consider 3 urns. urn acontains 2 white and 4 red balls, urn bcontains 8 white and 4 red balls, and urn ccontains 1 white and 3 red balls. if 1 ball is selected from each urn, what is the probability that the ball chosen from urn awas white given that exactly 2 white balls were selected?

Answer:7.07 m

Step-by-step explanation:

ab=5

ab=bc

bc=5

(ab)^2+(bc)^2=(ac)^2

25+25=50

ac^2=50

ac=7.07

Step-by-step explanation:

x = number of children

y = number of adults

1.25x + 2.25y = 294.75

this has many different solutions.

we would need a total number of persons in the pool in order to solve that to a single solution.

so, it could be 131 adults and 0 children.

for every reduction of 5 adults we can add 9 children and keep the same total

so, it could be 126 adults and 9 children

121 adults and 18 children

116 adults and 27 children

...

1 adult and 234 children

how did I get to the 5 to 9 ratio ?

1.25 is 5/4.

2.25 is 9/4

so, I was looking for the smallest common multiple of 5 and 9. which is 45 or 5×9. there is no simpler ratio between them.

so, the ticket price of 9 children is the same as the ticket price of 5 adults.

in order to keep the total of $294.75, when I reduce the number of adults, I have to compensate by adding children with the same amount of ticket prices.

this does not charge the fact that your teacher gave you an incomplete problem to solve.

but maybe your teacher wanted you to discover this problem.

The given problem can be solved by using the properties of the parabola.

The following statements are true about the function and its graph are as follows;

The value of a is 1 which is positive then the parabola opens upward.

What is a parabola?

A parabola is a plane curve that is mirror-symmetrical and roughly U-shaped in mathematics. It fits several seemingly disparate mathematical descriptions, all of which can be shown to define the same curves. A point and a line are two ways to describe

According to the question,

1. The value of the function when f(-10) is,

                         [tex]f(x)=x^2-5x+12\\\\f(-10) =(-10)^2-5(-10)+12\\\\f(-10)=100+50+12\\\\f(-10)=162[/tex]

So the first option is false.

2. The graph of the function is a parabola.

  The value of a is 1 which is positive then the parabola opens upward.

3.  The graph contains the point f(x) = 20,

                                   [tex]f(x)=x^2-5x+12\\\\f(20) =(20)^2-5(20)+12\\\\f(20)=400-100+12\\\\f(20)=312\\[/tex]

       The graph contains the point (20, 312).

4.  The graph contains the point f(x) = 0,

                                    [tex]f(x)=x^2-5x+12\\\\f(0) =(0)^2-5(0)+12\\\\f(0)=0-0+12\\\\f(0)=12\\[/tex]

       The graph contains the point (0, 12).

Hence, the given problem can be solved by using the properties of the parabola. The following statements are true about the function and its graph are as follows;

The value of a is 1 which is positive then the parabola opens upward.

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The remainder will be (k - 1) or (2k - 1) after using the remainder theorem.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

The remainder theorem:

f(x) = 2x² - 3x + 1

f(x) is divided by (x - k)

The remainder = f(k)  

The remainder = 2k² - 3k + 1

After factoring:

(k - 1)(2k - 1)

The remainder will be (k - 1) or (2k - 1)

Thus, the remainder will be (k - 1) or (2k - 1) after using the remainder theorem.

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Answer:

x = 16, y = -4

Step-by-step explanation:

First, we can say that "x = the first number" and "y = the second number"

The first number plus twice the second number is 8:

x + 2y = 8

Twice the first number plus the second number totals 28:

2x + y = 28

Next, we solve the system of equations.

x + 2y = 8 ---> 2x + 4y = 16 ---> 2x = 16 - 4y

2x + y = 28  ---> 2x = 28 - y

16 - 4y = 28 - y

-4y + y = 28 - 16

-3y = 12

y = -4

Now, we plug "y = -4" into either one of the equations to find x:

x + 2(-4) = 8

x + -8 = 8

x = 8 + 8

x = 16

Answer:

864 seats

Step-by-step explanation:

A theater has 36 rows. Each row has 24 seats. About how many seats does the theater have?​

36 * 24 = 864 seats

Answer:

The one where the line passes 5 on the y-axis. Last pic

Answer:

your fourth option is your answer

It will take 8 weeks so that janice and oliver have the same amount of marbles.

What do you mean by linear expression?

An algebraic expression known as a linear expression has terms that are either constants or variables raised to the first power. Alternatively put, none of the exponents can be greater than 1.

Coefficients in linear equations can be either positive or negative values. The exponent is important. The entire equation becomes non-linear when a single variable is raised to a power greater than 1.

Let number of weeks be x

According to question, Janice currently has 26 marbles and is collecting 3 per week and Oliver currently has 10 marbles and is collecting 5 per week.

This means ,

26 + 3x = 10 + 5x

26 - 10 = 5x - 3x

16 = 2x

x = 16/2 = 8

Therefore, it will take 8 weeks so that janice and oliver have the same amount of marbles.

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Answer:

15%

Step-by-step explanation:

[tex]\frac{7225-8500}{7225}=-15\%[/tex]

Given:

h(x) = 3x - 5

Find:

h(-2)

________

h(-2) = 3·(-2) - 5 = - 6 - 5 = - 11

Answer:

- 11

Answer:

x = 7, y = 4

Step-by-step explanation:

simultaneous equation:

3x-y=17

4x+y=-3

The statements are true or false.

The standard form of 4.4 x 10-4 is 0.00044.

= 4.4 * 10^-4

= 4.4/10^4

= 4.4/10000

0.00044 = 0.00044

This statement is true.

The standard form of 6.39 x 10^5

= 6.39 * 100000

= 639*1000

639000 ≠ 63,900,000

This statement is false

The standard form of 3.02 x 10^10 is 3,020,000,000.

= 3.02 * 10^10

= 3.02 *10000000000

= 3,020,000,0000

This statement  is false.

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Answer:

28%

Step-by-step explanation:

38.40 - 30 = 8.40

x : 100 = 8.40 : 30

x = 8.40 * 100 / 30

x = 840/30

x = 84/3 = 28%

0.6 cup of gliter is used for 1 cup of glue and 1.6 cup of gliter glue is made with 1 cup of glue.

Part A

Given that,

15 cup of gliter is for 25 cup of glue ,

Therefore, "X" cup of gliter is for 1 cup of glue

X = (1*15)/25

X= 0.6 cup of gliter

Part B,

Given that,

From part A 0.6 cup of gliter is for 1 cup of glue

Thus, 1 cup of glue and 0.6 cup of gliter when mixed will form "Y" cup of gliter glue

Now, Y= 0.6 cup of gliter + 1 cup of glue

Y= 1.6 cup of gliter glue

which approximates to 2 cup of gliter glue.

An equation in slope-intercept form that represents the total cost of the membership is y = 5x + 265.

The number of aerobics classes that Carly took at $500 one year is 47 aerobics classes.

In order to write the equation in slope-intercept form, we would have to determine the slope of the line representing the total cost of the membership.

Mathematically, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Substituting the given parameters into the formula, we have;

Slope, m = (290 - 270)/(5 - 1)

Slope, m = 20/4

Slope, m = 4

At point (1, 270), an equation of this line in slope-intercept form can be calculated by using this standard formula:

y = mx + c

Where:

Substituting the given points into the formula, we have;

y = mx + c

270 = 5(1) + c

Intercept, c = 270 - 5

Intercept, c = 265.

Therefore, the required equation is given by:

y = 5x + 265

For the number of aerobics classes at $500 one year, we have:

500 = 5x + 265

5x = 500 - 265

5x = 235

x = 235/5

x = 47 aerobics classes.

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Answer: y=-4/3x+2

Step-by-step explanation:

First, find the slope: -2-2/3-0 = -4/3

Next, choose one pair of points and insert them into the y=mx+b equation:

2=-4/3(0)+b

Simplify the equation: 2=0+b —>  2=b

Final equation: y=-4/3x+2

The solution for z is    [tex]z=\frac{nm}{(n-m)}[/tex]

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

The equation is    [tex]\frac{z}{m} -\frac{z}{n}=1[/tex]

On simplifying , we get

[tex]\frac{(zn-zm)}{nm} =1[/tex]

Multiply both sides by 'nm' , we get

[tex]zn-zm=nm[/tex]

Taking z as the common term in LHS , we get

[tex]z(n-m)=nm[/tex]

Divide by ( n - m ) on both sides ,we get

[tex]z=\frac{nm}{(n-m)}[/tex]

Since , n ≠ m

n - m ≠ 0

So , the solution is [tex]z=\frac{nm}{(n-m)}[/tex]

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Answer:

30

Step-by-step explanation:

WX = 22
WY = 26
WZ = 30

22 + 4 = 26
26 + 4 = 30

Answer:

50%

Step-by-step explanation:

62-31=31

31/62x100%

=50

Answer:

120

Step-by-step explanation:

360

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We can conclude that the value of r(2) which is -6 and x - 2 is not the factor for r(x).

So, we know that the equation is:

Now, calculate the equation when x = 2.

Now, we can conclude that:

Therefore, we can conclude that the value of r(2) which is -6 and x - 2 is not the factor for r(x).

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The equation of the line passing through (4,1) and perpendicular to y=1/2x-1 is y = -2x+9.

According to the question,

We have the following information:

A line passes through (4,1) and perpendicular to y=1/2x-1.

Now, the slope of the given line is 1/2.

We know that the slope of the perpendicular line is given by -1/m.

Slope of perpendicular line = -1/(1/2)

Slope of perpendicular line = -2

Equation of the required line:

(y-y') = m(x-x')

(y-1) = -2(x-4)

y-1 = -2x+8

y = -2x+8+1

y = -2x+9

Hence, the equation of the line passing through (4,1) and perpendicular to y=1/2x-1 is y = -2x+9.

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Assumption about the sample underlies the hypothesis test is; the samples comes from a population of tires with 60,000 miles where 5% of tires are worn out.

From the information given, the null and alternative hypothesis are:

Null hypothesis;

The proportion of tire that are worn out after 60,000 miles is equal to 5% or 0.05

[tex]H_{0} :p=0.05[/tex]

Alternative hypothesis;

The proportion of tire that are worn out after 60,000 miles is less than 5% or 0.05

[tex]H_{a} :p < 0.05[/tex]

Hence the assumption about the sample underlies the hypothesis test is; the samples comes from a population of tires with 60,000 miles where 5% of tires are worn out.

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The correct statement is "Similar, due to SSS and a scale factor of 0.29. Triangle QRS is similar to triangle VUT".

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. If two or more figures have the same shape, but their sizes are different, then such objects are called similar figures.

Given that, two triangles Δ QRS and Δ VUT

We have,

QR/VU = RS/UT = QS/VT = 2/7 = 0.29

Hence, the two triangles are similar by SSS property with a scale factor of 0.29

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600 milliliters of the solution will be needed.

Given:

Let x be the solution needed.

A neonate order is 0.03 mg/kg of a 1:10,000 solution. the patient weighs 4.4 lb.

4.4 lb = 1.99581 kg

4.4 lb ≈ 2 kg

neonate order = 2*0.03

= 2*3/100

= 6/100

= 0.06 mg

1 : 10000 = 0.06 : x

1/10000 = 0.06/x

x = 0.06 * 10000 / 1

= 0.6*1000

= 6*100

= 600 milliliters.

Therefore 600 milliliters of the solution will be needed.

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It will takes 15 weeks before Jeremy and Katie have the same amount of money saved up.

Define Expression

An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Given,

Jeremy has balance in his savings account = $120

Each week Jeremy adds amount to his account = $14

Katie has balance in her savings account = $180

Each week Katie adds amount to her account = $10

Let, x = number of weeks

At the end of each week Jeremy has = 120 + 14x

At the end of each week Katie has = 180 + 10x

As we want to have same amount in both the account for that just equate the values of each week of Jeremy and Katie.

120 + 14x = 180 + 10x

14x - 10x = 180 - 120

4x = 60

x = 15

Hence, it will takes 15 weeks before Jeremy and Katie have the same amount of money saved up.

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Answer:

u = 15

Step-by-step explanation:

It appears that you have already created an equation to solve for u and just need help solving it

So we have 8² + u² = 17²

==> simplify exponents

64 + u² = 289

==> subtract 64 from both sides

u² = 225

==> take the square root of both sides

u = 15

y=7.5x+52.5

y2-y1/x2-x1

100-85/6-4 = 7.5

60=7.5+b

b=52.5