MATHEMATICS COLLEGE

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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If f(x) = x2 + 2x + 1 and g(x) = 3(x + 1)2, which is anequivalent form of f(x) + g(x)?
O x2 + 4x + 2
O 4x2 + 2x + 4
O 4x2 + 8x + 4
o 10x2 + 20x + 1

Answers

The equivalent form of f(x) + g(x), if f(x) = x² + 2x + 1 and g(x) = 3(x + 1)² is

4x² + 8x + 4, so option C is correct.

What is a function?

In the case of a function from one set to the other, each element of X receives exactly one element of Y. The function's domain and co-domain are respectively referred to as the sets X and Y as a whole.

Given:

f(x) = x² + 2x + 1 and g(x) = 3(x + 1)²

Calculate the equivalent form as shown below,

f(x) + g(x) = x² + 2x + 1 + 3(x + 1)²

Simplify the above equation,

f(x) + g(x) = x² + 2x + 1 + 3(x² + 2x + 1)

f(x) + g(x) = x² + 2x + 1 + 3x² + 6x + 3

f(x) + g(x) = 4x² + 8x + 4

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the answer should be C

HELP MEEEEEEEEEEEEEEEEEEE I DONT GET IT

Answers

The graph goes up by 10 each time. And if we start at the bottom of the graph, and count up to where the line hits another point of the graph. It goes up by 30, and moves right 10. So that means the slope is 3. Hope this helps!

A random sample of 150recent donations at a certainblood bank reveals that
45 were type A blood.Does this suggest that the
actual percentage of type A
donations is less than40%, the percentage of the
population having type A
blood? Carry out a testof the appropriate
hypotheses using a significance
level of0.01.

Answers

Answer:

Null hypothesis: $p\geq 0.4$

Alternative hypothesis: $p < 0.4$

$z=\frac{0.3 -0.4}{\sqrt{(0.4(1-0.4))/(150)}}=-2.5$

$p_v =2*P(Z<-2.5)=0.0124$

If we compare the p value obtained and the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that the true proportion is not significantly lower than 0.4 or 40% at 1% of significance.

Step-by-step explanation:

1) Data given and notation

n=150 represent the random sample taken

X=45 represent the people with type A blood

$\hat p=(45)/(150)=0.3$ estimated proportion of people with type A blood

$p_o=0.4$ is the value that we want to test

$\alpha=0.01$ represent the significance level

Confidence=99% or 0.99

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion of people type A blood is less than 0.4:

Null hypothesis: $p\geq 0.4$

Alternative hypothesis: $p < 0.4$

When we conduct a proportion test we need to use the z statisitc, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{(p_o (1-p_o))/(n)}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.3 -0.4}{\sqrt{(0.4(1-0.4))/(150)}}=-2.5$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.01$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(Z<-2.5)=0.0124$

A number, n, is multiplied by -3/8. The product is -0.5 What is the value of n?

Answers

Answer:

n=4/3

Step-by-step explanation:

n*(-3/8)=-0.5

n=0.5/3/8

n=1/2 / 3/8

n=4/3

Check:

4/3*-3/8=-0.5

4/3*-3/8=-1/2

-1/2=-0/5

CORRECT!

The ratio of green marbles to total marbles in a bag is 2:9. The ratio of red marbles to total marbles in the same bag is 1:3. Which of the following statements is true

Answers

Answer:

answers is 2/3 ok hi your answers

2. "three times the sum of a number and 7”.

Answers

The required equation is 3*(n + 7).

It is required to find the equation.

What is equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.

Given:

Let the number be n.

The sum of a number and 7 is n + 7

Three times the sum of a number and 7 is

3*(n + 7).

Therefore, the required equation is 3*(n + 7).

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Answer:

3 * (7 + n)

Step-by-step explanation: