the square root of the sum of twice a number and 3 is 6. find the number​

Therefore , the solution of the given problem of area comes out to be

r = 8.

The term "area" describes the amount of space occupied by a 2D form or surface. We use cm2 or m2 as our units for measuring area. A shape's area is determined by dividing its length by its breadth.

Here,

A 90 degree sector occupies 1/4 of a circle, which has 360 degrees. Consequently, the area of the whole circle can be written as

Sector Size/Sector Area = Circle Area/360

16 ft2/90 = n/360

(360) (16 ft2)/90 = n

(4)(16 ft2) = n

The total size of the circle is n = 64 ft2.

Since Area of a Circle equals r2,

∏r2 = 64

r2 = 64/∏

r = √(64/∏)

We multiply by / to get by rationalizing the denominator.

r = √(64∏)/√(∏2) Then using the denominator's square root, we can obtain the solution of

r = √(64∏)/∏

r = 8

Therefore , the solution of the given problem of area comes out to be

r = 8.

To know more about area, visit

https://brainly.com/question/27683633

#SPJ1

Answer:

224

Step-by-step explanation:

360.-136.

Answer:

$191.25

Step-by-step explanation:

multiply 255 dollars by 25 percent, and then divide the answer by one hundred, then deduct that result from the original price.

(255 x 25)/100 = $63.75

255 - 63.75 = $191.25

Answer:

given;

previous year price of gas= $4.35

price of gas has been increased by 30%

now,price of gas in present year=?

we have;

price of gas in present year=priceof

previous year+30%of price of previous year.

so ,price of gas in present year=4.35+30%of4.35

=$4.35+30/100×4.35

=$4.35+1.305

= $5.655. ans....

therefore, the price of gas in present year is ;$5.655.

Answer: 4*(x+12)=52.

Answer:

#9= 100 degrees but I'm not sure about #10.

Step-by-step explanation:

We know that a triangle has a total of 180 degrees.

So we add 16, 34, and 30

16+34+30=80

Then we subtract the amount from the total degrees of a triangle.

180-80

= 100 degrees

I hope this helps:)

It can be observed that number 108 lie between 100 and 121, two numbers which are perfect square.

So square root of 108 fall between square root of 100 and square root of 121.

Determine the square root of 100 and 121.

So square root of 108 fall between two integers 10 and 11.

Complete Question

The complete question is shown on the first uploaded image

Answer:

a

 center is  0.275

 \(SE = 0.063\)

b

 center is  0.275

 \(SE = 0.020\)

Step-by-step explanation:

considering question a

From the question we are told that

   The sample size is  n  =  50

 The proportion of  US adults are college graduates is  p = 0.275

Generally the center is equivalent to the proportion so the center is  0.275

Generally the standard error is  

      \(SE =  \sqrt{\frac{p *  (1- p)}{ n} }\)

=>   \(SE =  \sqrt{\frac{0.275 *  (1- 0.275)}{ 50} }\)

=>   \(SE = 0.063\)

considering question b

    The sample size is  n  =  500

      The proportion of  US adults are college graduates is  p = 0.275

     Generally the center is equivalent to the proportion so the center is  0.275

     Generally the standard error is  

      \(SE =  \sqrt{\frac{p *  (1- p)}{ n} }\)

=>   \(SE =  \sqrt{\frac{0.275 *  (1- 0.275)}{ 500} }\)

=>   \(SE = 0.020\)

In the sampling distribution, the center of the sampling distribution is 0.275 and the standard error is 0.063.

A sampling distribution simply means the probability distribution that is gotten from a larger number of samples that are drawn from a population.

In this case, the center of the sampling distribution is 0.275 and the standard error is 0.063. The standard error will be:

= [p × (1 - p)]/n

= [0.275 × (1 - 0.275)]/50

= 0.0039875

= ✓0.0039875

= 0.063

Also, when the sample is 500, the center of the sampling distribution is 0.275 and the standard error is 0.020.

Learn more about sampling distribution on:

https://brainly.com/question/15205225

Answer:

-27

Step-by-step explanation:

5(-3)^3(5)^-1

5(-27)(1/5)

-135(1/5)

-135/5

-27

Hopes this helps please mark brainliest

Answer:

41. 48 years and 3 months.

Step-by-step explanation:

41.

let's use the compound interest formula. The formula for compound interest is:

\(\bold{A = P * (1 + r)^n}\)

Where:

A is the final amount

P is the principal (initial investment)

r is the interest rate per period

n is the number of periods

we have,

P= $5000

A=$15000

r=2.3%

Now substituting value

\(15000=5000(1+\frac{2.3}{100})^n\\15000=5000(1.023)^n\\\frac{15000}{5000}=(1.023)^n\\3=(1.023)^n\)

doing logarithms of both sides of the equation.

We can use the natural logarithm (ln) to solve for n. The equation becomes:

\(ln(3) = ln(1.023)^n\)

Using the logarithmic property\(lna^b = b * ln(a),\) we can rewrite the equation as:

ln(3) = n * ln(1.023)

n=\(\frac{ln \:3}{ln\:1.023}\)

n=48.313 years approximately 48 years and 3 months.

Answer:

41. 49 years

42. 34 years and 12 days

Step-by-step explanation:

As the account increases by a constant percentage each year, we can use the exponential growth formula to write a function to model the situation.

\(\boxed{\begin{minipage}{8 cm}\underline{Exponential Growth Formula}\\\\$ f(t)=a\left(1+r\right)^{t}$\\\\where:\\\\ \phantom{ww}$\bullet$ $f(t)$ is the account balance. \\ \phantom{ww}$\bullet$ $a$ is the principal amount.\\ \phantom{ww}$\bullet$ $r$ is the interest rate (in decimal form). \\ \phantom{ww}$\bullet$ $t $ is the time (in years). \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula, and solve for t:

\(\begin{aligned}f(t)&=a(1+r)^t\\\\\implies 15000&=5000(1+0.023)^t\\15000&=5000(1.023)^t\\3&=(1.023)^t\\\\\textsf{Take natural logs:} \quad \ln (3)&=\ln (1.023)^t\\\ln (3)&=t\ln (1.023)\\t&=\dfrac{\ln (3)}{\ln (1.023)}\\t&=48.3129760...\end{aligned}\)

The account balance will reach $15,000 during the 48th year. As the interest is applied annually, we need to round up to the nearest whole year. Therefore, the account balance will reach $15,000 after 49 years.

Note: At the end of 48 years, the account balance will be $14,893.63, and after 49 years it will be $15,236.18.

\(\hrulefill\)

As the baseball's value increases by a constant percentage each year, we can use the exponential growth formula to write a function to model the situation.

\(\boxed{\begin{minipage}{8 cm}\underline{Exponential Growth Formula}\\\\$ V(t)=a\left(1+r\right)^{t}$\\\\where:\\\\ \phantom{ww}$\bullet$ $V(t)$ is the value of the baseball card. \\ \phantom{ww}$\bullet$ $a$ is the initial value of the card in 1980.\\ \phantom{ww}$\bullet$ $r$ is the interest rate (in decimal form). \\ \phantom{ww}$\bullet$ $t $ is the time (in years). \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula, and solve for t:

\(\begin{aligned}V(t)&=a(1+r)^t\\\\\implies 2000&=200(1+0.07)^t\\2000&=200(1.07)^t\\10&=(1.07)^t\\\\\textsf{Take natural logs:} \quad \ln (10)&=\ln (1.07)^t\\\ln (10)&=t\ln (1.07)\\t&=\dfrac{\ln (10)}{\ln (1.07)}\\t&=34.0323838...\end{aligned}\)

The value of the baseball card will reach $2,000 during the 34th year - after 34 years and 12 days. As this is not an investment account where interest is applied annually, we don't need to round up. Therefore, the baseball card will be worth $2,000 after 34 years and 12 days.

Answer:

okHow big of fire

Step-by-step explanation:

Answer:

Step-by-step explanation:

Dissolving in rubbing alcohol (like 70% alcohol) works much better because it contains enough water to dissolve the compound, but alcohol to help the fire. Then, you can mix the dissolved salt with any liquid fuel. Alternatively, use a spray bottle to spritz a blue flame to turn it yellow.

Answer:

the area of the rectangle is A=L•W

The length is 3m less than twice its width W: L+ 3m=2W...->, L=2W-3m

A=L-W

27m²=(2W-3m)-W

27m2=2w2-3m-W

2w2-3wm-27m2=0

....use quadratic formula -(-3m)+ (-3m)²-4-2-(-27m²)

W=

2-2

w=(3m± √9m²+216m²)

w=(3m+ √225m²)

W=(3m± 15m...you need only positive root because width cannot be negative

W= 3m+15m

4

W=. 4

18m

W=4.5m ......now find the L

L=2.4.5m-3m

L=9m-3m

L=6m

Answer:

W = 4.5cm

L = 6cm

Step-by-step explanation:

The Error checking button provides an automatic means of checking for mathematical errors within formulas of a worksheet.

The modeling process begins with the framing of a conceptual model that shows the relationships between the various parts of the problem being modeled.

Arrows pointing from the selected cell to cells that depend on the selected cell are generated by using the Trace dependents button of the Formula Auditing group.

nodes in an influence diagram represent part of the model

The Trace Precedents button, located in the Formula Auditing group, creates arrows pointing to the selected cell from cells that are part of the formula in that cell

The Error checking button provides an automatic means of checking for mathematical errors within formulas of a worksheet.

To know more about error checking button brainly.com/question/1278871

#SPJ4

Answer:

(x-5,y-1) traslation

Step-by-step explanation:

Hope this helps!❆

The inequality expression that corresponds to the solution of the inequality graph is x² + 3x - 3 < 0.

option B.

The inequality expression that corresponds to the solution of the inequality graph is determined by simplifying the equations as follows;

The solution of the graph,

x > -4 and x < 1

The first equation with "≥" is ruled out because the graph doesn't have a thick dot.

Let's simplify the second expression;

x² + 3x - 3 < 0

solve using quadratic formula;

x > -3.79 or x < 0.79

The third expression is ruled out since its solution will be complex.

For the last expression;

x² + 3x - 3 > 0

x < -3.79 or x > 0.79

Thus, the correct inequality expression is x² + 3x - 3 < 0.

Learn more about inequality expression here: https://brainly.com/question/25275758

#SPJ1

Answer:

5

Step-by-step explanation:

took the test

The coordinates of the point that divides the line segment from J to K into a ratio of 2:3 are P(-5,7), and the y-coordinate is 7, the correct option is D.

Ratio is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

We are given that;

Ratio= 2:3

Now,

Let the point we are looking for be denoted as P(x,y), and let the ratio be 2:3, which means that the distance from J to P is 2/5 times the distance from J to K.

Using the distance formula, we can find the distance between J and K as:

d = sqrt((x2-x1)^2 + (y2-y1)^2)

= sqrt((-8 - (-3))^2 + (11 - 1)^2)

= sqrt(25 + 100)

= sqrt(125)

The distance from J to P is 2/5 of the total distance, which is:

(2/5)d = (2/5)sqrt(125) = 2sqrt(5)

Using the ratio formula, we get:

x = (3* (-3) + 2 * (-8)) / (3+2) = -5

y = (31 + 211) / (3+2) = 7

Therefore, by the given ratio answer will be 7.

Learn more about the ratio here:

brainly.com/question/13419413

#SPJ7

To find the probability that Naomi selects both white balls, we need to consider the total number of possible outcomes and the number of favorable outcomes.

Total number of outcomes:

Naomi selects 2 balls without replacement, so the total number of outcomes is the number of ways she can choose 2 balls out of the total number of balls in the bag. This can be calculated using combinations:

Total outcomes = C(20, 2) = (20!)/(2!(20-2)!) = (20 * 19)/(2 * 1) = 190

Number of favorable outcomes:

Naomi needs to select 2 white balls. There are 2 white balls in the bag, so the number of favorable outcomes is the number of ways she can choose 2 white balls out of the 2 white balls in the bag:

Favorable outcomes = C(2, 2) = 1

Probability = Favorable outcomes / Total outcomes = 1/190

Therefore, the correct answer is (G) 1/190.

Answer:

The single decimal multiplier is 26%.

Step-by-step explanation:

Since we have given that

You use to increase by 5% followed by 20% increase.

So, the single decimal multiplier would be

Hence, the single decimal multiplier is 26%.

The question is incomplete. Here is the complete question.

USA Today reported that 36% of adult drivers admit that they often or sometimes talk on a cell phone when driving. This was based on a random sample of 1004 adult drivers.

a) What is a 90% confidence interval for the true proportion of adult drivers who have often or sometimes talk on a cell phone when driving?

b) What is a 95% confidence interval for the true proportion of adult drivers who have often or sometimes talk on a cell phone when driving?

c) What is a 99% confidence interval for the true proportion of adult drivers who have often or sometimes talk on a cell phone when driving?

d) What do you notice?

Answer and Step-by-step explanation: The way to calculate confidence interval for proportions is by using the following formula:

\(z(\sqrt{\frac{p(1-p)}{n} } )\)

where

p is the sample population proportion

n is the number of individuals in the sample

z is z-score associated of the % of confidence

a) A 90% confidence has a z-score of z = 1.645

Calculating:

Interval = \(1.645(\sqrt{\frac{0.36(1-0.36)}{1004} } )\)

Interval = \(1.645(\sqrt{0.00023} )\)

Interval = \(1.645(0.01515)\)

Interval = 0.025

A 90% Confidence interval for true population is between 0.335 and 0.385.

b) A 95% confidence has a z-score of z = 1.96

Since the sample parameter didn't change, the interval will be:

Interval = 1.96(0.01515)

Interval = 0.03

For a 95% confidence, interval is between 0.33 and 0.39.

c) A 99% confidence has a z-score of z = 2.58

Interval = 2.58(0.01515)

Interval = 0.39

For a 99% confidence, interval is between -0.03 and 0.75

d) Confidence interval tells you how certain your results from polling or survey would represent the real population's behaviour. In the experiment above, as the percentage of certainty grows, closer the real population proportion actually is for adult drivers who often or sometimes talk on a cell phone when driving.

Answer:

She will make $97.5 after 10 hours of work

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

32/2 x 100% = 1600 %

Part A: There are 28 green beans in the garden. Part B: There are 80 plants that are either pumpkin or tomato. Part C: There are 52 more corn plants than cucumber plants.

A circle graph, often called a pie chart, is a circular graph with sectors on it, each representing a particular category or set of data. Each sector's area or angle is proportionate to the amount it stands for. In data visualisation, circle graphs are frequently used to show the relative sizes or proportions of several categories or groups within a dataset. They can instantly convey the distribution of data without the need for laborious numerical calculations, which makes them effective for presenting data that is divided into discrete groups. However, if the data is not presented in a clear and simple manner or if the sectors are not precisely drawn to scale, circle graphs may be deceiving.

Part A: The percentage of green beans in the circle graph is 14%.

14% of 200 = 0.14 x 200 = 28

Part B: The circle graph shows:

pumpkin plants and tomato plants is 20% + 20% = 40%.

40% of 200 = 0.40 x 200 = 80

Part C: The corn plants is 36% and the percentage of cucumber plants is 10%.

36% of 200 - 10% of 200 = (0.36 x 200) - (0.10 x 200) = 72 - 20 = 52

Learn more about circle graph here:

https://brainly.com/question/13298277

#SPJ1

The percentage that can be filled with $3 in 1990 is: 29.41%

To calculate percentage growth rate:

Beginning:

Calculate the difference (increase) between the two numbers you are comparing. after that:

Divide the increment by the original number and multiply the result by 100. Growth rate = increment / original number * 100.  

We are told that it cost $3 to fill a gas tank as at 1970.

Now, there was a percentage price increase of (78.8 - 23.1)% = 55.2% from 1970 to 1990. Thus:

Cost of a gallon in 1970 = $0.36

Thus, number of gallons bought with $3 = 3/0.36 = 8.33 gallons at full tank

Now, in 1990, the cost is $1.23 and as such:

Quantity that can be bought = 3/1.23 = 2.45 gallons

Percentage of tank filled = 2.45/8.33 * 100% = 29.41%

Read more about Percentage increase at: https://brainly.com/question/11360390

#SPJ1

The angle in degrees is 873.1843.

Let the measure of the angle be θ in degrees. Therefore, the measure of the same angle in gradians is (θ × π/180).

According to the given information, the number of degrees of a certain angle added to the number of gradians of the same angle is 152.(θ) + (θ × π/180) = 152.

Simplifying the above equation, we get:(θ) + (θ/180 × π) = 152.

Multiplying both sides of the equation by 180/π, we get:

θ + θ = (152 × 180)/π2θ = (152 × 180)/πθ = (152 × 180)/(3.14)θ = 873.1843

Thus, the angle in degrees is 873.1843.

For more such questions on angle, click on:

https://brainly.com/question/25770607

#SPJ8

The value of x in each of the case is given below.

Perimeter of a straight sided figures or objects is the total length of it's boundary.

The given figures are squares.

Perimeter of a square is the sum of the length of four sides. Since all the sides are equal,

Perimeter of square = 4s, where s is the length of a side

1. Length of one side is x and the perimeter is 20.

4x = 20

x = 20 / 4 = 5

2. Length of one side is x and the perimeter is 26.

4x = 26

x = 26 / 4 = 6.5

3. 4(x + 3) = 32

4x + 12 = 32

4x = 20

x = 20 / 4 = 5

Length of a side = x + 3 = 8

4. 4(x + 3) = 38

4x + 12 = 38

4x = 26

x = 26 / 4 = 6.5

Length of a side = x + 3 = 9.5

5. 4 (2x - 5) = 48

8x - 20 = 48

8x = 68

x = 68 / 8 = 8.5

Length of one side = 2x - 5 = (2 × 8.5) - 5 = 12

6. 4 (2x - 5) = 64

8x - 20 = 64

8x = 84

x = 84 / 8 = 10.5

Length of a side = 2x - 5 = (2 × 10.5) - 5 = 16

7. 4 (10 - x) = 40

40 - 4x = 40

4x = 0

x = 0

Length of one side = 10 - x = 10 - 0 = 10

8. 4(8 - x) = 40

32 - 4x = 40

4x = -8

x = -2

Length of a side = 8 - -2 = 10

Hence the values of x and side lengths are found.

Learn more about Perimeters here :

https://brainly.com/question/30252651

#SPJ1

Answer:

The maximum distance between supports for the beam to support a weight of 1600 lb is also 4.5 feet.

Step-by-step explanation:

We are given that weight P is inversely proportional to the distance D between the supports of the beam, and for this certain type of wooden beam, we have:

P = 7200/D

To find the distance between supports needed to carry 1600 lb, we can substitute P = 1600 in the above equation and solve for D:

1600 = 7200/D

D = 7200/1600

D = 4.5 feet

So the distance between supports needed to carry 1600 lb is 4.5 feet.

To find the maximum distance between supports for the beam to support a weight of 1600 lb, we can use the same equation and solve for P = 1600:

1600 = 7200/D

D = 7200/1600

D = 4.5 feet

Therefore, the maximum distance between supports for the beam to support a weight of 1600 lb is also 4.5 feet.