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3 years ago

Two angles are complementary. The sum of the larger angle and 4 times

Mathematics

1 answer:

belka [17]3 years ago

5 0

Answer:

20°

Step-by-step explanation:

Let x be the larger angle and y be the smaller angle.

Since they are complementary,

x+y = 90 => x=90-y

x+4y = 150

90-y+4y = 150

90 + 3y = 150

3y = 150-90

3y = 60

y = 20°

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-4/3x+1/6 <7/9 please answer asap

xz_007 [3.2K]

Answer:x=−24/11

Step-by-step explanation:

Simplifies to:

x−86x=79

Let's solve your equation step-by-step.

x−86x=79

Step 1: Cross-multiply.

x−86x=79

(x−8)*(9)=7*6x

9x−72=42x

Step 2: Subtract 42x from both sides.

9x−72−42x=42x−42x

−33x−72=0

Step 3: Add 72 to both sides.

−33x−72+72=0+72

−33x=72

Step 4: Divide both sides by -33.

−33x−33=72−33

x=−2411

8 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

Triangle JKL has vertices J(−2, 2) , K(−3, −4) , and L(1, −2) . Write the coordinate notation for a translation of 8 units right

Dovator [93]

Triangle JKL has vertices J(−2, 2) , K(−3, −4) , and L(1, −2) .

Rule: (x, y)→(x + 8, y + 1 )

J’ (-2, 2) → (-2 + 8, 2 + 1 ) → (6, 3 )
K’ (-3, -4) → (-3 + 8, -4 + 1 ) → (5, -3 )
L’ (1, -2) → (1 + 8, -2 + 1 ) → (9, -1)

J’ (6,3)
K’ (5,-3)
L’ (9,-1)

Hope this helps!

3 0

2 years ago

Can someone plot the dots please for 25 points. please

Temka [501]

Put them in the mueller when it says .5

7 0

3 years ago

What is the principal of simple interest

sasho [114]

Answer:

Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.

Step-by-step explanation:

Does this help☺

4 0

3 years ago