A cryptarithm is a math puzzle in which the digits in a simple equation are replaced with letters. Each digit is represented by only one letter, and each letter represents a different digit. So, for example, we might represent 51+50 = 101 as AB + AC = BCB. In the cryptarithm SEND + MORE = MONEY, what digit does the letter Y represent?

Answers

Answer 1
Answer:

Answer:

\large \boxed{\sf \begin{aligned}9567&\n+1085&\n----&-\n10652&\n\end{aligned}}

Step-by-step explanation:

Hello, let's do it step by step and see what we can find.

\begin{aligned}\text{ SEND}&\n+\text{ MORE}&\n-----&-\n\text{ MONEY}&\n\end{aligned}

We assume that M is different from 0, otherwise we could find several different solutions I would think.

It means that S + M is greater than 10, otherwise the number of digit of the result would have been 4 and not 5.

The only possible number for M is then 1. M = 1

\begin{aligned}\text{ SEND}&\n+\text{ \boxed{1}ORE}&\n-----&-\n\text{ \boxed{1}ONEY}&\n\end{aligned}

But then, S can only by 9, otherwise S + 1 < 10. S = 9

S + 1 = 10 + O if there is no carry over, so S = 9 + O

1 + S + 1 = 10 + O if there is a carry, so S = 8 + O

So O = 0 or O = 1. Wait !? M is already equal to 1 so O must be 0

E cannot be equal to N so 1 + E = N, meaning that there must be a carry over from column second from the right.

and E < 9 as we know that there is no carry over from column 3 from the right.

N + R = 10 + E => 1 + E + R = 10 + E => R = 9, impossible, as S=9

or 1 + N + R = 10 + E => 1 + 1 + E + R = 10 + E => R = 8

And there is a carry over from the column 1 from the right, so:

Y cannot be 0 or 1, as already used so D + E > 11

8 and 9 are already taken so we could have 7 + 5 = 12, 7 + 6 = 13 and that's it.

It means that E is 7 or D is 7.

If E is 7 then E+1=9=N, impossible, so D = 7

Then, E is 5 or 6

if E = 6 E + 1 = N = 7, impossible, so E = 5 and N = 6.

And 7 + 5 = 12 so Y = 2.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you


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Type your response in the box.Janet and Patrick are buying stuffed frogs each month to give to a charity. Pattern 1 describes Janet's collection overthe first three months. Pattern 2 describes Patrick's collection. Study both patterns, and fill in the table based onyour observations.
The table shows the distances and times that four people ran. Without making any calculations, who ran the fastest?

Choose the equation that represents the graph of the widest parabola?O y = 4x²
O y = -5x²
O y = 2x²
O y = - 3x²

Answers

Answer:

y = 2x^2

Step-by-step explanation:

Answer:

2x²

Step-by-step explanation:

Suppose a quiz contains 20 true/false questions. You know the correct answer to the first 10 questions. You have no idea of the correct answer to questions 11 through 20 and decide to answer each using the coin toss method. Calculate the probability of obtaining a total quiz score of at least 85%

Answers

Answer:

0.1719

Step-by-step explanation:

Given that:

A quiz contains 20 questions and 10 questions have been answered rightly

We are to determine the probability of getting a total quiz score of 85%

i.e 0.85 (20) = 17

Let's not forget that 10 is correctly answered out of 17. that implies that we only have 7 more questions to make a decision on.

where;

n = 10,

p + q = 1, 0.5 + q = 1

q = 1 - 0.5

q = 0.5

Let X be the random variable that follows the binomial distribution. Then ;

P(X = x) =(^n_x) p^x q^(n -x)

where x = 7

P(X \geq 7) =P(X=7)+P(X=8)+P(X=9)+P(X=10)

P(X \geq 7) =(^(10)_7})\ 0.5^7 \ 0.5 ^(10-7) + (^(10)_(8))\ 0.5^8 \ 0.5 ^(10-8)+(^(10)_9})\ 0.5^9 \ 0.5 ^(10-9)+ (^(10)_(10)})\ 0.5^(10) \ 0.5 ^(10-10)

P(X ≥ 7) = 0.1719

A rectangular garden measures 26ft by 37ft. Surrounding (and bordering) the garden is a path 2ft wide. Find the area of this path. Be sure to include the correct unit in your answer.

Answers

26*37=962sqft
Add 4 ft to both numbers (2ft per side)
30*41=1230sqft
Subtract out the garden area
1230-962=268sqft
The path is 268 sq ft

Victor collects data on the price of a dozen eggs at 8 different stores.median: $ 1.55
Find the lower quartile and upper quartile of
the data set.
lower quartile: $
upper quartile: S
?
$1.39 $1.40 $1.44 $1.50 $1.60 $1.63 $1.65 $1.80

Answers

Answer:

Lower quartile: $1.42

Upper quartile: $1.64

Step-by-step explanation:

The median is the middle value when all data values are placed in order of size.

The ordered data set is:

$1.39 $1.40 $1.44 $1.50 $1.60 $1.63 $1.65 $1.80

There are 8 data values in the data set, so this is an even data set.

Therefore, the median is the mean of the middle two values:

\implies \sf Median\;(Q_2)=(\$1.50+\$1.60)/(2)=\$1.55

Place "||" in the middle of the data set to signify where the median is:

$1.39 $1.40 $1.44 $1.50 ║ $1.60 $1.63 $1.65 $1.80

The lower quartile (Q₁) is the median of the data points to the left of the median.  As there is an even number of data points to the left of the median, the lower quartile is the mean of the the middle two values:

\implies \sf Lower\;quartile\;(Q_1)=(\$1.40+\$1.44)/(2)=\$1.42

The upper quartile (Q₃) is the median of the data points to the right of the median.  As there is an even number of data points to the right of the median, the upper quartile is the mean of the the middle two values:

\implies \sf Upper \;quartile\;(Q_1)=(\$1.63+\$1.65)/(2)=\$1.64

Answer:

to find the lower quartile and upper quartile of the given dataset, we need to first arrange the data in ascending order:

$1.39, 1.40, 1.44, 1.50, 1.60, 1.63, 1.65, 1.80$

The median of the dataset is given as $1.55$. Since there are an even number of data points, the median is the average of the two middle values, which in this case are $1.50$ and $1.60$.

Now, we need to find the lower quartile and upper quartile. The lower quartile is the median of the lower half of the data set, and the upper quartile is the median of the upper half of the data set.

The lower half of the dataset is $1.39, 1.40, 1.44, 1.50$. The median of this half is the average of the middle two values, which are $1.40$ and $1.44$.

Therefore, the lower quartile is $1.42$.

The upper half of the dataset is $1.60, 1.63, 1.65, 1.80$. The median of this half is the average of the middle two values, which are $1.63$ and $1.65$.

Therefore, the upper quartile is $1.64$.

Hence, the lower quartile of the dataset is $1.42$ and the upper quartile is $1.64$.

You finish 3 homework problems in 10 minutes,Your friend finishes 9 homework problems in 1/2 hour.Are you and your friend working at the same rate?

Answers

Yes because 3 home work problems takes 10 min and 10x3 =30 and that’s a half hour

A ladder leaning against a building makes an angle of 78° with the ground. The foot of the ladder is 5 feet from the building. How long is theladder?

Answers

Answer:

390 because 78 is the width and 5 is length of the building so you need to 78x5 to get your answer