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4 years ago

5

Write and solve an equation to find three consecutive integers such that three times the sum of the first two integers is the sa

me as thirteen more than four times the third integer.

1 answer:

kherson [118]4 years ago

6 0

Let the integers be x, x+1, and x+2
3(x+x+1)=13+4(x+2)
3(2x+1)=13+4x+8
6x+3=4x+21
2x=18
x=9

the integers are 9,10,11

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What is the tangent of an equal to

elena-s [515]

The tangent of x is defined to be its sine divided by its cosine: tan x = sin x cos x . The cotangent of x is defined to be the cosine of x divided by the sine of x: cot x = cos x sin x .

3 0

3 years ago

Alan deposited $300 into a savinga account. At the end of the first year, the amount of money in the account has increased to $3

Step2247 [10]

He had put in $300 and got out $336 at the end of the year.
This means an increase of $36 over a year.

10% of $300 = $30 dollars
This shows that he definitely got more than a 10% increase.

Alan got $6 more than $30 so to find 6 from 30, you divide by 5

so ( 10% = $30 ) divided by 5 = ( 2% = $6 )

Adding the amount of money and percentages gives you 12% = $36

So the amount of mpercentage increase is 12%

Overall the amount of money in his bank now compared to when he deposited it, he has 112% in the bank.

4 0

3 years ago

A newsgroup is interested in constructing a 90% confidence interval for the proportion of all Americans who are in favor of a ne

Evgen [1.6K]

Answer:

a. With 90% confidence the proportion of all Americans who favor the new Green initiative is between 0.6290 and 0.6948.

b. If the sample size is changed, the confidence interval changes as the standard error depends on sample size.

About 90% percent of these confidence intervals will contain the true population proportion of Americans who favor the Green initiative and about 10% percent will not contain the true population proportion.

Step-by-step explanation:

We have to calculate a 90% confidence interval for the proportion.

The sample proportion is p=0.6619.

$p=X/n=370/559=0.6619$

The standard error of the proportion is:

$\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.6619*0.3381}{559}}\\\\\\ \sigma_p=\sqrt{0.0004}=0.02$

The critical z-value for a 90% confidence interval is z=1.6449.

The margin of error (MOE) can be calculated as:

$MOE=z\cdot \sigma_p=1.6449 \cdot 0.02=0.0329$

Then, the lower and upper bounds of the confidence interval are:

$LL=p-z \cdot \sigma_p = 0.6619-0.0329=0.6290\\\\UL=p+z \cdot \sigma_p = 0.6619+0.0329=0.6948$

The 90% confidence interval for the population proportion is (0.6290, 0.6948).

3 0

3 years ago

How to find cp if loss and sp are given

velikii [3]

Step-by-step explanation:

$\tt{ \: H \: E \: Y \: \: T \: H \: E \: R\: E \: }$ !

When Loss and Selling price ( SP ) are given , Cost price ( CP ) can be found out using the following formulae :

✰ $\large{ \boxed{ \boxed{ \tt{CP = Loss + SP}}}}$

$\text{How \: did\: we \:get \:the \: formula : \: CP \: = Loss \: + \: SP} \:$ ?

We simply derived the formula from Loss = CP - SP.

First , Swap the sides of the equation :

⟶ $\text{CP - SP = Loss}$

Move SP to right hand side and change it's sign :

⟶ $\text{CP = Loss + SP}$

This is how , CP can be obtained when we are given loss and SP.

Hope I helped ! ♡

Have a wonderful day / night ! ツ

# $\underbrace{ \tt{C \: a \: r \: r \: y \: \: O \:n \: \: L \: e \: a \: r \: n \: i \: n \: g}}$ !!

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8 0

3 years ago

Can someone help on a construction of a tangent to a circle please, need pictures if possible

Anit [1.1K]

Wassup

Steps:

1. Draw a line connecting the point to the center of the rectangle

2. Then construct a perpendicular bisector to the line drawn in step 1

3. Place the compass on the midpoint of the line, adjust its length to reach the end point, and draw an arc across the circle

4. Where the arc crosses the circle will be the tangent points. So connect the endpoint to the tangent point

Hope the picture helps you too

5 0

3 years ago