5- Calculate the radius of a circle whose area is equal to the sum of the areas of 3 circles of radii 2cm, 3cm and 4cm
respectively.​

The total surface area of the figure is 92 m².

The surface area of a figure is the sum of the whole sides of the figure.

Therefore,

surface area = 4 × 4 + 4 × 4 + 6 × 4 + 2 × 4 + 1 / 2 (2 + 6)3.5 +  1 / 2 (2 + 6)3.5

Hence,

surface area = 16 + 16 + 24 + 8 + 14 + 14

Therefore,

surface area = 32 + 24 + 8 + 28

surface area = 56 + 8 + 28

surface area = 92 m²

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Answer:

8.5

Step-by-step explanation:

4 + (6)(6)/8=

17/2 = 8.5

Answer:

8.5

Step-by-step explanation:

6 x 6 = 36/8 = 4.5 + 4 = 8.5

The regression equation between the variables is y = 1.03x + 62.12 and the blood pressure on the left arm given that the systolic blood pressure in the right arm is 85 mm Hg is 149.67

From the table of values, we make use of the following representations:

Using the above representations, we can now plot our data values on a graphing calculator

From the graphing calculator, we have the following summary:

The regression equation is

y = bx + a

Where

b = SP/SSX = 618.8/601.2 = 1.02927

a = MY - bMX = 156.4 - (1.03*91.6) = 62.11843

This gives

y = 1.03x + 62.12

Hence, the regression equation between the variables is y = 1.03x + 62.12

To predict the blood pressure on the left arm given that the systolic blood pressure in the right arm is 85 mm Hg, we have

y = 1.03 * 85 + 62.12

Evaluate

y = 149.67

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The function to model the water used by the car wash on a shorter day is (C) [tex]4x^{3} +7x^{2} -14x-6[/tex].

To find the function to model the water used by the car wash on a shorter day:

Given that the amount of water used on normal days is given by the equation:

The amount of decrease in water used is modeled by the equation:

To get the function [tex]C(x)[/tex] that models the water used by the car wash on a shorter day you subtract equation (2) from equation (1).

Therefore, the function to model the water used by the car wash on a shorter day is (C) [tex]4x^{3} +7x^{2} -14x-6[/tex].

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The correct question is shown below:

The water usage at a car wash is modeled by the equation w(x) = 5x3 9x2 − 14x 9, where w is the amount of water in cubic feet and x is the number of hours the car wash is open. the owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. the amount of decrease in water used is modeled by d(x) = x3 2x2 15, where d is the amount of water in cubic feet and x is time in hours. write a function, c(x), to model the water used by the car wash on a shorter day.

(A) c(x) = 5x3 7x2 − 14x − 6

(B) c(x) = 4x3 7x2 − 14x 6

(C) c(x) = 4x3 7x2 − 14x − 6

(D) c(x) = 5x3 7x2 − 14x 6

Answer:

  $0.04

Step-by-step explanation:

The cost per ounce is found by dividing the cost by the number of ounces.

In 2 gallons, there are 2×128 fl.oz. = 256 fl.oz. Then the cost per ounce is ...

  cost/ounces = $10.24/(256 fl.oz) = $0.04 /fl.oz.

The cost of the laundry detergent is $0.04 per fluid ounce.

__

Additional comment

Keeping the units with the numbers in a calculation can give you confidence that the calculated result has the units you want it to have.

The number of hours it will take both the surveyor and apprentice to complete the same job is 15/56 hours.

If the two work together;

Time taken for both to complete the task = Surveyors rate of work + Apprentice rate of work

= 1/8 + 1/7

= (7+8) / 56

= 15/56 hours

Therefore, the number of hours it will take both the surveyor and apprentice to complete the same job is 15/56 hours.

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Answer: [tex]\Large\boxed{C.~21}[/tex]

Step-by-step explanation:

The goal of the question

Find the value of 2abcosC

Given information

a = 4

b = 3

c = 2

Given formula (Law of Cosine)

[tex]c^2=a^2+b^2-2abcosC[/tex]

Substitute values into the formula (Leave 2abcosC as it is)

[tex](2)^2=(4)^2+(3)^2-2abcosC[/tex]

Simplify the exponents

[tex]4=16+9-2abcosC[/tex]

Simplify by addition

[tex]4=25-2abcosC[/tex]

Add 2abcosC on both sides

[tex]4+2abcosC=25-2abcosC+2abcosC[/tex]

[tex]4+2abcosC=25[/tex]

Subtract 4 on both sides

[tex]4 + 2abcosC-4=25-4[/tex]

[tex]\Large\boxed{2abcosC=21}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

C

Step-by-step explanation:

a² + b² - 2abcosC = c² ( subtract a² + b² from both sides )

- 2abcosC = c² - a² - b² ( multiply through by - 1 )

2abcosC = a² + b² - c²

a, b, c are the sides opposite vertices A, B, C

here a = 4 , b = 3 , c = 2 , then

a² + b² - c²

= 4² + 3² - 2²

= 16 + 9 - 4

= 25 - 4

= 21

Answer:

"Unary Association" I believe

The surface area of the shape is 117.8 km²

From the question, we are to determine the surface area of the figure

The given figure is a cone.

Total surface area of a cone  = Area of circular part + Curved surface area

Total surface area of a cone = πr² + πrl = πr(r + l)

Where r is the radius

and l is the slant height

From the given information,

r = 3 km

l = 9.5 km

The total surface area of the cone = π×3(3+9.5)

The total surface area of the cone = 3π(12.5)

The total surface area of the cone = 117.8 km²

Hence, the surface area of the shape is 117.8 km²

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Answer:

D

Step-by-step explanation:

I did the assignment

hope this helps :)

4 andfirst find x by finding its smallest factor

The solution to the given system of equation is -7 and 7

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

Given:

4x² = 196

4x²/4= 196/4

x² = 49

x=√49

x= ±7

Hence, the solution to the given system of equation is -7 and 7

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According to the developed scale, a radiant day is 16 times brighter than a dim day.

We assume the brightness of a dim day to be x.

According to the developed scale, the brightness of an illuminated day will be 4 times that of a dim day.

Thus, the brightness of an illuminated day = 4*the brightness of a dim day = 4x.

According to the developed scale, the brightness of a radiant day will be 4 times that of an illuminated day.

Thus, the brightness of a radiant day = 4*the brightness of an illuminated day = 4*4x = 16x.

Now, the ratio of the brightness of a radiant day to the brightness of a dim day = 16x:x = 16x/x = 16:1.

Thus, according to the developed scale, a radiant day is 16 times brighter than a dim day.

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The question provided is incomplete. The complete question is:

"Suppose you have developed a scale that indicates the brightness of sunlight. Each category in the table is 4 times brighter than the next lower category. For example, a day that is dazzling is 4 times brighter than a day that is radiant. How many times brighter is a radiant day than a dim day?

Dim=2

Illuminated=3

Radiant=4

Dazzling=5"

Answer:

B. -1/3

Step-by-step explanation:

Choose 2 points. From the lower points count up until it is in line with the other point. Then count left until you reach the second point.

Rise/Run

Rise=1

Run=-3

[tex]-\frac{1}{3}[/tex]

Hope this helps!

Answer: -1/3 is the answer

Step-by-step explanation:

The distance of the spaceship in discuss as in the task content given can be evaluated as; 800miles.

The distance travelled by the spaceship in discuss can be evaluated by means of the slope of the linear relationship as follows;

Hence it follows from ratios that by observation, the linear relationship has a slope of 200mi/min.

Consequently, we can evaluate the distance travelled after 4 minutes as;

Distance = 200 × 4 = 800mi.

Ultimately, the distance travelled per minute by the spaceship is; 800mi.

Remarks:

600 miles

520 miles

800 miles

1,080 miles

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Based on the amount of oranges bought, those sold at a profit and those sold at a loss, the overall profit is 14.2%

Assume that the buying price was $1 each.

The amount earned from 60% of them is:

= 60% x 100,000 x 1

= $60,000

The profit from selling 50% of the remaining is:

= (50% x 40,000) x 1.60

= $32,000

The loss from selling the other 50%:

= (50% x 40,000) x 0.90

= $22,222.22

Total selling price:

= 60,000 + 32,000 + 22,222.22

= $114,222.22

Total profit:

= (114,222.22 - 100,000) / 100,000

= 14.2%

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the equation with these solutions is:

0 = x^2 - 6x + 6

Remember that a quadratic equation with the solutions a and b is written as:

0 = (x - a)*(x - b)

Here we have the solutions:

Then we can write a quadratic equation of the form:

0 = (x - (3 + √3) )*(x - (3 - √3) )

0 = (x - 3 - √3)*(x - 3 + √3)

Expanding that, we get:

0 = x^2 - 6x + 9 - 3

0 = x^2 - 6x + 6

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The number of quick car and premium car washes ordered are 75 and 50 respectively.

The system of equation models the situation

x + y = 125

5x + 8y = 775

Therefore,

5x + 5y = 625

5x + 8y = 775

3y = 150

divide both sides 3

3y / 3 = 150 / 3

y = 50

Therefore,

x + y = 125

x + 50 = 125

x = 125 - 50

x = 75

Therefore, the number of quick car and premium car washes ordered are 75 and 50 respectively.

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Answer:

50 and 75

Step-by-step explanation:

Answer:

12 sqrt (10)

Step-by-step explanation:

S = (12 + 11 + 7) / 2 = 15

A = sqrt (s(s-a)(s-b)(s-c))

= sqrt (15(15-12)(15-11)(15-7))

= sqrt (15*3*4*8)

= sqrt (1440)

= 12 sqrt (10)

Answer:

tanya 22

leah12

Step-by-step explanation:

i hope it

help ...

The points in a scatter plot cluster closely around the regression line, the correlation can be said to be the proportion of variance in Y that is determined or explained by X.

It is critical to understand that a correlation coefficient of zero indicates that there is no linear courting, but there can also nonetheless be a strong relationship among the 2 variables.

If one point of a scatter diagram is farther from the regression line than a few other factor, then the scatter diagram has as a minimum one outlier. If two or extra points are the identical farthest distance from the regression line not a commonplace prevalence), then every of those points is an outlier.

When the y variable has a tendency to increase because the x variable increases, we say there may be a high-quality correlation between the variables. when the y variable has a tendency to lower as the x variable increases, we are saying there's a bad correlation between the variables.

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The length of the diagonal of the canvas = 27 inches.

The correct option is D.

A fundamental relationship in Euclidean geometry between a right triangle's three sides is known as the Pythagorean theorem, or Pythagoras' theorem. The area of the square whose side is the hypotenuse is said to be equal to the total of the areas of the squares on the other two sides.

the Hight of the rectangle = 18 inches

the angle it form sinθ = H/P

H = 18

P =

cosθ = 48

cosθ = H/P

cosθ =18/P

P = 18/cosθ

 = 29.60

= 27

The length of the diagonal of the canvas = 27 inches.

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let's firstly convert the mixed fractions to improper fractions and them proceed.

[tex]\stackrel{mixed}{6\frac{1}{7}}\implies \cfrac{6\cdot 7+1}{7}\implies \stackrel{improper}{\cfrac{43}{7}} ~\hfill \stackrel{mixed}{3\frac{5}{9}}\implies \cfrac{3\cdot 9+5}{9}\implies \stackrel{improper}{\cfrac{32}{9}} \\\\\\ \stackrel{mixed}{4\frac{1}{6}}\implies \cfrac{4\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{25}{6}} ~\hfill \stackrel{mixed}{1\frac{1}{3}}\implies \cfrac{1\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{4}{3}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{ ~~ \frac{6\frac{1}{7}}{x}+3\frac{5}{9} ~~ }{4\frac{1}{6}}~~ = ~~1\frac{1}{3}\implies \cfrac{ ~~ \frac{ ~~ \frac{43}{7} ~~ }{x}+\frac{32}{9} ~~ }{\frac{25}{6}}~~ = ~~\cfrac{4}{3}\implies \cfrac{ ~~ \frac{43}{7x}+\frac{32}{9} ~~ }{\frac{25}{6}}~~ = ~~\cfrac{4}{3}[/tex]

[tex]\cfrac{43}{7x}+\cfrac{32}{9}~~ = ~~\cfrac{25}{6}\cdot \cfrac{4}{3}\implies \cfrac{43}{7x}+\cfrac{32}{9}~~ = ~~\cfrac{50}{9}\implies \cfrac{43}{7x}~~ = ~~\cfrac{50}{9}-\cfrac{32}{9} \\\\\\ \cfrac{43}{7x}~~ = ~~\cfrac{18}{9}\implies \cfrac{43}{7x}=2\implies 43=14x\implies \cfrac{43}{14}=x\implies 3\frac{1}{14}=x[/tex]

The linear functions with their slopes ranked from least to greatest are given as follows:

E. I, K, J.

A linear function is modeled by:

y = mx + b

In which:

In this problem, we have that:

Hence the linear functions with their slopes ranked from least to greatest are given as follows:

E. I, K, J.

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The margin of sampling error for a 95% confidence interval is 9.7%

The formula for margin of error here is;

E = z√(p(1 - p)/N)

where;

n is sample size

z is the z score

p is the sample proportion

z-score for a 95% confidence interval from tables is 1.96.

We are given;

p = 43% = 0.43

n = 100

Thus;

E = 1.96√(0.43(1 - 0.43)/100)

E =  0.097 = 9.7%

Thus, we can conclude that  the margin of sampling error for a 95% confidence interval is 9.7%

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To know if the classmate’s family is actually wealthy, one will need to know their assets and their debt.

In financial accounting, an asset means a resource that is owned or controlled by a business or an economic entity. An asset is anything that can be used to produce positive economic value.

Assets represent the value of ownership that can be converted into cash and the examples of personal financial assets include cash and bank accounts, real estate, personal property like furniture and vehicles, and investments such as stocks, mutual funds, and retirement plans.

In this case, through the assets, one will be able to know that they're wealthy. The debt is an obligation that requires one party, the debtor, to pay money or other agreed-upon value to another party, the creditor. This is the money that they owe.

The asset should more than the debt.

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The height of the flagpole is 12.4 meters and the altitude of the balloon is 29.1 meters

See attachment for the diagram, when redrawn

Start by calculating the length AB using the following tangent function

tan(22) = BC/AB

This gives

tan(22) = 9/AB

Make AB the subject

AB = 9/tan(22)

Evaluate the quotient

AB = 22.3

The length DB is then calculated using:

tan(9) = DB/AB

This gives

tan(9) = DB/22.3

Make DB the subject

DB = 22.3 * tan(9)

Evaluate

DB = 3.35

The height of the flagpole is then calculated as:

Height = DB + BC

This gives

Height = 3.35 + 9

Evaluate

Height = 12.35

Approximate

Height = 12.4

Hence, the height of the flagpole is 12.4 meters

The diagram that illustrates the scenario is added as an attachment

Calculate the value of y using the following tangent functions

tan(57) = x/y and tan(72) = (15 + x)/y

Make y the subject in tan(57) = x/y and tan(72) = (15 + x)/y

y = x/tan(57) and y = (15 + x)/tan(72)

Substitute y = x/tan(57) in y = (15 + x)/tan(72)

x/tan(57) = (15 + x)/tan(72)

Evaluate the tangent ratios

x/1.5 = (15 + x)/3.1

Cross multiply

3.1x = 22.5 + 1.5x

Evaluate the like terms

1.6x = 22.5

Divide by 1.6

x = 14.1

The altitude of the balloon is then calculated as:

Altitude = 14.1 + 15

Altitude = 29.1

Hence, the altitude of the balloon is 29.1 meters

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Answer:

14m

Step-by-step explanation:

Please refer to the attached figure
B is the position where John is standing, His eyes are at point A, 2 meters from the ground

D is the base of the cliff and E is the top of the cliff

∠EAC is the angle at which John looks up to the cliff and is given as 45°

BD is the distance from the cliff given as 12m

So AC is also 12m

∠ACE is 90°

Therefore ∠AEC is 180-(45+90) = 45° since AEC forms a triangle and sum of angles in a triangle = 180°

In the ΔAEC, by the law of sines
12/sin(45) = EC/sin(45) . This means EC = 12 since the denominators cancel out

Since point C is 2 meters above ground(the base of the cliff) add 2 and we get the height of the cliff as 12+2 = 14m

Answer:

B. 183

Step-by-step explanation:

m<L = (1/2)[m(arc)KN - m(arc)KM)]

35 = (1/2)(177x - 107x)

70 = 70x

x = 1

m(arc)KN = 177x = 177

m(arc)NMK = 360 - m(arc)KN

m(arc)MNK = 360 - 177

m(arc)MNK = 183

Yes, the correlation coefficient is statistically significance

The precise metric used in a correlation analysis to quantify the strength of the linear relationship between two variables is the correlation coefficient. In a correlation report, the r stands for the coefficient.

Given,

Sample size, n = 11

Where ρ is the population correlation.

Then the number of degrees of freedom is, df = n-2 = 11-2 = 9

The corresponding critical correlation value re for a significance level of a 0.01, for a two-tailed test is た= 0.254

Here,

The null hypothesis,  = ρ - 0 is rejected

Suppose lr> re 0.254

Because on the sample correlation provided, we know that lrl = 0.599>=0.254.

Here, it is clear that the null hypothesis is rejected.

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