Rafael ate one-fourth of a pizza and Rocco ate one-third of it. What fraction of the pizza did they eat?

They ate

Answer:

50"

В

A

mC

m B

mA

Step-by-step explanation:

Answer:

Step-by-step explanation:

The natural logarithm of x is generally written as ln x, loge x, or sometimes, if the base e is implicit, simply log x.

Answer:

Ln x as opposed to log x

Step-by-step explanation:

Answer:

a) 0.5447

b) 0.0228

c) 0.4325

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Normal distribution with a mean of 9.6 minutes and a standard deviation of 2.3 minutes.

This means that [tex]\mu = 9.6, \sigma = 2.3[/tex]

a. between 5 and 10 min

This is the p-value of Z when X = 10 subtracted by the p-value of Z when X = 5. So

X = 10

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{10 - 9.6}{2.3}[/tex]

[tex]Z = 0.17[/tex]

[tex]Z = 0.17[/tex] has a p-value of 0.5675

X = 5

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{5 - 9.6}{2.3}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a p-value of 0.0228

0.5675 - 0.0228 = 0.5447 probability that a randomly received emergency call is between 5 and 10 minutes.

b. less than 5 min

p-value of Z when X = 5, which from item a), is 0.0228, so 0.0228 probability that a randomly received emergency call is of less than 5 minutes.

c. more than 10 min

1 subtracted by the p-value of Z when X = 10, which, from item a), is of 0.5675.

1 - 0.5675 = 0.4325

0.4325 probability that a randomly received emergency call is of more than 10 minutes.

Answer:

They have different areas and different perimeters

Answer:

It's answer is - 9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4......

Answer:

9ft =2.743m

kjhgfdfvhhgddfcvh

Answer:

Step-by-step explanation:

If the roots are 7 and 3, then x = 7 and x = 3 are solutions. In factor form, x = 7 is (x - 7); in factor form, x = 3 is (x - 3). We FOIL these together to get

[tex]x^2-3x-7x+21[/tex] which simplifies to

[tex]x^2-10x+21[/tex] and we distribute in the 4:

[tex]4(x^2-10x+21)[/tex] to get

[tex]4x^2-40x+84[/tex] which is another way to write the last choice you're given.

Step-by-step explanation:

a printed record of the balance in a bank account and the amounts that have been paid into it and withdrawn from it, issued periodically to the holder of the account.

(f-g)x= -x²+13x+13

Hope it helps you....

Problem 22

a)

The face cards are Jack, Queen, King. We have four copies of each.

There are 3*4 = 12 face cards total.

12/52 represents the probability of picking a face card.

4/52 represents the probability of picking an ace, since we have 4 aces out of 52 cards. We don't drop to 51 since we put the first card back.

Multiplying the fractions gives (12/52)*(4/52) = 48/2704 = 3/169

----------------------

b)

We do the same steps as before, but the 4/52 will be changed to 4/51. This is because the first card is not put back.

(12/52)*(4/51) = 48/2652 = 4/221

========================================================

Problem 23

a)

4/52 represents the probability of picking a '2', and it also represents the probability of picking a '10' if we put the first card back

(4/52)*(4/52) = 16/2704 = 1/169

----------------------

b)

We'll change the second instance of 4/52 into 4/51 because that first card isn't put back

(4/52)*(4/51) = 16/2652 = 4/663

========================================================

Problem 24

a)

4/52 = probability of picking an ace

12/52 = probability of picking a face card

4/52 = probability of picking '7'

Each denominator is 52 because we are putting the cards back

(4/52)*(12/52)*(4/52) = 192/140608 = 3/2197

----------------------

b)

We do the same thing as before, but we decrease the denominator by 1 each time we pull out another card

(4/52)*(12/51)*(4/50) = 192/132600 = 8/5525

========================================================

Problem 25

a)

The probability of picking a king is 4/52. This is the same whether we're on the first king, second or third. This is because we're putting the card back.

(4/52)*(4/52)*(4/52) = 64/140608 = 1/2197

----------------------

b)

Now that the cards aren't put back, we'll have the denominators drop by 1 each time (52,51,50)

So the probability is

(4/52)*(4/51)*(4/50) = 64/132600 = 8/16575

Answer:

A

Step-by-step explanation:

Step 1, setting variables:

We already know the exact height of the prism: 6 feet. We can set the unknown width as variable x, and length as x+2 (length is two feet more than width).

Step 2, writing equations:

Great! We have everything now. Let us write the equation by substituting our variables in:

[tex]V=l*w*h\\V=6w(w+2)\\[/tex]

Ok! Let us expand the equation:

[tex]V=6w^2+12w[/tex]

[tex]\fbox{A}[/tex]

I hope this helps! Let me know if you have any questions :)

Answer:

it should look like a U shape. Its called a parabola

(0,0) is the bottom center.

Step-by-step explanation:

Answer:

I think choose (1)

[tex]125 ^{ \frac{1x}{3} } [/tex]

Answer:

29/35

Step-by-step explanation:

Least common denominator of 5 and 7 is 35

[tex]\frac{2}{5}=\frac{2*7}{5*7}=\frac{14}{35}\\\\\frac{3}{7}=\frac{3*5}{7*5}=\frac{15}{35}\\\\\frac{2}{5}+\frac{3}{7}=\frac{14}{35}+\frac{15}{35}\\\\ \ = \frac{14+15}{35}\\\\ = \frac{29}{35}[/tex]

Answer:

25m²

Step-by-step explanation:

it might be helpful for you

Answer:

x = 2 ± [tex]\frac{\sqrt{2} }{2}[/tex]

Step-by-step explanation:

Answer:

The correct answer is "0.3410, 0.4990".

Step-by-step explanation:

Given values are:

[tex]n=150[/tex]

[tex]p=\frac{63}{150}[/tex]

  [tex]=0.42[/tex]

At 95% confidence interval,

C = 95%

z = 1.96

As we know,

⇒ [tex]E=z\sqrt{\frac{p(1-p)}{n} }[/tex]

By substituting the values, we get

       [tex]=1.96\sqrt{\frac{0.42\times 0.58}{150} }[/tex]

       [tex]=1.96\sqrt{\frac{0.2436}{150} }[/tex]

       [tex]=0.0790[/tex]

hence,

The confidence interval will be:

= [tex]p \pm E[/tex]

= [tex]0.42 \pm 0.079[/tex]

= [tex](0.3410,0.4990)[/tex]

Answer:

(a+b)²=a²+b²+2ab

Step-by-step explanation:

The square of sum of two terms is equal to the squared plus squared plus times product of and . In mathematics, the plus whole squared algebraic identity is called in three ways. The square of sum of two terms identity.

Answer:

275, 350, 450, 550, 675

Step-by-step explanation:

Arrange in order

275, 300, 450, 490, 675

range 275 to 675

median 450

mean 438

---------------------------

Raise 300 to 350

Raise 490 to 550

New set of prices

275, 350, 450, 550, 675

range 275 to 675     same

median 450     same

mean 460    increased

Answer:

One set of prices could be: {275,300,450,600,675}

Another set could be: {275,300,450,600,675}

There are many other solutions possible.

====================================================

Explanation:

A = {450, 275, 675, 490, 300}

B = {275, 300, 450, 490, 675}

Set A is the original set of values in the order they were given to you. Set B is the sorted version of set A from smallest to largest.

The mean is found by adding up the values and dividing by 5 (because there are five items in the set).

The mean is (275+300+450+490+675)/5 = 2190/5 = 438. The shopkeeper wants to increase the mean to something larger, but keep the median and range the same.

The median is the middle most number. In set B, we can see that is 450. So the median is 450. We want to keep the median the same at 450.

The range is the difference in min and max

range = max - min = 675-275 = 400

We want to keep the range at 400

---------------------------

There are a number of ways to increase the mean, while keeping the median and range the same.

Let's say we keep the min and max the same. In order to increase the mean, we need to increase the 490 (second largest value) to something larger. Let's bump that up to 600 for instance.

Recomputing the mean gets us

(275+300+450+600+675)/5 = 2300/5 = 460

The old mean was 438 and the new mean is now 460. The mean has increased. This is due to the larger price pulling on the mean to get the mean to increase.

The median is still 450 because it's still in the direct middle of set C

C = {275,300,450,600,675}

The range is still the same as well because we haven't changed the min and max.

---------------------------

So one possible set could be

C = {275,300,450,600,675}

We could also have

D = {275,400,450,500,675}

The difference is that the 300 bumped to 400, and the 600 dropped to 500. You should find that the median and range are the same, while the mean is 460.

There are many possible solutions here.

Answer:

2

Step-by-step explanation:

log2^8 + log3(1/3)

=>3 + (-1)

=>2

Answer:

See explanation

Step-by-step explanation:

Given

Represent the balls with the first letters

[tex]W =1[/tex]

[tex]R =1[/tex]

Solving (a): P(F) --- White balls twice

The event of F is:

[tex]F = \{(W,W)\}[/tex]

So:

[tex]P(F) = P(W) * P(W)[/tex]

[tex]P(F) = \frac{n(W)}{n} * \frac{n(W)}{n}[/tex]

[tex]P(F) = \frac{1}{2} * \frac{1}{2}[/tex]

[tex]P(F) = \frac{1}{4}[/tex]

Solving (b): P(G) --- two different colors

The event of G is:

[tex]G = \{(W,R),(R,W)\}[/tex]

So:

[tex]P(G) = P(W) * P(R) + P(R) * P(W)[/tex]

[tex]P(G) = \frac{n(W)}{n} * \frac{n(R)}{n} + \frac{n(R)}{n} * \frac{n(W)}{n}[/tex]

[tex]P(G) = \frac{1}{2} * \frac{1}{2} + \frac{1}{2} * \frac{1}{2}[/tex]

[tex]P(G) = \frac{1}{4} + \frac{1}{4}[/tex]

[tex]P(G) = \frac{1}{2}[/tex]

Solving (c): P(H) --- White picked first

The event of H is:

[tex]H = \{(W,R),(W,W)\}[/tex]

So:

[tex]P(H) = P(W) * P(R) + P(W) * P(W)[/tex]

[tex]P(H) = \frac{n(W)}{n} * \frac{n(R)}{n} + \frac{n(W)}{n} * \frac{n(W)}{n}[/tex]

[tex]P(H) = \frac{1}{2} * \frac{1}{2} + \frac{1}{2} * \frac{1}{2}[/tex]

[tex]P(H) = \frac{1}{4} + \frac{1}{4}[/tex]

[tex]P(H) = \frac{1}{2}[/tex]

Solving (d): F and G, mutually exclusive?

We have:

[tex]F = \{(W,W)\}[/tex]

[tex]G = \{(W,R),(R,W)\}[/tex]

Check for common elements

[tex]n(F\ n\ G) = 0[/tex]

Hence, F and G are mutually exclusive

Solving (e): G and G, mutually exclusive?

We have:

[tex]G = \{(W,R),(R,W)\}[/tex]

[tex]H = \{(W,R),(W,W)\}[/tex]

Check for common elements

[tex]n(G\ n\ H) = 1[/tex]

Hence, F and G are not mutually exclusive

9514 1404 393

Answer:

  6

Step-by-step explanation:

Any of the three can be in first place.

Any of the remaining two can be in 2nd place.

The remaining swimmer will be in 3rd place.

There are 3 × 2 × 1 = 6 possible orderings of the swimmers.

Answer:

fourteen thousand five hundred and eighty seven point twenty five.

Step-by-step explanation:

The given number is 14587.25.

We need to write it in standard form.

7 is in ones place, 8 is in tens place, 5 is in hundreds place, 4 is in thousands place and 1 is in ten-thousands place.

So,

14587.25 = fourteen thousand five hundred and eighty seven point twenty five.

Answer:

x = 1.9

Step-by-step explanation:

Thanks to a theorem we can use this proportion

10.47 : 4.44 = 4.44 = x

x = (4.44^2)/10.47 = 1,882865 = 1.9

Answer:10.25-r= hourly rate

Step-by-step explanation:

Answer:

Foss

Step-by-step explanation:

The term line is not defined in Euclidean geometry. ... These words are point, plane and line and are referred to as the "three undefined terms of geometry".

Answer:

LINE is not defined by Euclidian geometry

Step-by-step explanation:

In Euclidean geometry, there are 3 terms that are considered "undefined" they are; point, line and plane.  I think it is because considered undefined because they are described, but not every formally defined.

As in a shape I mean I hope I am right,

==============================================

Explanation:

The recursive rule

f(n+1)=f(n)-3

can be rearranged to

f(n) = f(n+1)+3

after adding 3 to both sides

----------------

Now let's say we plug in n = 3

f(n) = f(n+1)+3

f(3) = f(3+1)+3

f(3) = f(4)+3

f(3) = 22+3

f(3) = 25

Repeat for n = 2

f(n) = f(n+1)+3

f(2) = f(2+1)+3

f(2) = f(3)+3

f(2) = 25+3

f(2) = 28

Each time we keep adding 3 to get the previous term (since the original recursive rule says to subtract 3 to get the next term; we just go backwards of what the instructions say).

Lastly, we can find that f(1) = f(2)+3 = 28+3 = 31 making the answer to be choice C.

-6(3x-2/3)

=(-6).3x-(-6).2/3

=-18x-(-4)

=-18x+4