Christina is tying tow pieces of string together to make a single piece. Her knot will reduce the lenght of each piece by 1/4 inch. If one piece is 3 1/4 inches long and the other is 5 1/2 inches long, what will be the length of the single piece of string?

Answer:

The girls had a higher average in the reading test than the boys.

Step-by-step explanation:

To find the solution, you need to find the mean (average) of the group of boys and group of girls each. The mean of numbers can be found by dividing the sum of all numbers by the amount of numbers there are.

Lets start by finding the mean of the boys group. Find the sum of all numbers:

[tex]2.0 + 3.9 + 4.3 + 4.9 + 6.0 = 21.1[/tex]

Now divide the sum by how many numbers, or in this case, how many boys did the test:

[tex]21.1 \div 5 = 4.22[/tex]

The mean, average, of the tests conducted by the group of boys is 4.22.

Repeat the same for the girls group:

[tex]2.8 + 3.8 + 4.5 + 5.2 + 5.9 = 22.2 \\ 22.2 \div 5 = 4.44[/tex]

The mean, average, of the tests conducted by the group of girls is 4.44.

Compared to 4.22, 4.44 is bigger than 4.22.

Answer:

mixture a because there's not so much purple.the more purple the darker it is

Answer:

The mixture B is a lighter shade of purple.

Step-by-step explanation:

In order to answer the question, we first need to calculate the proportion of purple in both mixtures. The mixture that has the lowest proportion of purple will be the lighter one.

For mixture A :

5 cups of purple

2 cups of white paint

⇒ Mixture A is made with 5 + 2 = 7 cups of paint in which 5 are cups of purple. Therefore, we can calculate the proportion of purple as :

[tex]\frac{5CupsOfPurple}{7CupsInTheMixture}=\frac{5}{7}=0.7143[/tex]

This means that approximately 71.43% of the mixture A is made of purple paint.

For mixture B :

15 cups of purple paint

8 cups of white paint

⇒ Mixture B is made with 15 + 8 = 23 cups of paint in which 15 are cups of purple. Therefore, we can calculate the proportion of purple as :

[tex]\frac{15CupsOfPurple}{23CupsInTheMixture}=\frac{15}{23}=0.6522[/tex]

This means that approximately 65.22% of the mixture B is made of purple paint.

If we compare the proportions :

[tex]0.7143>0.6522[/tex] ⇒ [tex]Proportion_{A}>Proportion_{B}[/tex]

We conclude that the mixture B is a lighter shade of purple because it has the lowest proportion of purple (we can also think that mixture B has the highest proportion of white)

Answer:

The answer to your question is: 95 yards

Step-by-step explanation:

Data

1 inch   ----------------  5 yards

19 inches ------ ? yards

We can solve this problem with a rule of three

              1 inch ------------------ 5 yards

             19 inches --------------   x

             x = (19)(5) / 1 = 95 yards

Answer:

it was wrong!!

Step-by-step explanation:

Answer:

$1.91

Step-by-step explanation:

This means the cost of the item to you is $1.91. You will pay $1.91 for a item with original price of $2.25 when discounted 15%. In this example, if you buy an item at $2.25 with 15% discount, you will pay 2.25 - 0.3375 = 1.91 dollars.

Answer:

1.91

Step-by-step explanation:

1- 2.25

2- 2.25÷100= 0.0225 find 1 percent

3- 0.0225×15=0.3375 find the 15 percent

4- 2.25-0.3375=1.9125 subtract the discount of the original price

5- 1.91 round off to two decimals

Answer:

The answer to your question is:   x > - 32/9

Step-by-step explanation:

                                            -5/2(3x+4)<6-3x

Multiply by 2                      -5(3x + 4) < 12 - 6x

Simplify                             -15x - 20 < 12 - 6x

Add +6x                            -15x + 6x -20 < 12 - 6x + 6x

Simplify                            - 9x - 20 < 12

Add + 20                          -9x -20 + 20 < 12 + 20

Simplify                            -9x  <  32

Divide by -9                     -9/-9 x > 32/-9

Simplify                             x > - 32/9

Answer:

  74 days

Step-by-step explanation:

The proportion left after d days is ...

  p = (1/2)^(d/100)

When that proportion is 60%, we have ...

  .60 = .50^(d/100)

  log(.60) = (d/100)log(.50) . . . . . take logarithms

  100·log(.60)/log(.50) = d ≈ 73.697 ≈ 74 . . . days

4.5 Is the answer required

Answer: 2

Step-by-step explanation: got it right :)

Answer:

The functions are inverses; f(g(x)) = x ⇒ answer D

[tex]h^{-1}(x)=\sqrt{\frac{x+1}{3}}[/tex] ⇒ answer D

Step-by-step explanation:

* Lets explain how to find the inverse of a function

- Let f(x) = y

- Exchange x and y

- Solve to find the new y

- The new y = [tex]f^{-1}(x)[/tex]

* Lets use these steps to solve the problems

∵ [tex]f(x)=\sqrt{x-3}[/tex]

∵ f(x) = y

∴ [tex]y=\sqrt{x-3}[/tex]

- Exchange x and y

∴ [tex]x=\sqrt{y-3}[/tex]

- Square the two sides

∴ x² = y - 3

- Add 3 to both sides

∴ x² + 3 = y

- Change y by [tex]f^{-1}(x)[/tex]

∴ [tex]f^{-1}(x)=x^{2}+3[/tex]

∵ g(x) = x² + 3

∴ [tex]f^{-1}(x)=g(x)[/tex]

∴ The functions are inverses to each other

* Now lets find f(g(x))

- To find f(g(x)) substitute x in f(x) by g(x)

∵ [tex]f(x)=\sqrt{x-3}[/tex]

∵ g(x) = x² + 3

∴ [tex]f(g(x))=\sqrt{(x^{2}+3)-3}=\sqrt{x^{2}+3-3}=\sqrt{x^{2}}=x[/tex]

∴ f(g(x)) = x

∴ The functions are inverses; f(g(x)) = x

* Lets find the inverse of h(x)

∵ h(x) = 3x² - 1 where x ≥ 0

- Let h(x) = y

∴ y = 3x² - 1

- Exchange x and y

∴ x = 3y² - 1

- Add 1 to both sides

∴ x + 1 = 3y²

- Divide both sides by 3

∴ [tex]\frac{x + 1}{3}=y^{2}[/tex]

- Take √ for both sides

∴ ± [tex]\sqrt{\frac{x+1}{3}}=y[/tex]

∵ x ≥ 0

∴ We will chose the positive value of the square root

∴ [tex]\sqrt{\frac{x+1}{3}}=y[/tex]

- replace y by [tex]h^{-1}(x)[/tex]

∴ [tex]h^{-1}(x)=\sqrt{\frac{x+1}{3}}[/tex]

Answer:

  [1] = 6

  x = -3/2 is the root

Step-by-step explanation:

A perfect square trinomial is of the form ...

  (a + b)² = a² +2ab +b²

You have ...

Then the factorization is ...

  16w² +48w +36 = (4w +6)²

This will be zero when x = -6/4 = -3/2.

Answer:

The answer to your question is:    Y = (13, -14)

Step-by-step explanation:

Data

midpoint = mp = (6, -3)

one endpoint = X = (-1, 8)

second endpoint = Y = (x, y)

Formula

Xmp = (x1 + x2) / 2

Ymp = (y1 + y2) / 2

Process

                    x2 = 2xmp - x1

                    y2 = 2ymp - y1

                   x2 = 2(6) - (-1)                     y2 = 2(-3) - 8

                   x2 = 12 + 1                          y2 = -6 - 8

                   x2 = 13                               y2 = - 14

                   Y = (13, -14)

Answer:

The answer is c. $48,000

Step-by-step explanation:

To find the free cash flow, we need to take into account the money that is entering the company and the money that is being used.  Money that we are earning is possitive, and money being spend goes with a minus.

The net cash, the $50,000 is our sales column. And is money entering the company.

The Investment would be our CAPEX or directly we can use it as investment. And this money is being spended.

The dividends, are the payments that we are doing to the board of directors or the share holders. Since we are paying others, we know this money is being used.

The equation here is:

Sales - Investment - Dividends = Free Cash Flow

So it $50,000 - $1,000 - $1,000 = $48,000

Final answer:

The factorization of x² + 3x - 4 is (x + 4)(x - 1), which can be verified using algebra tiles that represent these factors and the product.

Explanation:

The factors of x² + 3x - 4 can be determined by looking for two numbers that multiply to -4 (the constant term) and add up to +3 (the coefficient of the middle term x). Through factor pairs of -4 (e.g., -1 and 4, or 2 and -2), we notice that (+4) and (-1) are the numbers that meet the criteria because 4 × (-1) = -4 and 4 + (-1) = 3. Therefore, the factorization is (x + 4)(x - 1). To use algebra tiles, you would arrange them into a rectangle where the length and width represent the factors of the quadratic expression, and the product area represents the entire expression.

Answer:

18 quarters

30 pennies

15 dimes

Step-by-step explanation:

Let number of quarters be q, number of pennies be p, number of dimes be d

The value of pennies is 0.01, the value of quarters is 0.25 and value of dimes is 0.10.

Jack has 63 pennies, dimes, and quarters worth $6.30:

We can write:

p + q + d = 63

0.01p + 0.25q + 0.10d = 6.30

Also, the number of dimes is three less than the number of quarters:

We can write:

d = q - 3

Now we have written 3 equations. Replacing 3rd equation in 1st gives us:

p + q + (q-3) = 63

p + 2q -3 = 63

p + 2q = 66

Solving for p:

p = 66 - 2q

Now we can use this and the 3rd equation and replace p and d with q:

0.01p + 0.25q + 0.10d = 6.30

0.01(66-2q) + 0.25q + 0.10(q-3) = 6.30

Solving for q, gives us:

[tex]0.01(66-2q) + 0.25q + 0.10(q-3) = 6.30\\0.66-0.02q+0.25q+0.10q-0.3=6.30\\0.36+0.33q=6.30\\0.33q=5.94\\q=18[/tex]

There are 18 quarters

Since, p = 66 - 2q, there are:

p = 66 - 2 (18) = 30 pennies

Also,

d = q - 3, so d = 18 - 3 = 15 dimes

Hence, there are:

18 quarters

30 pennies

15 dimes

Answer:

Step-by-step explanation:

1. The magnitude of the multiplier is 6, so the magnitude of the new vector is 6×(15 m) = 90 m. The sign on the multiplier is negative, so the new vector will be in the opposite direction of East. It will be 90 m West.

__

2. The components can be found from ...

  (8.9 m/s)(cos(-40°), sin(-40°)) ≈ (6.82, -5.72) m/s

__

One or both of the components will usually be irrational if the angle is a rational number of degrees not a multiple of 90°. Here, we have rounded to 2 decimal places.

Final answer:

The x-component of vector A is 4.00 units east, and the y-component of vector A is -3.00 units south, calculated using the cosine and sine functions respectively.

Explanation:

The student has asked for the components of vector A which has a magnitude of 5.00 units and is at an angle of 36.9° south of east. To find the components of a vector, we use trigonometric functions. The component along the x-axis (east-west direction) is found using the cosine function, and the component along the y-axis (north-south direction) is found using the sine function. Since the angle is south of east, the x-component will be positive and the y-component will be negative in our coordinate system.

The x-component of vector A (Ax) is calculated as:

Ax = A * cos(θ) = 5.00 * cos(36.9°) = 5.00 * 0.800 = 4.00 units

The y-component of vector A (Ay) is calculated as:

Ay = A * sin(θ) = 5.00 * sin(36.9°) = 5.00 * 0.600 = 3.00 units

Therefore, the components of vector A are 4.00 units east and -3.00 units south.

Answer

The first one

Step-by-step explanation:

The product of a number and 3 is 6 more than the number

The product of a number = n x 3

6 more than the number = n + 6

Put them together and its =

n x 3 = n + 6

I hope this helps :)

Sorry if its wrong

The product of a number and 3 is 6 more than the number is n.3 = n + 6.

A numerical expression is of the form of numbers and their operations.

According to the question given we have to model a numerical expression from the statement given which is The product of a number and 3 is 6 more than the number.

Let the number be 'n'.

∴ Product of a number and 3 which is 3×n is 6 more than the number n + 6.

So, 3n = n + 6.

3n - n = 6.

2n = 6.

n = 6/3.

n = 2.

This can also be written as n.3 = n + 6.

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Answer:

y+1.4=1.9 (x-4.5)

Step-by-step explanation:

The slope is the number in front of the brackets, which must be positive 1.9. This eliminates the last option. It is y+1.4 because the formula is y-y1=m (x-x1)

So once you substitute values

y--4.5=1.9 (x-4.5)

y+4.5=1.9 (x-4.5)

An equation of the line in point-slope form is: B. y + 1.4 = 1.9(x - 4.5)

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

y - y₁ = m(x - x₁)

Where:

At data point (4.5, -1.4) and a slope of 1.9, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-1.4) = 1.9(x - 4.5)  

y + 1.4 = 1.9(x - 4.5)

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Answer:

MN = sqrt(34)

Step-by-step explanation:

First, draw the segment FN. The diagonal, MN, of the prism is the hypotenuse of triangle NFM. Triangle NFM is a right triangle with legs FN and FM and hypotenuse MN.

Leg FM of triangle NFM has length 4 cm.

We need to find the length of leg FN.

Look at the base of the prism which is square UNAF. FN is a diagonal of that square. Now think of right triangle FUN with legs UN and UF, each of length 3 cm. We can find FN with the Pythagorean theorem.

(UF)^2 + (UN)^2 = (FN)^2

3^2 + 3^2 = (FN)^2

(FN)^2 = 18

FN = sqrt(18)

Now we know FN. We use FN and FM as legs and find MN, the hypotenuse of triangle NFM.

(FN)^2 + (FM)^2 = (MN)^2

18 + 4^2 = (MN)^2

18 + 16 = (MN)^2

(MN)^2 = 34

MN = sqrt(34)

Answer:

23

Step-by-step explanation:

or 2.8 but try 23 frist

The percentage of increase of total number of students on the honor roll is obtained as 22.97%.

A percentage is a value that indicates 100th part of any quantity.

A percentage can be converted into a fraction or a decimal by dividing it by 100.

And to convert a fraction or a decimal into percentage, they are multiplied by 100.

The number of boys and girls on the honor code last year is given as 132 and 90.

Then, the total number is 132 + 90 = 222.

When, the number of boys increased by 25%, it can be obtained as,

⇒ 132 + 25% × 132 = 165

And, the number of girls increased by 20% can be obtained as,

⇒ 90 + 20% × 90 = 108

Now, the total number of students is 165 + 108 = 273.

The percent increase can be obtained as follows,

Change in the total number ÷ Initial number × 100

⇒ (273 - 222) ÷ 222 × 100 = 22.97%

Hence, the percent value of the increase in the number is 22.97%.

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Answer:

C - 4x4+14x2y+49y2

Step-by-step explanation:

Just took the test

To determine which option is a factor of the given expression, we need to check each option individually. After checking, we find that option 2, 2x^2 + 7y, is a factor.

To determine which of the given options is a factor of the expression 24x^6 - 1029y^3, we need to check each option individually.

Option 1: 24 - We can verify if 24 is a factor by dividing 24x^6 - 1029y^3 by 24 and checking if there is no remainder.

Option 2: 2x^2 + 7y - We can substitute values for x and y and simplify the expression to see if it equals zero for any values.

Option 3: 4x^4 + 14x^2y + 49y^2 - We can substitute values for x and y and simplify the expression to see if it equals zero for any values.

After checking each option, we can determine that option 2, 2x^2 + 7y, is a factor of the expression 24x^6 - 1029y^3.

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Answer:

The answer to your question is: 30 boxes

Step-by-step explanation:

Data:

A packing crate measures 0.40 m 0.40 m 0.25 m.

boxes of cookies measure 22.0 cm 12.0 cm 5.0 cm

Formula

Volume of a rectangular prism: l x w x h

Volume of the bigger prism = 40 cm x 40 x 25 cm = 40 000 cm3

Volume of the smaller prism = 22 x 12 x 5 = 1320 cm3

Then we divide the volumes = 40000 / 1320 = 30.3 boxes

Answer:

Option E.

Step-by-step explanation:

Let the intended length of Rebecca's swimming is = x units

and we assume the length of the pool = l units

Now it is given in the question that " She covers one fifth of her intended distance "

That means distance covered = [tex]\frac{x}{5}[/tex]

" After swimming six more lengths of the pool she had covered one quarter of her intended distance"

So [tex]\frac{x}{5}+6(l)=\frac{x}{4}[/tex]

[tex]6l=\frac{x}{4}-\frac{x}{5}[/tex]

[tex]6l=\frac{x}{20}[/tex]

x = 20×(6l)

x = 120l

Therefore, Rebecca has to complete 120 lengths of the pool.

Option E is the answer.

Answer:

  ray

Step-by-step explanation:

A ray is a line that extends in one direction from its end point.

[tex]\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{-4})~\hspace{10em} \stackrel{slope}{m}\implies 0 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{0}[x-\stackrel{x_1}{(-3)}]\implies y+4=0(x+3) \\\\\\ y+4=0\implies y=-4[/tex]

Answer: Hi, first lets give our variables some names.

Lets call Ks to Karen's salary and Js to Jason's salary.

then, in 1995:

Ks₁ - Js₁ = 2000$

in 1998:

Ks₂ - Js₂ = 2440$

now, we know that  Ks₂ = (1 +p)*Ks₁ and   Js₂ = (1+p)*Js₁

so we can write the second equation as:

p*(Ks₁ - Js₁ ) = 2440$

replacing the parentesis with the first equiation

(1+p)*(2000$) = 2440$

(1+p)= 2440/2000 = 1.22

so p = 0.22, or a 22%

The answer will be 13

since he give you the C and X

you just need to add them and then subtract them from 90 degree

51+26-90=13

I hope this will helps you.

the result of subtracting[tex]\( (4x^2 - x) \)[/tex]  from [tex]\( -3x^2 \) is \( \boxed{-7x^2 + x} \).[/tex]

To subtract [tex]\( (4x^2 - x) \) from \( -3x^2 \)[/tex], we need to distribute the negative sign to each term inside the parentheses and then perform the subtraction.

Given:

[tex]\( -3x^2 - (4x^2 - x) \)[/tex]

Step 1: Distribute the negative sign inside the parentheses:

[tex]\( -3x^2 - 4x^2 + x \)[/tex]

Step 2: Combine like terms:

[tex]\( (-3x^2 - 4x^2) + x \)[/tex]

[tex]\( = -7x^2 + x \)[/tex]

Therefore, the result of subtracting[tex]\( (4x^2 - x) \)[/tex]  from [tex]\( -3x^2 \) is \( \boxed{-7x^2 + x} \).[/tex]

Answer:

Probability: 50%

odds: 5:5

Step-by-step explanation:

Answer:

The probability is 50% that ball will be green.

Odds 5:5

Numbers of ways to draw a green marbles: number of ways to draw another marbles.

Step-by-step explanation:

Consider the provided bag of marble.

The bag contains 5 green marble, 3 blue marbles and 2 red marbles.

The total number of marbles are: 5+3+2=10

The probability of getting a green marble is: 5/10=0.5

That means the probability is 50% that ball will be green.

Drawing green marbles means we want marble should be green and ODDs of drawing a green marble means the marble is not green.

There are 5 green marbles, so there are 5 outcomes that we want (out of 10 outcomes total)

There are 10-5 = 5 outcomes that we don't want a green marble.

Number of outcomes we want is 5

Number of outcomes we don't want is 5

Odds in favor = (wanted outcomes):(unwanted outcomes)

Odds in favor = 5:5

Numbers of ways to draw a green marbles: number of ways to draw another marbles.

Answer:

-1, 2, 5, 8, 11

Step-by-step explanation:

There is an easy and fast way to solve this. A linear function means that the steps on y and x are constant.

On the x axis you are walking 5 steps each column, so you start from 5, plus 5 steps is 10, plus 5 steps is 15, plus 5 steps is 20, plus 5 steps is 25.

Now you have to do the same for the y axis, but you have to use your brain.

You start from -1, and you have to reach 11, using the same number of steps for each column, just like before the necessarily with the same number.

You start from -1, plus 3 steps is 2, plus 3 steps is 5, plus 3 steps is 8, plus 3 steps is 11. Done.

You can use maths also, but it will take time.

You need to find that function. A linear function can be written as:

[tex]y = mx + q[/tex]

You have two points of the line, (5, -1) and (25, 11), but you need to find the y coordinate of other three points.

Let's find the line by substituting those points in the general function of the line:

[tex] - 1 = 5m + q \\ 11 = 25m + q[/tex]

This is a system of two equations with two variables, m and q. You can solve it. From the first equation you have that:

[tex]q = - 1 - 5m[/tex]

Put this in the second equation to know the value of m:

[tex]11 = 25m + ( - 1 - 5m)[/tex]

[tex]11 = 25m - 1 - 5m \\ 20m = 12 \\ m = \frac{12}{20} = \frac{3}{5} [/tex]

Now you can use this in the first equation to know the value of q:

[tex]q = - 1 - 5( \frac{3}{5} ) \\ q = - 1 - 3 \\ q = - 4[/tex]

So your line is:

[tex]y = \frac{3}{5} x - 4[/tex]

If you want to know the y coordinates that you are missing, you just need to put the corresponding x coordinate in this function and you will find the same results as before.

To fill in a table for a linear function, you need to understand the relationship between x and y in a linear function (y = mx + b), calculate y values for given x values using this relationship, and arrange these pairs in the table.

To fill in a table that represents a linear function, we need to understand that in a linear function, the change in the output (y) is constant for every unit change in the input (x). The relationship between x and y can be written as y = mx + b, where m is the slope and b is the y-intercept.

Here's a simple example. For a linear function y = 2x + 1, if your x values are 1, 2, and 3, the y values would be y(1) = 2*1+1 = 3, y(2) = 2*2+1 = 5, y(3) = 2*3+1 = 7. So the table would look like:

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Answer:

D

Step-by-step explanation:

There are 1.61 km in 1 mi.

10 mi × (1.61 km/mi) = 16.1 km