Mr. Yi buys vegetables at a market. He purchases 6 pounds of potatoes, p, and 3 pounds of onions, n, for $18. Onions cost twice as much as potatoes. To determine the unit price for each item, his daughter sets up and solves the system of equations shown.

6p + 3n = 18 and 2n = p
6(2n) + 3n = 18
12n + 3n = 18
15n = 18; n = $1.20
Onions cost $1.20 per pound.
Analyze the daughter’s solution. Which statements are true? Check all that apply.

The equation 2n = p should be 2p = n.
The equation 6p + 3n = 18 should be
6n + 3p = 18.
The actual cost of the onions is $3.00 per pound.
Potatoes cost $0.60 per pound.
Potatoes cost $1.50 per pound.
Potatoes cost $2.40 per pound.

sin^-1(-1/2) enter directly into a calculator and you'll find your answer

The point on a line that is at an equal distance from either end.

Hence, the equation of the line [tex]Q[/tex]  to the midpoint of [tex]AP[/tex] is [tex](AP,Q)=(\frac{3}{4},\frac{13}{4})[/tex].

What is midpoint ?

The point on a line that is at an equal distance from either end.

Here, the coordinates of [tex]A(1,-1),P(3,7),Q(\frac{-1}{2},\frac{7}{2})[/tex]

The general formula of the midpoint is

[tex](x_m,y_m)=(\frac{x_1+x_2}{2},\frac{y_1+t_2}{2})[/tex]

The equation of [tex]AP[/tex] is

[tex]AP=(\frac{1+3}{2},\frac{7-1}{2})\\AP=(\frac{4}{2},\frac{6}{2})\\AP=(2,3)\\[/tex]

The equation of the line [tex]Q[/tex]  to the midpoint of [tex]AP[/tex] is

where [tex]AP(2,3),Q(\frac{-1}{2},\frac{7}{2})[/tex].

[tex](AP,Q)=(\frac{2+\frac{-1}{2}}{2},\frac{3+\frac{7}{2}}{2})\\(AP,Q)=(\frac{\frac{4-1}{2}}{2},\frac{\frac{6+7}{2}}{2})\\(AP,Q)=(\frac{\frac{3}{2}}{2},\frac{\frac{13}{2}}{2})\\\\(AP,Q)=(\frac{3}{4},\frac{13}{4})\\[/tex]

Hence, the equation of the line [tex]Q[/tex]  to the midpoint of [tex]AP[/tex] is [tex](AP,Q)=(\frac{3}{4},\frac{13}{4})[/tex].

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Answer:

Step-by-step explanation:

We can observe:

According to  Hınge theorem if two sides of different triangles are equal and the angles between the two sides are different, then the larger angles has greater side opposite to it.

As TU is opposite to the larger angle, and SV is opposite to smaller angle, then TU > SV.

Correct angle choice is B.

Answer:

x = -12

Step-by-step explanation:

x/-3 + 5 - 5 = 9 - 5

x/-3 = 4

x/-3 (-3) = 4(-3)

x = -12

Answer:  

150 marks

Step-by-step explanation:

Every meter has 5 marks.

30 meters × 5 marks = 150 marks

Using the properties of compound interest we can calculate that Jacob will have $1485 more than Brandon in his account.

Brandon invested $7,900 at the rate of 6 1/8% compounded daily.

Principal = $7900

Time = 15 years

Rate = 6 1/8% = 49/8 %

Amount earned after n years:

[tex]A=P (1+\frac{r}{n})^{nt}[/tex]  

Now we will use these values to find the amount at the end of 15 years.

P = 7900

r = 0.06625

n = 365

t = 15

[tex]A=P (1+\frac{.06125}{365})^{15\times 365}[/tex]

or, A = 19797.104...

or, A ≈ 19797.1

Again, Jacob invested the same sum at compound interest monthly at

6 5/8% .

Amount earned after 15 years:

P = 7900

r = 6.125

n = 12

t = 15

[tex]A=P (1+\frac{.06625}{12})^{15\times 12}[/tex]

or, A = 21282.383..

or, A ≈ 21282.38

Amount earned by Jacob more than Brandon

= $21282.38 - $19797.1

= $148785.283..

≈ $1485

Hence Jacob will have $1485 more than Brandon in his account.

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Answer:

(9,1), Z(5,1)

Step-by-step explanation:

The probability of choosing 3 men and 3 women to form the committee is 0.4329 and the probability to select exactly 2 people from the human resources is 0.4545.

It is given that there are 12 employees.

The number of male employees is 6

number of female employees is 6

A committee of 6 is to be formed. We need to find the probability that out of 6, 3 are male and 3 are female.

Let A be the event of having 3 men and 3 women on the committee

The total number of ways to choose 6 people is

¹²C₆

Probability = number of favorable outcomes / total number of outcomes

n(A) = ⁶C₃   X  ⁶C₃

Therefore,

P(A) = (⁶C₃   X  ⁶C₃) / ¹²C₆

= (20  X  20) / 924

= 400/924

= 0.4329

It is given that the number of employees in human resources from the group is 4

Let B be the event to choose exactly 2 employees from the human resource

n(B) = ⁴C₂  X  ⁸C₄

P(B) = ⁴C₂  X  ⁸C₄ / ¹²C₆

= 6 X 70 / 924

= 420 / 924

= 0.4545

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The equation would represents the graph is y = 20000 + 1750x and the graph has been plotted

From the table

The investment in 1 year = $20000

The investment in 2 year = $21750

The investment in 3 year = $23500

The investment in 4 year = $25250

The investment in 5 year = $27000

Then the equation will be

y = 20000 + 1750x

Where y is the investment in dollars

x is the number of years

Draw the graph as number of years in x axis and the amount of investment in y axis

Hence, the equation would represents the graph is y = 20000 + 1750x and the graph has been plotted

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Answer:

pick any two points

im going to chose (1,3) and (3,7)

so the equation y2-y1/x2-x1

1 = x1

3=y1

3=x2

7=y2

so 7-3/3-1 is 4/2

which is 2

y≤-3x+4 has lesser than or equal to symbol so we shade the below line.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Relationship between two expressions or values that are not equal to each other is called 'inequality.

y≤-3x+4 is the given inequality.

The sign of the inequality will let you know which half-plane to shade. If the symbol ≥ or > is used, shade above the line. If the symbol ≤ or < is used shade below the line.

In the inequality we have lesser than or equal to symbol so we shade the below line.

Hence, y≤-3x+4 has lesser than or equal to symbol so we shade the below line.

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It will take 25 minutes for the two containers to have the same amount of water .

In the question ,

it is given that ,

water present in container A = 200L

water present in container B = 500L

rate at which the water is filling in container A= 6 liter/minute

rate at which the water is draining in container B = 6 liter/minute

let the time taken = m minutes ,

So , According to the question ,

the equation representing the situation is  

200 + 6m = 500 - 6m

Simplifying further , we get

6m + 6m = 500 - 200

12m = 300

m = 300/12

m = 25

Therefore , It will take 25 minutes for the two containers to have the same amount of water .

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In accordance to Thales's theorem, the geometric system has a missing side length of 15 units.

In this problem we find a geometric system formed by two proportional trapezoids. This similarity and proportionality is defined by Thales's theorem, which states that a triangle segmented by several lines parallel to each other and parallel to the base of the figure creates triangles and quadrilaterals proportional to each other.

Then, two figures of the given trapezoids are represented by side proportionality ratios. Then, the proportionality ratio is described and its variable x is cleared within by algebra properties:

First, define the proportionality ratio associated to the geometric system:

4 / (10 + 4) = (21 - x) / 21

Second, simplify the equation and clear the variable x:

4 / 14 = 1 - x / 21

2 / 7 = 1 - x / 21

42 / 7 = 21 - x

6 = 21 - x

x = 21 - 6

x = 15

The missing length is equal to 15 units.

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The greatest number of outfits Jose can buy is 6

The given parameters are:

Let the number of new biking outfits be x

So, we have

New bicycle + 4 * price of bicycle reflectors + Pair of a bike gloves + New biking outfits ≤ Budget

This gives

284.52 + 4  * 15.65 + 11.31 + 31.95x ≤ 580

This gives

358.43 + 31.95x ≤ 580

Solve the inequality

31.95x ≤ 221.57

Divide

x ≤ 6.93

This gives

x ≤ 6

Hence, the greatest number of outfits is 6

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The probability that the proportion of the sample who are iphone users is between 45% and 50% be 22.87%.

The probability that more than 50% of americans are iphone users be 11.12%.

(a)We know, p = 0.47 and n = 100. First, we should check our conditions for the sampling distribution of the sample proportion.

np = (100)(0.47) = 47 and n(1 - p) = (100)(1 - 0.47) = 53

Since, X will have a sampling distribution that is approximately normal with mean = 0.47

and

standard deviation =  √(0.47)(0.53)/100 ≈ 0.05

P(0.45<X<0.50) = P((0.45 - 0.47)/0.05 < Z < (0.50-0.47)/0.05)

P(0.45<X<0.50)  ≈ 0.2287

Therefore, if the true proportion of Americans who own an iPhone is 47%, then there would be a 22.87% chance that we would see a sample proportion between 45% and 50% when the sample size is 100.

(b) Now, p = 0.47 and n = 50.

np = (50)(0.47) = 23.5 and n(1 - p) = (50)(1 - 0.47) = 26.5

Since, X will have a sampling distribution that is approximately normal with mean = 0.47

and

standard deviation =  √(0.47)(26.5)/50 ≈ 0.25

P(X>0.50) = P(Z > (0.50-0.47)/0.25)

P(X>0.50)  ≈ 0.1112

Therefore, if the true proportion of Americans who own an iPhone is 47%, then there would be a 11.12% chance that we would see a sample proportion more than 50% when the sample size is 50.

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Store´s B bottle cost less per ounce.

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. LHS = RHS is a common mathematical formula.

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:

Store A  

Cost of a 8-ounce bottle of water: $14

Store B

Cost of bottle: y= 1.5x

Cost per ounce (A)

=$14/ 8

= $1.75per ounce

Cost per ounce (B); $1.5 per ounce

So, $1.75 > $1.5

Hence, Store´s B bottle cost less per ounce.

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Answer:

(-11/24)

Step-by-step explanation:

  3         5

------- - -------

  8         6

 3(3)    5(4)

------- - -------

 8(3)     6(4)

  9        20       - 11

------- - ------- = -------

  24      24        24

I hope this helps!

The empirical likelihood that George can stand up on his own the very next time Angie knocks him over would be 3/146.

For the given question.

Therefore, it follows that we are doing an experimental calculation based on the observation whether George will indeed be able to stand again the following time.

empirical probability = 3/146

Thus, the empirical likelihood that George can stand up on his own the very next time Angie knocks him over would be 3/146.

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Answer:

115.226337449

Step-by-step explanation:

84/0.729= 115.226337449

And thank you and your welcome

Answer:  the quotient of 84/0.729 is 115.226337

Answer:

(C.) 5/13

Step-by-step explanation:

The sine proportion is opposite / hypotenuse

Given the reference angle, the side measuring 5 units is the opposite side and the side measuring 13 units (and opposite of the right angle) is the hypotenuse

Thus, sine is 5/13

A- the area of the plot as a function of x. is 6 x^2 +10x-5

B- the perimeter of the plot as a function of x is 10x+8

A rectangle plot of land has a width of 3x+5 feet,

and a length of 2x-1 feet.

A) the area of the plot as a function of x is given by

A= length * width

  = ( 2x-1) * ( 3x+5)

  =6 x^2 +10x-5

B) the perimeter of the plot as a function of x

P = 2( l+ W)

  = 2 (( 2x-1) +( 3x+5))

  = 2( 5x +4)

  = 10x +8

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The equation of the parabola with the vertex (3,5) in the form of f(x)=a(x-h)^2+k is f(x)=7(x-3)^2+5.

In the given question we have to find the equation of parabola in the form of f(x)=a(x-h)^2+k

The given function is f(x)=7x^2.

The given vertex = (3,5)

The equation of the parabola with the vertex of (h,k) is

y=a(x-h)^2+k

On comparing we get; a=7, h=3, k=5

Now putting the value

f(x)=7(x-3)^2+5

Hence, the equation of the parabola with the vertex (3,5) in the form of f(x)=a(x-h)^2+k is f(x)=7(x-3)^2+5.

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The minimum score needed to receive a grade of A is 88.51

Let, X, be the scores of the student's

X follows Normal Distribution with mean = μ = 73 and standard deviation = σ = 11

The professor has informed us that 7.93 percent of her students received grades of A.

That is  P( X > a ) = 7.93% = 0.0793 .

We have to find a.

P( X > a ) = 7.93% = 0.0793

So, P( X <=  a ) = 1 - 0.0793 = 0.9207

Using function = NORMINV( probability , μ ,σ )

a = NORMINV( 0.9207, 73 , 11 ) = 88.51

The minimum score needed to receive a grade of A is 88.51

We have to find P( X <= 57.93 )

Using function = NORMDIST( x, μ , σ , 1 )

P( X <= 57.93 ) =NORMDIST( 57.93 , 73 , 11 , 1 ) = 0.0853 = 8.53%

8.53 percent of students failed the course

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The solution set for the given quadratic equation is (-0.62, -5.38).

The given equation is 3x(x+6)=-10.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Now, 3x(x+6)=-10

⇒ 3x²+18x=-10

⇒ 3x²+18x+10=0

By comparing 3x²+18x+10=0 with ax²+bx+c=0, we get

a=3, b=18 and c=10

Using quadratic formula x = [-b ± √(b² - 4ac)]/2a

= [-18 ± √(18² - 4×3×10)]/2×3

= [-18 ± √(324 - 120)]/6

= [-18 ± √(204)]/6

= [-18 ± √(204)]/6

= [-18 ± 14.28]/6

= [-18 + 14.28]/6 and [-18 - 14.28]/6

= -0.62 and -5.38

Hence, the solution set for the given quadratic equation is (-0.62, -5.38).

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Answer:

D

Step-by-step explanation:

Answer:

140

Step-by-step explanation:

2x+5x+40=180

7x+40=180

7x=140

x=20

5x+40=BCD

5(20)+40

100+40

140

The vertex is (-2,2), axis of symmetry is x = -2 and the parabola is downward.

From the graph:

vertex:

The vertex of a parabola is the point at the intersection of the parabola and its line of symmetry.

here vertex = (-2,2)

Axis of symmetry:

The axis of symmetry is the vertical line that goes through the vertex of a parabola so the left and right sides of the parabola are symmetric.

x = -2.

Parabola:

It is clearly visible that the parabola is facing downward so it is a downward parabola.

Therefore the vertex is (-2,2), axis of symmetry is x = -2 and the parabola is downward.

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The correlation coefficient of the data (0,1132), (1,1107), (2,1000), (3,1019) is -0.89

Correlation coefficients are used to measure how strong a relationship is between two variables

Given: (0,1132), (1,1107), (2,1000), (3,1019)

x    >>>>     y     >>>>  x²  >>>>       y²  >>>>   xy

0              1132            0            1281424         0

1               1107             1            1225449       1107

2              1000           4            1000000      2000

3               1019            9            1038361       3057

................................................................................................

6               4258         14            4545234      6164

.................................................................................................

The formula for the correlation coefficient is:

r = ( n∑xy -(∑x)(∑y) ) / ( √(n∑x² - (∑x)²) .√(n∑y² - (∑y)²) )

From the table:

∑x = 6, ∑y = 4258, ∑x² = 14, ∑y² = 4545234 and ∑xy = 6164

n = 4 (number of data points)

Substituting the values into the formula will give:

r = ( 4×6164 -(6)(4258) ) / ( √(4×14 - (6)²) .√(4×4545234 - (4258²) )

r = 24656-25548 / √(20).√(50372)

r = -892/√(1007440)

r = -0.89

Therefore, the correlation coefficient is -0.89

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The probability that the second ball drawn is a purple ball  is (e) 0.5833

From the question, we have the following parameters that can be used in our computation:

Green balls = 10

Purple balls = 14

This means that the total number of balls is

Total = 10 + 14

Evaluate the equation

So, we have

Total = 24

From the question, we understand that the ball is replaced

So, the probability that the second ball is purple ie

P(second purple) = purple/total

This gives

P(second purple) = 14/24

Evaluate

P(second purple) = 0.5833

Hence, the probability is (e) 0.5833

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