Represent 56÷ 8 = 7 using subtraction. Explain your reasoning.

Each small square on this scale weighs 1 unit. Each larger square weighs 10 units. The weight of the triangle x is unknown. The

Iteru [2.4K]

The equation to represent the relationship of the weights shown on the scale s $22 + x = 34$

The weights are given as:

$Small\ Square = 1$

$Larger\ Square = 10$

The total weight on one side, where there are 4 small squares and 3 large squares is:

$Total =4\times Small\ Square + 3 \times Larger\ Square$

$Total =4\times 1 + 3 \times 10$

$Total =34$

The total weight on the other side, where there are 2 small squares, 2 large squares and 1 triangle is:

$Total =2\times Small\ Square + 2 \times Larger\ Square + 1\times triangle$

$Total =2\times 1+ 2 \times 10+ 1\times triangle$

$Total =2+ 20+ 1\times triangle$

$Total =22+ 1\times triangle$

$Total =22+ triangle$

The weight of the triangle is x.

So, we have:

$Total =22+ x$

The weights on both sides are equal, because the scale is balanced.

So, we have:

$22 + x = 34$

Hence, the equation is $22 + x = 34$

Read more about equations at:

brainly.com/question/2972832

7 0

3 years ago

You have a coin that is not weighted evenly and therefore is not a fair coin. Assume the true probability of getting heads when

Alexandra [31]

Answer:

$X \sim Binom(n=157, p=0.52)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

And we want this probability:

$P(X$

And we can use the following Excel code to find the exact answer:

"=BINOM.DIST(75,157,0.52,TRUE)"

And we got 0.1633

The other way to solve the problem is using the normal approximation

We need to check the conditions in order to use the normal approximation.

$np=157*0.52=81.64 \geq 10$

$n(1-p)=157*(1-0.52)=75.36 \geq 10$

So we see that we satisfy the conditions and then we can apply the approximation.

If we appply the approximation the new mean and standard deviation are:

$E(X)=np=157*0.52=81.64$

$\sigma=\sqrt{np(1-p)}=\sqrt{157*0.52(1-0.52)}=6.26$

We want this probability:

$P(X$

And using the continuity correction we have this:

$P(X$

We can use the z score given by this formula $Z=\frac{x-\mu}{\sigma}$ .

$P(X< 76.5)=P(\frac{X-\mu}{\sigma}< \frac{76.5-81.64}{6.26})=P(Z < -0.821)=0.206$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=157, p=0.52)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

And we want this probability:

$P(X$

And we can use the following Excel code to find the exact answer:

"=BINOM.DIST(75,157,0.52,TRUE)"

And we got 0.1633

The other way to solve the problem is using the normal approximation

We need to check the conditions in order to use the normal approximation.

$np=157*0.52=81.64 \geq 10$

$n(1-p)=157*(1-0.52)=75.36 \geq 10$

So we see that we satisfy the conditions and then we can apply the approximation.

If we appply the approximation the new mean and standard deviation are:

$E(X)=np=157*0.52=81.64$

$\sigma=\sqrt{np(1-p)}=\sqrt{157*0.52(1-0.52)}=6.26$

We want this probability:

$P(X$

And using the continuity correction we have this:

$P(X$

We can use the z score given by this formula $Z=\frac{x-\mu}{\sigma}$ .

$P(X< 76.5)=P(\frac{X-\mu}{\sigma}< \frac{76.5-81.64}{6.26})=P(Z < -0.821)=0.206$

4 0

4 years ago

Solve for x 12 (x + 2)/ B O 14 O 10 12 06

Makovka662 [10]

Answer:

opposite sides of ||gram are equal and parallel therefore

12=x+2

12-2=x

10=x

pls mark as brainliest

6 0

3 years ago

Will mark brainlist for anyone who answers these parts correctly and properly showed their work.

Degger [83]

Answer:

D. 21/26

Step-by-step explanation:

Slope (m) = y2-y1/x2-x1

Input coordinates into formula:

m=5-(-16)/18-(-8)

m=21/26

8 0

3 years ago

Read 2 more answers

If 3x - 4y = 15 and -2x + 3y = 10, then x - y = ?

valkas [14]

Answer:

x - y = 25

Step-by-step explanation:

3x - 4y = 15

-2x + 3y = 10

Add the two equations together

3x - 4y = 15

-2x + 3y = 10

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

x - y = 25

3 0

3 years ago

Read 2 more answers