solve the nonlinear system of equations. State the number of solutions.

Answer: 3.6

Step-by-step explanation:

2/x=5/9

Multiply(x)

2=5/9x

Divide by 5/9

x=3.6

Hope it helps <3

Answer:

84π mm^2

Step-by-step explanation:

formula for circumference is 2πr where r is the radius of circle

Given,The circumference of the base of a cylinder is 24π mm

Thus,

2πr= 24π mm

=> r = 24π mm/2π = 12 mm

________________________________________

A similar cylinder has a base with circumference of 60π mm.

radius for this cylinder will be

2πr= 60π mm

r =   60π mm/2π = 30mm

______________________________________________

Given

The lateral area of the larger cylinder is 210π mm2

lateral area of cylinder is given by  2πrl

where l is the length of cylinder

thus,

r for larger cylinder = 30mm

2π*30*l  = 210π mm^2

=> l = 210π mm^2/2π*30 = 3.5 mm

___________________________________________

the lateral area of the smaller cylinder

r = 12 mm

l = 3.5 mm as both larger and smaller cylinder are same

2πrl  =  2π*12*3.5 mm^2 = 84π mm^2 answer

Answer:

33.6pi mm2 is the correct answer

edge 2021

Step-by-step explanation:

The circumference of the base of a cylinder is 24π mm. A similar cylinder has a base with circumference of 60π mm. The lateral area of the larger cylinder is 210π mm2.

What is the lateral area of the smaller cylinder?

17.1π mm2

33.6π mm2

60π mm2

84π mm2

Answer:

[tex]\boxed{x = 8}[/tex]

Step-by-step explanation:

For NO ║ KJ, The two triangles must be similar and their sides must be proportional.

So, the proportion of their sides is:

=> [tex]\frac{x-4}{x} = \frac{x-3}{x+2}[/tex]

Cross Multiplying

[tex]\sf x (x-3)= (x-4)(x+2)\\Multiplying\\x^2-3x = x^2+2x-4x-8\\x^2-3x = x^2-2x-8\\Subtracting\ x^2\ to \ both \ sides\\ -3x = -2x -8\\Adding \ 2x\ to\ both\ sides\\-3x+2x = -8\\-x = -8\\[/tex]

x = 8

So, For x = 8, NO will be parallel to KJ.

Answer:

25%

Step-by-step explanation:

First you have the fraction of 3/12 and need to turn it into a decimal. So to do that you divide 3 by 12 = 0.25. So your percent is 25%

Answer:

$70.33

Step-by-step explanation:

sticker price = $93.78

discount coupon in percentage = 25%

Thus, discount will be 25% of sticker price

discount amount = 25% of  $93.78 = 25/100 *  $93.78 = $23.45

Thus, amount paid = sticker price - discount amount  =  $93.78-$23.45

amount paid = $70.33

actual cost to you will be what after discount applied is $70.33

Answer:

Step-by-step explanation:

Easy way to solve

5^4 = 625.

5^12=244140625.

Thus, 625m=244140625.

Divide both sides by 625/

m=390625, or 5^8.

Better way to solve

When dividing by exponents [tex]x^{4}/x^{2} =x^{4-2}=x^2[/tex]

Thus, simply do 12-4=8 to know that m=5^8.

Hope it helps <3

Answer:

Step-by-step explanation:

(5⁴)m = 5¹²

Divide both sides by 5⁴

((5⁴)m)/5⁴ = 5¹²/5⁴

m = 5⁸

Answer:

62

Step-by-step explanation:

180-116 makes us find out that angle C is 64, thus to find out the inner angles you gotta do 64+ (2x+4)+(3x-13)=180

You follow this operation, find out x and perform 3(25)-13, which ends up giving you 62

Answer:

62°

Step-by-step explanation:

The sum of two interior angles in a triangle is equal to an exterior angle that is not sharing a common side

2x + 4 + 3x - 13 = 116° add like terms

5x - 9 = 116°

5x = 125° divide both sides by 5

x = 25 and angle A is 3x - 13 so 3×25 - 13 = 62°

Answer:

Step-by-step explanation:

Set notation { } is used in this case, to represent the domain and the range.

The values that go into T are the domain while the values that come out of T are the range.

The domain comprises all x (independent) values while the range comprises all y (dependent) values.

This should be applied in the clear definition of the relation T.

Answer:

The answer is option A

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

Equation of the line using point (1 , - 2) and slope 1/3 is

y + 2 = 1/3( x - 1)

Multiply through by 3

That's

3y + 6 = x - 1

Simplify

x - 3y - 1 - 6 = 0

We have the final answer as

Hope this helps you

Answer:

the probability that the average height of 25 randomly selected women will be bigger than 66 inches is 0.0013

Step-by-step explanation:

From the summary of the given statistical dataset

The mean and standard deviation for the sampling distribution of sample mean of 25 randomly selected women can be calculated as follows:

[tex]\mu_{\overline x} = \mu _x[/tex] = 64.5

[tex]\sigma_{\overline x }= \dfrac{\sigma}{\sqrt n}[/tex]

[tex]\sigma_{\overline x }= \dfrac{2.5}{\sqrt {25}}[/tex]

[tex]\sigma_{\overline x }= \dfrac{2.5}{5}[/tex]

[tex]\sigma_{\overline x }[/tex] = 0.5

Thus X [tex]\sim[/tex] N (64.5,0.5)

Therefore, the probability that the average height of 25 randomly selected women will be bigger than 66 inches is:

[tex]P(\overline X > 66) = P ( \dfrac{\overline X - \mu_\overline x}{\sigma \overline x }>\dfrac{66 - 64.5}{0.5} })[/tex]

[tex]P(\overline X > 66) = P ( Z>\dfrac{66 - 64.5}{0.5} })[/tex]

[tex]P(\overline X > 66) = P ( Z>\dfrac{1.5}{0.5} })[/tex]

[tex]P(\overline X > 66) = P ( Z>3 })[/tex]

[tex]P(\overline X > 66) = 1- P ( Z<3 })[/tex]

[tex]P(\overline X > 66) = 1- 0.9987[/tex]

[tex]P(\overline X > 66) =0.0013[/tex]

the probability that the average height of 25 randomly selected women will be bigger than 66 inches is 0.0013

Answer:

b = sqrt(57)

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

8^2 + b^2 = 11^2

64+ b^2 = 121

Subtract 64

b^2 = 121-64

b^2 =57

Take the square root of each side

b = sqrt(57)

[tex] v = \sqrt{4900} + \sqrt{8100} = 70 + 90 = 160[/tex]

Answer: D. 160

Answer:

Step-by-step explanation:

Permutation has to do with arrangement. If r objevt selected from n pool of objects are to be arranged in a straight line, this can be done in nPr number of ways.

nPr = n!/(n-r)!

If 5 people are to be chosen and arranged in a straight line, if there are 6 people to choose from, this can be done in  6P5 numbe of ways.

6P5 = 6!/(6-5)!

6P5 = 6!/1!

6P5 = 6*5*4*3*2*1

6P5  = 720 different ways

Answer:

648 followers

Step-by-step explanation:

Let first day=a1

Tripled followers everyday

Second day=a2=a1×3

Third day=a3=a2*3

Fourth day=a4=a3*3

Fifth day=a5=a4*3

a=8 followers

a2=a1×3

=3*8

=24 followers

a3=a2*3

=24*3

=72 followers

a4=a3*3

=72*3

=216 followers

a5=a4*3

=216*3

=648 followers

On the fifth day, Alex will have a total of 648 followers on his new social media account.

Answer:

624

Step-by-step explanation:

648 i used a calculator

Answer:

(D)  12

Step-by-step explanation:

Plug in the given values into the expression.  a = -2  b = -3

(-ab)(a)

[-(-2)(-3)](-2)

(-6)(-2)

12

Answer:

6.64 ft²

Step-by-step explanation:

Given the above triangle with 2 sides of lengths 3.2 ft and 4.7 ft respectively, and angle 62° in between, the following formula can be used to calculate the area: ½*a*b*sin(θ).

Thus, a and b are the 2 given sides and θ is the included angle in between both sides.

Therefore,

Area = ½*3.2*4.7*sin(62)

Area = ½*15.04*0.88295

Area = ½*13.279568

Area = 6.639784

Area = 6.64 ft² (to the nearest hundredth)

Answer:

Easiest way to do this is to get the X's on one side of the equals sign and the Y's on the other. Then, you can choose the one with the negative sign in it.

When you do that,

First one is 2x=0+y, or y = 2x

Second one is 2y=0+x, or 2y = x (weird right)

Third one is x=0+2y, or 2y = x (again, weird right)

Final one is 2y=0-x, or 2y = -x

The final one is the answer. Cheers, but don't forget to remember this for next time bro.

ANSWER :

6i - (1-i)

Step - by - step explanation:

( 4 + 2i ) - ( 1 - i )

( 4 + 2 × i) - ( 1 - i )

( 6× i ) - ( 1 - i )

= 6i- (1-i)

Hope this helps and pls mark as brainliest :)

Answer:

C. [tex] \frac{343}{18} pie [/tex]

Step-by-step explanation:

Given a circle of:

Radius (r) = 14

Measure of minor arc = 115°

We are required to find the length of DGE = length of major arc.

Length of arc is given as 2πr(θ/360)

Measure of the major arc DGE (θ) = 360 - 115 = 245°

Length of major arc DGE = [tex] 2*pie*14*\frac{245}{360} [/tex]

[tex] = 28*pie*\frac{49}{72} [/tex]

[tex] = \frac{28*49}{72} pie [/tex]

[tex] = \frac{7*49}{18} pie [/tex]

[tex] = \frac{343}{18} pie [/tex]

Length of arc DGE =

[tex] \frac{343}{18} pie [/tex]

Answer:

24.5 mpg

Step-by-step explanation:

(23,695 - 23,252) / 14 = 24.5mpg

Answer:

The car averaged a total of 24.5 miles per gallon between the two fillings

Step-by-step explanation:

Firstly, we calculate the difference between the mileages.

This will give us the total distance traveled.

That would be 23,695 - 23,352 = 343 miles

The tank capacity obviously is 14 gallons

So mathematically, miles per gallon averaged between the two fillings = distance traveled by the car/gallon of fuel used = 343/14 = 24.5 miles per gallon

Answer:

-k+8k=7k is the solution

Answer:

[tex]\boxed{\frac{x^2 }{8} }[/tex]

Step-by-step explanation:

The quotient is the result from division.

Let x be that number.

Division between x² and 8.

[tex]\frac{x^2 }{8}[/tex]

The algebraic expression representing the quotient of a number squared and eight is x²/8.

An algebraic expression is a combination of terms formed using mathematical operators (+, -, *, /). The terms are made by the combination of variables and constants.

In the question, we are asked to write an algebraic expression that represents the quotient of a number squared and eight.

We know that an algebraic expression constitutes both variables and constants.

We assume the number in the expression to be x.

The number squared is then represented by x².

The quotient of the number squared and eight can be represented as x²/8.

Therefore, the algebraic expression representing the quotient of a number squared and eight is x²/8.

Learn more about the algebraic expressions at

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Answer:

The answer is below

Step-by-step explanation:

A sugar refinery has three processing plants, all receiving raw sugar in bulk. The amount of raw sugar (in tons) that one plant can process in one day can be modelled using an exponential distribution with mean of 4 tons for each of three plants. If each plant operates independently,a.Find the probability that any given plant processes more than 5 tons of raw sugar on a given day.b.Find the probability that exactly two of the three plants process more than 5 tons of raw sugar on a given day.c.How much raw sugar should be stocked for the plant each day so that the chance of running out of the raw sugar is only 0.05?

Answer: The mean (μ) of the plants is 4 tons. The probability density function of an exponential distribution is given by:

[tex]f(x)=\lambda e^{-\lambda x}\\But\ \lambda= 1/\mu=1/4 = 0.25\\Therefore:\\f(x)=0.25e^{-0.25x}\\[/tex]

a) P(x > 5) = [tex]\int\limits^\infty_5 {f(x)} \, dx =\int\limits^\infty_5 {0.25e^{-0.25x}} \, dx =-e^{-0.25x}|^\infty_5=e^{-1.25}=0.2865[/tex]

b) Probability that exactly two of the three plants process more than 5 tons of raw sugar on a given day can be solved when considered as a binomial.

That is P(2 of the three plant use more than five tons) = C(3,2) × [P(x > 5)]² × (1-P(x > 5)) = 3(0.2865²)(1-0.2865) = 0.1757

c) Let b be the amount of raw sugar should be stocked for the plant each day.

P(x > a) = [tex]\int\limits^\infty_a {f(x)} \, dx =\int\limits^\infty_a {0.25e^{-0.25x}} \, dx =-e^{-0.25x}|^\infty_a=e^{-0.25a}[/tex]

But P(x > a) = 0.05

Therefore:

[tex]e^{-0.25a}=0.05\\ln[e^{-0.25a}]=ln(0.05)\\-0.25a=-2.9957\\a=11.98[/tex]

a  ≅ 12

Answer:

Step-by-step explanation:

The average salary in this city is $45,600.

Using the formula

z score = x - u /(sd/√n)

Where x is 46,356, u is 45,600 sd is 15,930 and n is 53.

z = 46,356 - 45600 / (15930/√53)

z = 756/(15930/7.2801)

z = 756/(2188.1568)

z = 0.3455

To draw a conclusion, we have to determine the p value, at 0.05 level of significance for a two tailed test, the p value is 0.7297. The p value is higher than the significance level, thus we will fail to reject the null and can conclude that there is not enough statistical evidence to prove that the average is any different for single people.

Answer:

.

Step-by-step explanation:

The value of A is A = 4³¹

Exponents are the base raised by power, it is written in the superscript of a number.

The expression is

[tex]\rm 4^{31x}\\[/tex]

To write in form Aˣ

A will be obtained by comparing the expressions

Aˣ = [tex]\rm 4^{31x}\\[/tex]

A = 4³¹

Therefore, the value of A is A = 4³¹.

To know more about Exponents

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Answer:

-2,-1,0,1,2,3

You just have to choose the numbers in between -3 to 3

Hope it helped ;)

Answer:

8 pounds

Step-by-step explanation:

2 x 3 = 6 tb of chili powder in pot 2

find pounds per tablespoon: 48 / 6 = 8 pounds

Answer:

1/2 pound per tablespoon

Step-by-step explanation:

Jaden sure does like his chili!

In the first and second pot, he uses 3 pounds worth of ground beef, which means, 12 ounces of something is a pound. And because Jaden had used 3 times the amount of chili powder in the second pot, he used 6 tablespoons worth of powder. 3 pounds divided by 6 equals 1/2.

Answer:

monomial

Step-by-step explanation: