Robin and Josie shared a bottle of green paint For an art project.Robin use 3/5 of the bottles. Together they used 17/20

Answer:

Step-by-step explanation:

A.  h = -2(1)² + 7(1) + 4 = 9 ft

B.  use the quadratic formula to find the 2 solutions to t when

y = f(t) = -2t² + 7t + 4 = 0         a=-2, b=7, c=4

the 2 solutions for t are:  -1/2, 4

halfway between t=-1/2 and t=4 is:  (-1/2 + 4) /2 = 1.75   (vertex of the parabola)

so, at t = 1.75 s, the toy is at its max. height:

h = -2(1.75)² + 7(1.75) + 4 = 10.125 ft

C.  Toy is in the air for 4 sec

The answer is 4 s because f(4) = 0, meaning the toy hits the ground after 4 sec

The equation of the line through (0, 1) and (c, 0) is

y - 0 = (0 - 1)/(c - 0) (x - c)   ==>   y = 1 - x/c

Let L denote the given lamina,

L = {(x, y) : 0 ≤ x ≤ c and 0 ≤ y ≤ 1 - x/c}

Then the center of mass of L is the point \((\bar x,\bar y)\) with coordinates given by

\(\bar x = \dfrac{M_x}m \text{ and } \bar y = \dfrac{M_y}m\)

where \(M_x\) is the first moment of L about the x-axis, \(M_y\) is the first moment about the y-axis, and m is the mass of L. We only care about the y-coordinate, of course.

Let ρ be the mass density of L. Then L has a mass of

\(\displaystyle m = \iint_L \rho \,\mathrm dA = \rho\int_0^c\int_0^{1-\frac xc}\mathrm dy\,\mathrm dx = \frac{\rho c}2\)

Now we compute the first moment about the y-axis:

\(\displaystyle M_y = \iint_L x\rho\,\mathrm dA = \rho \int_0^c\int_0^{1-\frac xc}x\,\mathrm dy\,\mathrm dx = \frac{\rho c^2}6\)

Then

\(\bar y = \dfrac{M_y}m = \dfrac{\dfrac{\rho c^2}6}{\dfrac{\rho c}2} = \dfrac c3\)

but this clearly isn't independent of c ...

Maybe the x-coordinate was intended? Because we would have had

\(\displaystyle M_x = \iint_L y\rho\,\mathrm dA = \rho \int_0^c\int_0^{1-\frac xc}y\,\mathrm dy\,\mathrm dx = \frac{\rho c}6\)

and we get

\(\bar x = \dfrac{M_x}m = \dfrac{\dfrac{\rho c}6}{\dfrac{\rho c}2} = \dfrac13\)

The center of mass for a uniform triangular shape is on its centroid. The y-coordinate of the center of mass of the lamina is 1/3 (independent of c).

If the surface is plane triangle approximately and mass is uniformally distributed, then its center of mass will lie on the centroid of that triangle.

The point of intersection of a triangle's medians is its centroid (the lines joining each vertex with the midpoint of the opposite side).

If the triangle has its vertices as  \((x_1, y_1), (x_2, y_2) , \: (x_3, y_3)\), then the coordinates of the centroid of that triangle is given by:

\((x,y) = \left( \dfrac{x_1 + x_2 + x_3}{3} + \dfrac{y_1 + y_2 + y_3}{3} \right)\)

For this case, the  triangular lamina has vertices (0, 0), (0, 1) and (c, 0)

Assuming its mass is spread regularly, the coordinates of its center of mass would be:

\((x,y) = \left( \dfrac{x_1 + x_2 + x_3}{3} + \dfrac{y_1 + y_2 + y_3}{3} \right)\\\\(x,y) = \left( \dfrac{0+0+c}{3} + \dfrac{0+1+0}{3} \right) = (c/3, 1/3)\)

Thus, the y-coordinate of the center of mass of the lamina is 1/3 (independent of c).

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Answer:

it will increase the production

Step-by-step explanation:

Answer:

Step-by-step explanation:

We would apply the future value which is expressed as

FV = C × [{(1 + r)^n - 1}/r]

Where

C represents the yearly payments of the young professional.

FV represents the amount of money

in your account at the end of 40 years.

r represents the annual rate.

n represents number of years or period.

From the information given,

r = 4% = 4/100 = 0.04

C = $76000

n = 40 years

Therefore,

FV = 76000 × [{(1 + 0.04)^40 - 1}/0.04]

FV = 76000 × [{4.8 - 1}/0.04]

FV = 76000 × 95

FV = P7220000

Using both hoses will take 10 minutes to fill up the kiddie pool. Mary can fill up 1/3 of the pool using the front yard hose in 10 minutes and 1/6 of the pool using the backyard hose in 10 minutes.

To solve this problem, we need to use the concept of rates. Let's assume the rate of the hose in the backyard is x, so the rate of the hose in the front yard is 2x (because it is twice as fast as the other hose).

The combined rate of the two hoses is x + 2x = 3x, which means they can fill the pool in 30/3x = 10/x minutes.

We know that the area of the pool is 600 square feet and each small rock covers 20 square feet, so we need a total of 600/20 = 30 small rocks to cover the pool.

Since the mass of each rock is 20 grams, the total mass of all 30 rocks is 30 x 20 = 600 grams.

To find the density, we divide the total mass (600 grams) by the total volume of the rocks (30 x 20 cubic feet = 600 cubic feet)

Density = 600g / 600 cubic feet = 1g/cubic foot

Therefore, the answer is B. 10 minutes for the pool to fill up, and the density of the rocks is 1 gram per cubic foot.

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To find the fraction of pocket money left after spending on transport and fruit, we need to subtract the amount spent from the total pocket money and express it as a fraction.

The student spends 18 out of 35 of his pocket money, which means he has (35 - 18) = 17 units of his pocket money left.

Therefore, the fraction of pocket money left can be written as 17/35.

The value of x for the equation 5x = 3x + 10 is 5 and for the equation 3x + x = 2x + 2 is 1.

The Latin term "Integer," which implies entire or whole, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers. The collection of whole numbers and negative numbers is known as an integer in mathematics. Integers, like whole numbers, do not include the fractional portion. Integers can therefore be defined as numbers that can be positive, negative, or zero but not as fractions.

The given equation is 5x = 3x + 10.

5x = 3x + 10

Subtracting 3x from both sides of the equation we have:

5x - 3x = 10

2x = 10

x = 5.

Substitute x = 5.

Check: 5(5) = 3(5) + 10; 25 = 25.

Similarly, 3x + x = 2x + 2

4x = 2x + 2

4x - 2x = 2

x = 1.

Hence, the value of x for the equation 5x = 3x + 10 is 5 and for the equation 3x + x = 2x + 2 is 1.

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Answer:4.98

Step-by-step explanation:

trust me

The answer to the given question is length is 17m and width is 6m

Given that a rectangle's length is 7 meters less than its width.

And also given the perimeter of the rectangle is 46 meters.

We know that the rectangle's perimeter is twice the sum of its length and width.

l - length of the rectangle

w - width of the rectangle

P - perimeter of the rectangle

Then we have P = 2 × (l + w)

Given that a rectangle's length is 7 meters less than its width.

⇒ l = 4 × w - 7

Given the perimeter of the rectangle is 46 centimeters.

⇒ 2 × ( l + w) = 46

⇒ 2 × (4w - 7 + w) = 46 (using the value of length given in terms of width)

⇒ 4w - 7 + w = 23 (dividing by 2 on both the sides)

⇒ 5w - 7 = 23

⇒ 5w = 23 + 7

⇒ 5w = 30

⇒ w = 6 (dividing both sides by 5)

Using the width value in the length equation, we get

l = 4 × 6 - 7

⇒ l = 24 - 7

⇒ l = 17

Therefore, The rectangle is 17 meters in length and 6 meters in width.

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Answer:

y=5x-2

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Because if you multiply 30 x 42, it will give you 1,260. That minus 240, its 1,020. :)

The net earnings of Todd if he worked for 42 hours is $1080.

Gross pay is defined as the total amount of money an employee receives for the time worked. It includes one's regular salary and overtime payment or bonuses or other compensations.

Gross pay does not deduct the taxes the employee has to pay.

Amount Toddy earns in an hour = $30

Tax payment = $240

Total hours Toddy worked = 42 hours

Regular hours= 40 hours

Amount Toddy earns in a regular hour = $30

Extra hour Toddy worked = 2 hours

Amount Toddy gets for an extra hours = 2 × 30 = $60   [double time]

Gross pay  = (regular hours × regular pay) + (extra hours × extra pay)

Gross Pay Toddy earned = (40 × 30) + (2 × 60)

                                          = 1200 + 120 = $1320

Net earnings Toddy earned = $1320 - $240 = $1080

Net earnings Toddy earns if he works for 42 hours assuming double time over 40 hours is $1080.

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Answer:

j

Step-by-step explanation:

Answer: The price of adult ticket is $ 13and child ticket is $12.Hope this will help u.....

Step-by-step explanation:

Answer:

Answer 1008

Step-by-step explanation:

Answer:

Final mixture is 120 gm

x = 10%      then   (120-x) = 25%

.25(120-x)    + .1 (x)    =  .15 (120)       solve for x= 10% amount

                                                                 then  25% amount = 120-x

Step-by-step explanation:

Answer:

0.5 quarts of orange juice per quart of punch

Step-by-step explanation:

1.5/3=0.5

Answer:

0.5

Step-by-step explanation:

Since 1.5 quarts are required for 3 quarts you need to divide 1.5 and 3.

1.5 ÷ 3 = 0.5

Answer:

100 or 80

Step-by-step explanation:

I HAD A SIMILAR QUESTION.

I'M SORRY IF ITS WRONG.

Using the distance formula, the length of segment PQ is:

C. √68 units

The distance formula is given as:

d = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).

Segment PQ has the following endpoints:

P(-2, 3)

Q(6, 1)

To find the length of segment PQ using the distance formula, we can apply the formula, where:

\((x_1, y_1)\)are the coordinates of point P

\((x_2, y_2)\) are the coordinates of point Q.

Given:

P(-2, 3) = \((x_1, y_1)\)

Q(6, 1) = \((x_2, y_2)\)

Let's substitute the values into the formula:

PQ = √[(6 - (-2))² + (1 - 3)²]

PQ = √[(8)² + (-2)²)

PQ = √(64 + 4)

length of segment PQ = √68 units

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Answer:

The order of operations says that operations must be done in the following order: parentheses, exponents, multiplication, division, addition, and subtraction. You can also create a little phrase to go along with this, like "Please Excuse My Dear Aunt Sally." Whatever you choose, make sure that you know all six steps of the order of operations very well. The order of operations tells us the order to solve steps in expressions with more than one operation. First, we solve any operations inside of parentheses or brackets. Second, we solve any exponents. Third, we solve all multiplication and division from left to right.

Step-by-step explanation:

hope this helps :)

A graph of the two (2) points (-0.5, 0) and (9, 0) that represent the distance which this object would travel in different amounts of time at that rate is shown in the image attached below.

Mathematically, a linear function is sometimes referred to as the slope-intercept form of a straight line and it can be modeled (represented) by this mathematical expression;

d = mt + b

Where:

Therefore, the required linear function that relates the distance (d) and speed (s) at time (t) seconds is given by this mathematical expression;

d(t) = 18t + 9

For instance when time (t) = -0.5 seconds, the distance traveled by this object placed on a conveyor belt is given by;

d(t) = 18t + 9

d(-0.5) = 18(-0.5) + 9

d(-0.5) = -9 + 9

d(-0.5) = 0 feet.

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Answer:

the probability is 2/12

you might have to explain what replacement means

Answer:

100

Step-by-step explanation:

40 / 100= .4

.4 x 45 = 18

18/18= 1

1x 100= 100

Answer:

100

Step-by-step explanation:

:D

Answer:

f[((5)] = g(5) = root of 5+7= root of 12

then f[( g(5)] = (root of 12 _ 3 )^2 = 12-9 =3

Answer:

g(1) = 1

Step-by-step explanation:

the absolute value function always gives a positive result, that is

| - a | = | a | = a

to evaluate g(1) substitute x = 1 into g(x)

g(1) = - 3| 1 - 2| + 4

    = - 3| - 1| + 4

   = - 3(1) + 4

  = - 3 + 4

  = 1

Answer:

3x + 60

Step-by-step explanation:

9(x + 7) ÷ 3(x - 1) =

9x + 63 ÷ 3x - 3 =

9x ÷ 3x + 63 - 3 =

3x + 60

Note: For the third equation which is 9x ÷ 3x and etc, you have to put alphabets and numbers at one side seperately to be able to simplify easily.

The probability that the cupcake picked at random contains walnuts is given as follows:

0.4 = 40%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

There are 30 cupcakes in a tin, hence the total number of outcomes is given as follows:

30.

The number of cupcakes with walnuts is given as follows:

Hence the probability that the cupcake picked at random contains walnuts is obtained as follows:

p = (3 + 9)/30

p = 12/30

p = 0.4.

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Answer:

Rule: dilation about the origin by a scale factor of 2

Step-by-step explanation:

Given

See attachment for QRST and Q'R'S'T

Required

The dilation rule

First, we calculate the scale factor (k)

From the attachment, we have:

\(QR = 4\)

\(Q'R' = 8\)

k, is then calculated as:

\(k = \frac{Q'R'}{QR}\)

\(k = \frac{8}{4}\)

\(k =2\)

Hence, QRST is dilated by a factor of 2

Answer:

Second one

Step-by-step explanation:

By is postive and C is positive so there wouldn't be any negatives or minus signs

Answer:

The Second One!

Step-by-step explanation:

Answer:

TRUE

Step-by-step explanation:

using the given data for the one way commuting of workers we can conclude that the spread is = 0.458493468

hence the correct option is TRUE

One way commuting is traveling of passengers using a single lane in both directions

Answer:

m∡x = 95°

m∡y = 147°

m∡z = 128°

Step-by-step explanation:

m∡z = 180-52 = 128

measure of third angle in left triangle = 180-(45+50) = 85°

m∡x = 180-85 = 95°

measure of top angle in right triangle = 180-(95+52) = 33°

m∡y = 180-33 = 147°