples 1+2=3 and doubling the result, the thief had 3*2=6 apples when he met the last guard.

Before that, he gave 2 apples to the second guard, thus he had 6+2=8 apples. Doubling it 8*2=16 is the number of apples he had when met the second guard.

Doing this again, 16+2=18. 18*2=36.

The thief took 36 apples.

Gave 18+2=20 to the first guard. He had 36-20=16 now.

Gave 8+2=10 to the second guard. He had 16-10=6 now.

Gave 3+2=5 to the third guard and got away with just one apple

Answer:

you didn't post the graph but (0,0) is the origin

Answer:

ok

Step-by-step explanation:

Answer:

- 5/6

Step-by-step explanation:

turn it into an improper fraction.

1 and 2/3 = 5/3

2 and 1/2 = 5/2

5/3 - 5/2 = 10/6 - 15/6

= -5/6

Answer:

First you have to change both of the mixed numbers to improper fractions. To do this you would multiply the denominator and the whole number then add the numerator.

1 2/3 = 5/3

-2 1/2 = -5/2

Find the least common denominator (LCM). Add the numerator, and keep the denominator the same.

The LCM for these two fractions would be 6 so to get to six you would multiply 5/3 by 2/2 and -5/2 by 3/3.

5/3 = 10/6

-5/2 = -15/6

Add the numerators (10 + -15 = -5), and keep the denominator the same (6). Therefore, the answer would be -5/6.