solve elimination method
3x+2y-15=0
5x-3y -25=0​

The probabilities for the given problem is calculated as 0.081 and 0.06 respectively.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

The zero value of probability indicates that the event will not happen while its value equal to one indicate that it will happen.

Given that,

There are 3 blue marbles, 5 red marbles and 4 green marbles.

Then, the total number of marbles is 12.

The given problem can be solved as follows,

Part A:

The probability of getting 1 blue and 2 green marbles is,

P( 1 blue and 2 green) = (³C₁ × ⁴C₂)/¹²C₃

                                     = ( 3 × 6)/ 220

                                     = 9/110

                                     = 0.081

Part B:

The probability of selecting one blue marble = 3/12 = 1/4

After one blue marble is selected, the remaining number of marbles is 11.

Thus, probability of selecting 3 red marbles is,

⁵C₃/¹¹C₃

= 10/165

= 0.06

Part C:

In the Part A the probability is calculated by taking the ratio of total number of ways of selecting 3 marbles and the number of ways of selecting 1 blue and 2 green marbles.

And, in Part B the number of ways is calculated from the remaining number of marbles after one blue marble is chosen.

Hence, the probabilities for the given parts in the question are 0.081 and 0.06 respectively.

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Answer:

13179

Step-by-step explanation:

It says half of the children are boys, which means division

26358 divided by 2 is 13179

Answer:

13,179

Step-by-step explanation:

the answer is 13,179 because 26,358 divided by 2 is 13,179

2=1/2

The total amount of money that they hared is 13000.

What is amount?

The amount of something is how much there is, or how much you have, need, or get. He needs that amount of money to survive. [ + of] I still do a certain amount of work for them.

Ann, ben and cheryl hare ome money in the ratio 3:7:10

Ben receive £650 more than Ann.

Ann = 3*650=1950

ben= 7*650=4550

cheryl hare ome = 10*650= 6500

The total amount of money that they hared 1950+4550+6500= 13000.

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The equation is $1.75+$0.85m= $8.75, after solving the value m =8.24 miles.

An algebraic expression contains one or more variables along with numbers show the equality among them.

we use equation to determine an unknown value. we create equation based on a mathematical statement and finally solve it.

The following is the solution of equation of the statement given in question.

Given, fee per mile = $0.85

Charges = $1.75

Total cost of ride = $8.75

let, m is the number of miles travelled

Now, the equation is $1.75+$0.85m = $8.75

                  after solving     0.85m = 7.00

                             m = 8.24 miles

hence, the Uber travelled 8.24 miles

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The unknown angle in the triangle is as follows:

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

A triangle can be named base on it's angles or sides. They include equilateral triangle, scalene triangle, Isosceles triangle, Right triangle, Acute triangle etc

Therefore, let's solve the angle C of the triangle as follows;

m∠C = 2x

x + 2x + 3x = 180

6x = 180

divide both sides by 6

x = 180 / 6

x = 30

Therefore,

m∠C = 2x = 2(30) = 60 degrees.

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The conclusion about the triangle is that the two triangles are congruent i.e they are equal

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.

In the figure, triangle ∆GHJ and ∆ GKM are the two triangles formed.

To prove that triangle GHJ = GKM

angle KGM= angle JGH ( opposite angles)

angle K = angle H (alternating angles)

Therefore angle H = angle J

since the three angles of each triangles are equal, we can say the triangles are congruent.

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Answer: Rose got the better deal!

Step-by-step explanation:

Rose got the better deal, she only spent .10 cents for every piece, while joe spent .15 cents and only got 10 pieces.

Answer:

Step-by-step explanation:

To solve this problem, we need to use the formula for the present value of a lump sum payment: $PV = FV \cdot (1 + r)^{-t}$, where $PV$ is the present value (the lump sum payment that needs to be made), $FV$ is the future value (the amount borrowed), $r$ is the annual interest rate, and $t$ is the number of years the money is borrowed for.In this case, we are given that $FV = 12,000$, $r = 8%$, and $t = 5$ years. Plugging these values into the formula, we get $PV = 12,000 \cdot (1 + 0.08)^{-5} = 12,000 \cdot 0.5987 = 7,184.40$.Therefore, the lump sum payment that needs to be made is $PV = \boxed{7184.40}$. The answer is $\boxed{\text{(a)}\ $16,800.00}$ is incorrect.

Answer:

[tex]\huge\boxed{\sf Option \ B}[/tex]

Step-by-step explanation:

= (2x + 4) - (3x² + 2x - 1)

Solve parenthesis

= 2x + 4 - 3x² - 2x + 1

Combine like terms

= -3x² + 2x - 2x + 4 + 1

[tex]\rule[225]{225}{2}[/tex]

After solving the given expression, the value obtained will be equal to 7/12.

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.

Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.

As per the given fraction in the question,

4/6 - 1/12

Take LCM as 12 and then solve,

= (8 - 1)/12

= 7/12

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Answer:

34

Step-by-step explanation:

-2(x - 14) = -40  Distribute the -2

-2x + 28 = -40   Subtract 28 from both sides

-2x = -68  Divide both sides by -2

x = 34

Check:

34- 14 = 20

-2(20) = -40

Answer:

9

Step-by-step explanation:

4×1/2=2 and adding on 7 would make 9

9

Expressions are mathematical statements without equal signs.

Expressions and Variables

Expressions are simply combinations of different numbers and operators. The reason 4a + 7 qualifies as an expression is because it has 2 values connected by an operator and no equal sign. In this expression, there is multiplication and addition.

Variables are letters in equations or expressions that represent some numerical value. Variables can represent any number, but in this case, we are told a = 1/2.

Solving the Expression

To solve the expression, all we need to do is plug 1/2 into the expression.

Then, multiply,

And add,

So, when a = 1/2, 4a + 7 = 9.

Answer:

It should be 5/6

Step-by-step explanation:

:)rawr

To find the number of sheep that he will sell, three-fourths of the total number of sheep he had must be calculated. For this, the fraction must be multiplied by the whole number:

[tex]\begin{gathered} \sf \frac{3}{4} \times 400 = \\ \\ \sf \frac{3}{4} \times \frac{400}{1} = \\ \\ \sf \frac{3 \times 400}{4 \times 1} = \\ \\ \sf \boxed{ \sf \frac{ \red{1200}}{ \red4}} = \blue{300}\end{gathered}[/tex]

Therefore, he will sell three hundred sheep.

Answer: She will sell 300 sheep

Step-by-step explanation:

1/4 of 400 sheep is 100 sheep, to find this by, taking 400 divided by 100

So 3/4 will be 300 sheep, to find this by taking 100 timed 3

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Answer:

no solution to the equation

Step-by-step explanation:

Answer:

no solution to the equation

The solution is x²

The monomial that will make the expression as a square of a sum or a difference of trinomial is x²

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 ,

Let the equation be represented as A

Now , a monomial that will make the expression as a square of a sum or a difference of trinomial is calculated as

(a-b)² = a² -2ab + b²

where a² = 36

taking square roots on both sides of the equation , we get

a = 6

-2ab = -12x

So , one of the variable is x

So , substituting the value of b = x , we get

( 6 - x )² = 36 - 12x + x²

Therefore , the value of the monomial is x²

Hence , The monomial that will make the expression as a square of a sum or a difference of trinomial is x²

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Answer: BELOW

Step-by-step explanation:

m<1 62°

m<2 39°

m<3 26°

m<4 55°

m<5 55°

m<6 35

A triangle is equal to 180° so you keep adding angles till you have all your answers.

Answer:

c) 72-34=38

Step-by-step explanation:

We will see that the amount of gasoline increased by 5.25 gallons over that five-day period.

Here we want to study the table to see the total change in the amount of gasoline over the five-day period.

Now we need to study the given graph:

Notice that each day we have the change of that particular day, then we just need to add all of these changes and we will get the total change.

Where the negative numbers mean that the gasoline was used, and the positive numbers represent a charge in the gasoline (so it increases).

C = -1.05 - 1.20 - 0.85 + 10.50 - 2.15 = 5.25

This means that, in total, the amount of gasoline increased by 5.25 gallons over that five-day period.

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to get the slope of any straight line, we simply need two points off of it, for Juliana and Emiliano let's use those points in the picture below.

[tex]\stackrel{\textit{\LARGE Juliana}}{(\stackrel{x_1}{2}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{2})} ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{2}}} \implies {\Large \begin{array}{llll} \cfrac{1 }{ 2 } \end{array}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{\LARGE Emiliano}}{(\stackrel{x_1}{1\frac{1}{2}}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{4\frac{1}{2}}~,~\stackrel{y_2}{3})} ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{4\frac{1}{2}}-\underset{x_1}{1\frac{1}{2}}}}\implies {\Large \begin{array}{llll} \cfrac{2}{3} \end{array}}[/tex]

The standard deviation of the scores is  6.48

For given set of scores,  88, 94, 80, 79, 74, and 83

Here, the number of observations = 6

The mean of the scores would be,

μ = Σx/n

μ = (88 + 94 + 80 + 79 + 74 + 83)/6

μ = 498/6

μ = 83

Using the formula of standard deviation,

σ = √((Xi−μ)^2)/n

σ = √[(88 - 83)² + (94 - 83)² + (80 - 83)² + (79 - 83)² + (74 - 83)² + (83 - 83)²]/6

σ = √(252/6)

σ = √42

σ = 6.48

Therefore,  the standard deviation = 6.48

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Answer: -6 and 5

Step-by-step explanation:

-6 and 5

x+y = -1

xy = -30

x=-1-y

y(-1-y)=-30

-y^2-y=-30

-y^2-y+30=0

(y-5)(5+6)

y=5,-6

The Variance of (A +2B) is 12.6724.

What is  Variance ?

Variability is measured by the variance. The average of the squared deviations from the mean is used to compute it. The degree of dispersion in your data collection is indicated by variance. The variance is greater in respect to the mean the more dispersed the data.

Here we have to select two card out of 6 card. now suppose we take 2 card (1,2 ) out of six card (1,2,3,4,5,6) . so here A=1 and B=2 but it is also possible that A=2 and B =1 because it represent same two card . Therefore here order of card matter.

Hence the posible out come of selecting 2 card are (without replacement)

-- (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) -- (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) -- (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) -- (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) -- (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) --

Therefore A+2B of this outcome are

A B A+2B

1 2 5

1 3 7

1 4 9

1 5 11

1 6 13

2 1 4

2 3 8

2 4 10

2 5 12

2 6 14

3 1 5

3 2 7

3 4 11

3 5 13

3 6 15

4 1 6

4 2 8

4 3 10

4 5 14

4 6 16

5 1 7

5 2 9

5 3 11

5 4 13

5 6 17

6 1 8

6 2 10

6 3 12

6 4 14

6 5 16

therefore there variance of A +2B can be computed as follows

x x2

5 25

7 49

9 81

11 121

13 169

4 16

8 64

10 100

12 144

14 196

5 25

7 49

11 121

13 169

15 225

6 36

8 64

10 100

14 196

16 256

7 49

9 81

11 121

13 169

17 289

8 64

10 100

12 144

14 196

16 256

[tex]\Sigma x=315[/tex]       [tex]\sum x^2=3675[/tex]

Therefore variance

[tex]$$\begin{aligned}& =\frac{\sum x^2-\frac{\left(\sum x\right)^2}{n}}{n-1} \\& =\frac{3675-\frac{(315)^2}{30}}{30-1} \\& =\frac{3675-3307.5}{29} \\& =12.6724\end{aligned}$$[/tex]

The Variance of (A +2B) is 12.6724.

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Answer: for 216 the answer is 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108 and 216

for 96 it is  1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.

for 64 it is  1, 2, 4, 8, 16, 32 and 64.

Step-by-step explanation:

Answer:

r ≤ 0

Step-by-step explanation in image.

Answer:

r<0

Step-by-step explanation:

r-(-1)<1

the oposite of -1 is 1

r+1<1

subatract 1 from both sides

r<1-1

subatract 1 from 1 to get 0

r<0

speed of plane's ground = 155.769 Km/h

Speed is the rate at which an object travels along a path over time, whereas velocity is the speed and direction of an item's motion. In other words, speed is a scalar value, but velocity is a vector.

Units of speed = meter per second

So ln [tex]$\triangle A O B$[/tex], we have

[tex]$$[/tex]A=65[tex]^{\circ}+45^{\circ}=110^{\circ} \\[/tex]

O A=[tex]150 \mathrm{~km} / \mathrm{h} \\[/tex]

A B=15 [tex]\mathrm{~km} / \mathrm{h}[/tex]

[tex]\end{aligned}[/tex]using cosine Rule

[tex]\cos A=\frac{O A^2+A B^2-O B^2}{2(O A)(A B)} \\[/tex]

[tex]\cos 110^{\circ}=\frac{(150)^2+(15)^2-O B^2}{2(150)(15)} \\[/tex]

[tex]4500 \cos 110^{\circ}=22500+225-0 B^2 \\[/tex]

[tex]-1539.09064=22725-0 B^2 \\[/tex]

[tex]O B^2=22725+1539.09064 \\[/tex]

[tex]O B^2=24,264.0906 \\[/tex]

[tex]O B=155.769351 \approx 155.769 \mathrm{~km} / \mathrm{hr} \\[/tex]

[tex]O B \approx 17 \mathrm{k}[/tex]

using sine rule

[tex]\frac{\sin (A O B)}{15}=\frac{\sin A}{O B} \\[/tex]

[tex]\frac{\sin (A O B)}{15}=\frac{\sin 110^{\circ}}{155.769351} \\[/tex]

[tex]\sin (A O B)=\frac{15 \sin 110^{\circ}}{155.769351}=\frac{14.0953893}{155.769351}[/tex]

[tex]\sin (A \cap B)=0.0904888491 \\[/tex]

[tex]A O B=\sin ^{-1}(0.0904888491) \\[/tex]

[tex]A D B=5.19173084^{\circ} \\[/tex]

[tex]A O B=5.2^{\circ}[/tex]

Direction of plane [tex]=65^{\circ}+5.2^{\circ} \\[/tex] = [tex]=70.2^{\circ}[/tex]

Direction N = 70.2° E

speed of plane's ground [tex]$=155.769 \mathrm{~km} / \mathrm{h}$[/tex]

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Answer: increasing by 0.25

Step-by-step explanation:

We get approximately 56 inches of rain during a 31-day month.

What is the rate in mathematics?

In mathematics, a rate is a ratio that compares two different quantities. It is a way to express the relationship between two quantities that have different units of measure. For example, you might express the rate at which you are traveling as miles per hour, which compares the distance you have traveled (in miles) to the time it took you to travel that distance (in hours).

To find the amount of rain the town received in a 31-day month, we need to determine the daily rainfall rate and then multiply it by the number of days in the month.

The town received 25 inches of rain in two weeks, which is equal to 25/2 = 12.5 inches per week. Since there are 7 days in a week, the daily rainfall rate is 12.5/7 = 1.79 inches per day.

If it kept raining at this rate for a 31-day month, the town would receive approximately 1.79 inches per day * 31 days = 55.9 inches of rain.

Hence, we get approximately 56 inches of rain during a 31-day month.

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We get approximately 56 inches of rain during a 31-day month.

What is the rate in mathematics?

In mathematics, a rate is a ratio that compares two different quantities. It is a way to express the relationship between two quantities that have different units of measure. For example, you might express the rate at which you are traveling as miles per hour, which compares the distance you have traveled (in miles) to the time it took you to travel that distance (in hours).

To find the amount of rain the town received in a 31-day month, we need to determine the daily rainfall rate and then multiply it by the number of days in the month.

The town received 25 inches of rain in two weeks, which is equal to 25/2 = 12.5 inches per week. Since there are 7 days in a week, the daily rainfall rate is 12.5/7 = 1.79 inches per day.

If it kept raining at this rate for a 31-day month, the town would receive approximately 1.79 inches per day * 31 days = 55.9 inches of rain.

Hence, we get approximately 56 inches of rain during a 31-day month.

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