please help with this question ​

Answer:

Sister = 15 years old

Brother = 12 years old

Step-by-step explanation:

Right now, if the brother is B years old and the sister is S years old, B = (4/5)S because the ratio from brother to sister is 4:5, so if one unit is X, B = 4X and S = 5X

Three years ago, the brother was B-3 years old and the sister was S-3 years old. Keeping one unit as X, we have

B = 3X

S = 4X

B-3 = (3/4)(S-3)

Therefore, we have a system of equations

B = (4/5)S

B-3 = (3/4)(S-3)

Substitute (4/5)S for B into the second equation to only have one variable

(4/5)S - 3 = (3/4)(S-3)

(4/5)S - 3 = (3/4)S - 9/4

add 3 to both sides and subtract (3/4)S from both sides to isolate the variable and its coefficient

(1/20)S = 3/4

multiply both sides by 20 to isolate the S

S = 15

B = (4/5)S = 12

Answer:

3/5  is the  probability that the fish is NOT black

Step-by-step explanation:

Because the total  number of fish is  5  and the probability of  the fish being black is 2/5 . So the number of fish left are 3   =  equal to the   the  probability that the fish is NOT black

The number of late insurance claim payouts per 100 should be measured with a p-chart. Therefore, the correct option is (e) p-chart.

A p-chart is a type of control chart used to monitor the proportion of nonconforming items in a sample, where nonconforming items are those that do not meet a certain quality standard or specification. In this case, the proportion of late insurance claim payouts would be the proportion of nonconforming items.

A p-chart is appropriate when the sample size is constant and the number of nonconforming items per sample can be either small or large. It is used to monitor the stability of a process and to detect any changes or shifts in the proportion of nonconforming items over time.

An X-bar chart and R-chart are used to monitor the mean and variability of a continuous variable, respectively, and would not be appropriate for measuring the number of nonconforming items.

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Step-by-step explanation:

You are given a pair of alternate interior angles which are both right angles and are formed by a transversal line cutting two lines. That means the pair of angles are congruent.

Use the Alternate Interior Angles Theorem and by that those two lines must be parallel.

Answer:0.375

Step-by-step explanation:

3/4=0.75

0.75/2=0.375

(3/4)/2=0.375

Answer:

D - none of the above is the correct answer

Answer:

trust me a shoe box or a board game box or a small container

Step-by-step explanation:

T0 = a³+4

T1 = a⁴x a¹ +4

T2= a³ + a³ + 4

T3= a⁴ + a⁴* a² + 4

T4= a⁴ + a⁴ x a¹ + 4

T5= a³ + a³ + a⁴+4

Answer:

hello,

Step-by-step explanation:

c(1)=5

c(2)=9

c(2)-c(1)=9-5=4

c(2)=9

c(3)=13

c(3)-c(2)=13-9=4

c(3)=13

c(4)=17

c(4)-c(3)=17-13=4

c(4)=17

c(5)=21

c(5)-c(4)=21-17=4

for n=1,2,...,k :

c(n+1)-c(n)=4 and c(n+1)=4*(n+1)+1=4n+5

c(1)=1

The quotient of the division problem is (x + 1)/(x +2). The result is obtained by determining the factors of the two quadratic equations.

The quadratic equation can be expressed as

ax² + bx + c = 0

Where c is a constant.

To find the factors of a quadratic equation, follow these steps!

Find the quotient of (x² + 2x + 1)/(x² + 3x + 2) = 0!

For quadratic equation x² + 2x + 1:

The common factors: (x + 1)(x + 1)

For quadratic equation x² + 3x + 2:

The common factors: (x + 2)(x + 1)

The quotient of the quadratic equations is

(x² + 2x + 1)/(x² + 3x + 2) = 0

(x + 1)(x + 1)/(x + 2)(x + 1) = 0

(x + 1)/(x + 2) = 0

Hence, the quotient of the quadratic equations is (x + 1)/(x + 2) = 0.

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Answer:

15x² + 14x - 8

Step-by-step explanation:

Apply the distributive property by multiplying each term in (5x - 2) by each term in (3x + 4).

5x(3x) + (-2)(3x) + 5x(4) + (-2)(4)

= 15x² - 6x + 20x - 8

Combine like terms:

15x² + 14x - 8

(3x + 4)(5x − 2) is the factored form of 15x² + 14x - 8.

hope this helps!

The rocket will reach its maximum height after 7.438 seconds.

An equation shows the relationship between numbers and variables in an expression.

Let y represent the height of the rocket x seconds after its launch.

Given that:

y = -16x² + 238x + 81

The height of the rocket is maximum when the rate of change is zero. Hence:

The rocket reaches it maximum at dy/dx = 0

dy/dx = -32x + 238

-32x + 238 = 0

32x = 238

x = 7.438

The rocket height would be maximum at 7.438 seconds.

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The original two-digit number is 10a + b = 10(3) + 6 = 30 + 6 = 36. The two-digit number is 45.

Let's assume the original two-digit number is represented as 10a + b, where 'a' represents the tens digit and 'b' represents the ones digit.

According to the given information, the sum of the digits is 9, so we have the equation:

a + b = 9 (equation 1)

When we interchange the digits, the resulting new number is greater than the original number by 27. This can be expressed as:

10b + a = 10a + b + 27

Simplifying this equation, we get:

9b - 9a = 27

b - a = 3 (equation 2)

To solve the system of equations formed by equations 1 and 2, we can subtract equation 1 from equation 2:

(b - a) - (a + b) = 3 - 9

-2a = -6

a = 3

Substituting the value of 'a' back into equation 1, we can find the value of 'b':

3 + b = 9

b = 6

Therefore, the original two-digit number is 10a + b = 10(3) + 6 = 30 + 6 = 36.

The two-digit number satisfying the given conditions is 45.

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The perimeter of a rectangle is 80x. The base is two times the height. In terms of x, The width and length of the  dimensions rectangle in terms of x are (80x/6) and (160x/6) respectively.

The dimensions of the rectangle in terms of x are as follows:

The perimeter of a rectangle is twice the sum of the length and the width. If the length and width of a rectangle are l and w, respectively, then the perimeter is 2(l + w).

According to the problem statement, the perimeter of a rectangle is 80x.

The width and length of a rectangle in terms of x are w and 2w, respectively. Because the base is two times the height.

Thus, we have the equation for the perimeter:

2 (l + w) = 80x Or,

substituting the value of l and w in terms of x, we have:

2 (2w + w) = 80x2(3w) = 80x6w = 80xw = 80x/6

The width of the rectangle, in terms of x is 80x/6. The length of the rectangle, in terms of x is 2(80x/6) or 160x/6.

Therefore, these are the dimensions of the rectangle.

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The required inequality is 4f<36 and at most 9 fishes can be bought.

An inequality is an inequation separated by <,>≥,≤. In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

Given here: The price of each fish is $4 and total budget is $36

Let ffishes can be brought then we have

4f<36

f<9

Hence, The required inequality is 4f<36 and at most 9 fishes can be bought.

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The rental cost for each movie is $2.25 and rental cost for each video game is $5.25.

Several equations that are solved simultaneously are referred to as simultaneous equations.

Due to the possibility of simultaneously or concurrently determining the solutions to the variables, simultaneous equations are also known as systems of equations.

Movies Video Games Total Cost

First month 5 3 $27.00

Second month 2 6 $36.00

Let's say that the price per movie is $x and the price per video game is $y.

Equations:

5x + 3y = 27... Equation 1

2x + 6y = 36... Equation 2

Multiply Equation 1 by 2:

10x + 6y = 54... Equation 3

Subtract Equation 2 from Equation 3:

10x + 6y = 54 -(2x + 6y = 36)

8x = 18

x = 2.25

= $2.25

To find y, substitute x = $2.25 in equation 1.

5x + 3y = 27

5(2.25) + 3y = 27

11.25 + 3y = 27

3y = 15.75

y = 5.25

y = $5.25

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The complete question is

One month Ahmad rented 5 movies and 3 video games for a total of $27. The next month he rented 2 movies and 6 video games for a total of $36. Find the rental cost for each movie and each video game.

Answer:

x -intercept  ---> (-6,0)

y-intercept ---> (0, 9)

Step-by-step explanation:

3x = -18

3x/3 = -18/3

x = (-6,0)

-2y = -18

-2y/-2 = -18/-2

y = (0, 9)

With that launch, the ball should have a horizontal range the initial speed of the ball is approximately 35.55 m/s.

To determine the initial speed of the ball, we can analyze the vertical and horizontal components of its motion separately.

Let's start by examining the vertical component. The ball is launched at an angle of 45 degrees, so the initial velocity can be divided into vertical and horizontal components:

V₀x = V₀ * cos(45°)   (horizontal component)

V₀y = V₀ * sin(45°)   (vertical component)

In this case, we want the ball to return to the launch level, which means the vertical displacement is zero. Using the equation for vertical displacement, we can find the time it takes for the ball to reach its maximum height:

Δy = V₀y * t - (1/2) * g * t²

Since Δy is zero (returning to the launch level), we can solve for t:

0 = V₀y * t - (1/2) * g * t²

Simplifying the equation, we get:

(1/2) * g * t² = V₀y * t

t = 2 * V₀y / g

Now we can move on to the horizontal component. We are given the horizontal range (R) as 120.0 m. The horizontal range is given by the equation:

R = V₀x * t

Substituting the expression for t we found earlier:

R = V₀ * cos(45°) * (2 * V₀y / g)

Since cos(45°) = sin(45°) = 1/√2, we can simplify further:

R = (V₀² / g) * (2 * 1/√2 * 1/√2)

R = (V₀² / g) * 1

R = V₀² / g

Now we can solve for the initial velocity, V₀:

V₀² = R * g

V₀ = √(R * g)

Plugging in the given values, where R = 120.0 m and g = 9.8 m/s²:

V₀ = √(120.0 * 9.8)

V₀ ≈ 35.55 m/s

Therefore, the initial speed of the ball is approximately 35.55 m/s.

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Answer:

y=-3/4x+11

Step-by-step explanation:

Graph the point and draw a line having -3/4 as a slope and see what the y intercept of that same line is. Then that y intercept goes after the -3/4x in the new equation.

The correct point-slope equation for the line that passes through the point (-4,-2) and is parallel to the line given by y = 5x + 44 is: A. y + 2 = 5(x + 4)

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

Since the line is parallel to y = 5x + 44, the slope is equal to 5.

At data point (-4, -2) and a slope of 5, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-2) = 5(x - (-4))  

y + 2 = 5(x + 4)

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Marisa can expect to make a profit with her company as per the given information. The profit she earns from the 49 pairs will cover the cost of repairing the one pair that needs repair.

Based on the profit analysis, Marisa can expect to make a profit with her company. The calculation and expiation are provided as follows:
Profit Calculation:

Marisa wants to make a profit of $5.00 on each pair of earrings. This means that for every pair sold, she will earn $5.00.
Cost of Repair:

Marisa has improved the quality control, resulting in only 1 pair in 50 need to be returned for repair. The cost of repairing each pair is $60.
Profit Analysis:

Let's analyze the profit situation.
  - For every 50 pairs sold, one pair will need repair, costing Marisa $60.
  - However, for the remaining 49 pairs, she will earn $5.00 profit on each, totaling $245.00 ($5.00 x 49).
  - So, the total profit from the 49 pairs will offset the cost of the one pair that needs repair.
Based on the profit analysis, Marisa can expect to make a profit with her company. The profit she earns from the 49 pairs will cover the cost of repairing the one pair that needs repair. Therefore, her company can be considered profitable.

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Answer:

2.25 per bowl.

Step-by-step explanation:

Two bowls of clam chowder cost 4.50.

\(\frac{4.50}{2}= \boxed{2.25}\)

Hope this helps.

Among the 5 options given in the question, the coordinates that satisfy the given inequalities are (1,8), (0,5), (-2,9). And the other two , donot satisfy the inequalities, hence (1,8), (0,5), (-2,9) are the required solutions.

The solutions to a system of linear inequalities are the coordinates that satisfy all the inequalities in the system. They are the points that are above the lines of the inequalities.

To determine if a point is a solution to a system of linear inequalities, we need to substitute the coordinates of the point into each inequality and check if it makes the inequality true. A point is a solution to the system if it makes all the inequalities true.

To check the solutions for the given linear inequallities,

1. y>-x+3

 for (1,8) , 8 > -1+3 i.e 8>2 , Hence Satisfied

  for (0,5) , 5> -0+3 i.e 5>3, Hence satisfied

  for (-2,9) , 9>-(-2) + 3 i.e 9>5, Hence satisfied

   for (0,0), 0>-0 +3 i.e 0>3 , Which is false

   for (-1,1) , 1 > 1 +3 ,i.e 1>4, which is false

2.y> 3x+1

 for (1,8) , 8 > 3*1+1 i.e 8>4 , Hence Satisfied

  for (0,5) , 5> 3*0+1 i.e 5>1, Hence satisfied

  for (-2,9) , 9>3*(-2) +1 i.e 9>-5, Hence satisfied

   for (0,0), 0>3*0+1 i.e 0>1 , Which is false

   for (-1,1) , 1 > 3*(-1)+1 ,i.e 1>-2, which is false

Hence the required solutions are (1,8), (0,5), (-2,9) which satisfy the both inequalities.

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Answer:

10

Step-by-step explanation:

1/3 of 24 is 8, and 1/4 is 6. 8+6=14, and 24-14=10. So I think that 10 people brought chips.

Answer:

10

Step-by-step explanation:

24 ÷ 3 = 8 so one third is 8

24 ÷ 4 = 6 so one fourth is 6

8 + 6 = 14 (14 people brought drinks or dessert)

24 - 14 = 10

ten people brought chips.

Answer:

1 gallon to 12 miles

Step-by-step explanation:

Distance = 300 miles

Gasoline used = 25 gallons

Expressing as a unit rate :

Distance covered per gallon of gasoline :

Distance / gasoline used

300 / 25

12 miles

Hence, the unit rate is :

1 gallon of gasoline = 12 miles

1 gallon of gasoline will cover 12 miles in distance.

Answer:

hi

Step-by-step explanation:

4 7/8 .4 3/4= 7/2 . 3 =21/2

Answer:

23 5/32

Step-by-step explanation:

Convert both 4 7/8 and 4 3/4 into improper fractions:

the first becomes 39/8, and the second becomes 19/4.  We then have:

39      19              

------ * -----   which comes out to 23.15625, or 23 5/32

  8       4                                      

Answer:

(edit) wait sorry i forgot slope-intercept form

Step-by-step explanation:

the answer should be y = - 4/3x - 2

Considering the proportional relationship, it is found that Charlotte should add 0.8 ounces of purple paint to 1 ounce of white paint.

A direct proportional relationship is given by the equation presented as follows:

y = kx.

Meaning that the output variable y is calculated as the multiplication of the input variable x and the constant of proportionality k.

In this problem, the relationship is given as follows:

Purple paint = k x white paint.

The shade of lavender she prefers uses 4​ fluid ounces of purple paint to 4​ fluid ounces of white paint, hence the constant is obtained as follows:

k = 4/5 = 0.8.

When she uses one ounce of white paint, the amount of purple paint is calculated as follows:

Purple paint = 0.8 x 1 = 0.8 ounces.

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Answer:

⅓ ×½ which will give you ⅙

Step-by-step explanation:

because

The probability that Manu will win the coin flip amongst others is 4/7

To determine the probability that Manu will win, we need to consider the possible outcomes of the coin flips.

Let's break down the scenarios:

Scenario 1: Manu wins on the first flip

- The probability of Manu winning on the first flip is 1/2, as he needs to flip heads right away.

Scenario 2: Manu wins on the second flip

- Juan flips tails (1/2 probability)

- Carlos flips tails (1/2 probability)

- Manu flips heads (1/2 probability)

- The probability of Manu winning on the second flip is (1/2) * (1/2) * (1/2) = 1/8.

Scenario 3: Manu wins on the third flip

- Juan flips tails (1/2 probability)

- Carlos flips tails (1/2 probability)

- Manu flips tails (1/2 probability)

- Juan flips heads (1/2 probability)

- Carlos flips heads (1/2 probability)

- Manu flips heads (1/2 probability)

- The probability of Manu winning on the third flip is (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2) = 1/64.

The pattern continues, and we can see that Manu's probability of winning decreases exponentially with each subsequent flip.

Therefore, the total probability of Manu winning is the sum of the probabilities from each scenario:

1/2 + 1/8 + 1/64 + ...

This is an infinite geometric series with a first term (a) of 1/2 and a common ratio (r) of 1/8.

Using the formula for the sum of an infinite geometric series:

Sum = a / (1 - r)

Sum = (1/2) / (1 - 1/8)

Sum = (1/2) / (7/8)

Sum = (1/2) * (8/7)

Sum = 4/7

Therefore, the probability that Manu will win is 4/7.

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