Ben drank 2/5 of a pitcher of lemonade Tonya drank 1/4of the lemonade. What fraction of the lemonade did they drink together?

To find the amount Mrs. Palmer originally had to spend on each daughter, we set up the equation as (x - 18) / 3 = y, where x is the total money she initially had and y indicates the amount spent on each daughter.

Let's denote the total amount Mrs. Palmer originally had as x.

We know she spent this on buying swimming items for her three daughters and had $18 left afterwards.

This infers that the total money she spent is (x - 18) dollars.

Since each daughter received a pair of goggles, a bathing suit, and a beach towel, this means she used this money to buy three sets of swimming items.

Therefore, the amount of money she spent on each daughter is equal to (x - 18)/3.

The equation to find out what x (the amount Mrs. Palmer originally had) is therefore:

(x - 18) / 3 = y

where y represents the amount she spends on each daughter.

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30

dividing the length and width by 2

10 ÷ 2 = 5 and 12 ÷ 2 = 6

he can plant 5 × 6 = 30 pumpkin plants

Divide 50 by 22: 2.27272727...

Round up to hundredth and your final answer is 2.27

hope that helps :)

Answers: The statement that express the same scale are Options B and C.

Solution:

A. 5 cm on the map represents 50 m in Chicago?

Rule of three:

1 cm represents 100 m

5 cm represents    x

x=(5 cm).(100 m) / (1 cm)

x=500 m

5 cm on the map represents 500 m in Chicago.

The statement A doesn't express the same scale.

B. 1 mm on the map represents 10 m in Chicago?

1 mm = 0.1 cm

Rule of three:

1 cm    represents 100 m

0.1 cm represents    x

x=(0.1 cm).(100 m) / (1 cm)

x=10 m

1 mm = 0.1 cm on the map represents 10 m in Chicago.

The statement B expresses the same scale.

C. 1 km in Chicago is represented by 10 cm on the map?

1 km = 1,000 m

Rule of three:

1 cm    represents 100 m

x         represents  1,000 m

x=(1 cm).(1,000 m) / (100 m)

x=10 cm

1 km = 1,000 m in Chicago is represented by 10 cm on the map.

The statement C expresses the same scale.

D. 100 cm in Chicago is represented by 1 m on the map?

100 cm = 1 m

Rule of three:

1 cm    represents 100 m

x         represents  1 m

x=(1 cm).(1 m) / (100 m)

x=0.01 cm

100 cm = 1 m in Chicago is represented by 0.01 cm on the map.

The statement D doesn't express the same scale.

Answer:

a,b,c d is incorrect but a,b,c is right

Step-by-step explanation:

just took the test

There are 5 days to a school week: Monday, Tuesday, Wednesday, Thursday and Friday.

Divide number of school days by 5 to find the number of weeks:

171 / 5 = 34.2 weeks.

The weeks start with Monday, so there would be 35 Mondays. ( 34 full weeks and the partial week would begin with a Monday)

Divide 171 by 7 (as there are 7 days in each week), obtaining 24.4.  There's one Monday in every 7 days, so in 168 days there'd be exactly 24 Mondays, and in 171 days there'd still be exactly 24 Mondays, with 3 days left over.

To find the answer,we need to first find the legth of the not given side of triangle by using Pythagoras theorem:

[tex] = \sqrt{{15 }^{2} -{ 9 }^{2} } \\ = \sqrt{144 }\\ = 12[/tex]

Therefore the side length is 12in.

Therefore the answer 12 in.

The total height of the stair is equivalent to 36 inches.

Pythagoras theorem states that the square of the hypotenuse is equivalent to the square of the base and perpendicular.

We can write the formula for Pythagoras theorem as -

(hypotenuse)² = (base)² + (perpendicular)²

We can write the height of the stairs as -

h = 3 x √(15² - 9²)

h = 3 x √(225 - 81)

h = 3 x √144

h = 3 x 12

h = 36 inches

Therefore, the total height of the stair is equivalent to 36 inches.

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Assuming the adults that have children and the ones that don't together make up the entire population of adults, then the number that have children will be ...

... 4200 - (3/8)×4200

... = 4200×(1 -3/8) = 4200×5/8 = 2625

2625 adults in Lakeview have children

We know:

The product of two negative numbers is positive.

Therefore

(-12)(12)(-6.3)(-0.2)(-15.9) = (-12)(-6.3) (-0.2)(-15.9)(12) > 0  ANSWER

(12)(-6.3)(-0.2)(-15.9) < 0

(-12)(12)(-6.3)(-0.2)(-15.9)(0) = 0

(12)(12)(6.3)(0.2)(-15.9) < 0

ONE solution was found, 1.5

Every 3 feet is $18. 18 divided by 3 equals 6.

24 divided by 6 equals 4. (So the second one is correct)

30 divided by 6 is 5, so the answer is not 30. it'd be 36.

48 divided by 6 is 8, so it is not 7.

72 divided by 6 is 12. But 6 multiplied by 9 equals 52. So, your answer is 52.

Hoped this helped,

-Anime

Answer: C

Step-by-step explanation:

Answer:

OPtion C is correct answer.

Step-by-step explanation:

Given that there is a system of equations as

y =-4x+3 and y =3x+1

Table is prepared with side by side values of y for a given x

From the table we are to find the solution of the system

On analysing the table we find that the difference between two y's is

0.5, -0.2, -0.9, -1.6, -2.3,-3

Hence we select the one which shows minimum difference i.e. -0.2

For this, x = 0.6

When x =0.6, y shows two values as 0.6 and 0.8

So we approximate y value as average of these two i.e. 0.7

So solution is

(0.6, 0.7)

the sum of the angles in a triangle = 180°, thus

x + [tex]\frac{1}{2}[/tex] x + [tex]\frac{1}{6}[/tex] x = 180

multiply through by 6

6x + 3x + x = 1080

10x = 1080 ( divide both sides by 10 )

x = 108

the angles are 108°, 54° and 18°

Since all the angles are different and the largest is 108°

The triangle is an obtuse scalene triangle

The measures of the angles of the triangle are approximately 108 degrees, 54 degrees, and 18 degrees. This type of triangle is a scalene triangle, as all of its angles are different.

To find the measures of the angles of a triangle whose angles are x, 1/2x, and 1/6x, we will use the fact that the sum of the angles in a triangle is always 180 degrees. The equation representing this is:

x + 1/2x + 1/6x = 180

Combine like terms:

1.6667x = 180

Then solve for x:

x ≈ 108 degrees

Now plug x into the original angle measures to get:

Angle 1 = 108 degrees

Angle 2 = 1/2x = 54 degrees

Angle 3 = 1/6x = 18 degrees

Lastly, in terms of the type of triangle, this is a scalene triangle because all of its angles are different.

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daniel will be 32 and his son will be 8

To find the number of boys, you can set up an equation using the given information. Solve the equation to find the number of boys.

To solve this problem, let's define a variable for the number of boys. Let x represent the number of boys.

According to the problem, we know that the amount of boys is 3 times the number of boys, minus 2. So the expression for the number of boys is 3x - 2.

We also know that the total number of people is 26. Therefore, we can set up an equation: 3x - 2 + x = 26.

By combining like terms and solving the equation, we can find the number of boys. The solution is x = 7. Therefore, there are 7 boys.

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If the angle is 90 degrees, then the complement would be 27, because 90 / 3 = 30, and 30 - 3 = 27. Basically, you divide the angle by 3 and subtract 3 to find the complement if this is the case.

Answer:

22⁰

Step-by-step explanation:

Angle = x

Complement = 90 - x

Given:

x = 3 (90 - x) + 2

x = 270 - 3x + 2

4x = 272

x = 68

Complement = 90 - 68 = 22⁰

Angles B and C are alternate interior angles where transversal BC cuts parallel lines AB and CD. Thus angles B and C are equal. Angle B is 65°.

Angle AEC is the exterior angle opposite interior angles A and B, which means its value is the sum of angles A and B.

∠AEC = ∠A +∠B = 47° +65°

∠AEC = 112°

8000 because u add an extra 0 if u multiple with a number with a zero or no

Answer:

Total gallons of fresh water in the tank [tex]3.1926*10^3[/tex] gallons.

Step-by-step explanation:

Percentage of fresh water = [tex]100%-6.1%[/tex]

                                            =93.9%

Total number of gallons of water in tank = [tex]3.4*10^3[/tex]   (given in the question)

Therefore,

Total gallons of fresh water in the tank   =  [tex]3.4*10^3*93.9/100[/tex]

                                                                  =[tex]3.1926*10^3[/tex] gallons.

c. (0, 3), (4, -1)

for (0,3): 3 = -0 + 3  good

for (4,-1): -1 = -4 + 3  good

(c)

Substitute the x-coordinate from each point into the equation and if equal to the corresponding y- coordinate then the point lies on the line

(a)

x = - 1 : y = 1 + 3 = 4 ≠ - 2

x = 1 : y = - 1 + 3 = 2 ≠ 4

(b)

x = 1 : y = 2 = 2

x = 0 : y = 0 + 3 = 3 ≠ - 3

(c)

x = 0 : y = 3 = 3 ← correct

x = 4 : y = - 4 + 3 = - 1 = - 1 ← correct

the pair of points is (c)

Area is the product of length and width. If you assume the dimensions are integers, you are looking for factors of 117 that differ by 4.

117 = 1×117 = 3×39 = 9×13

These last two factors differ by 4, so we know the dimensions of the barn are ...

... 9 ft wide by 13 ft long

The price of the small pots is $2.40 so you would have 2.4s ( multiply the number of small pots by the price)

She bought a total of 14 pots, so the number of large pots would be 14 - s ( subtract the number of small pots from the total )

Now you have:

L = 14-s

2.4s + 5.6(14-s) = 49.6

The answer is C.

9514 1404 393

Answer:

  25% increase

Step-by-step explanation:

A percentage change is calculated using the formula ...

  percent change = ((new value) - (old value))/(old value) × 100%

  = (500 -400)/400 × 100%

  = 100/400 × 100%

  = 25%

A positive percentage change indicates an increase.

The change from 400 to 500 is a 25% increase.

Answer:

The last quiz score must be at least an 80 to get the average to be a 70.

Step-by-step explanation:

In order to find this, you need to take the average of the 4 test scores along with the unknown test score (x). So, to find an average, we add all the numbers together and divide by the amount of tests taken. We can then set this equal to 70 since that is the minimum average.

(60 + 64 + 75 + 71 + x)/5 = 70 ------> Multiply both sides by 5

(60 + 64 + 75 + 71 + x) = 350 -----> Combine like terms

270 + x = 350 -----> Subtract 270 from both sides

x = 80

Givens

m<T = 120

m<C = 30

PC = 4

Find PC

Solution

4/sin(30) = PC / sin(120)         Note: this is the sine law.

Multiply both sides by sin(120)

[tex]\dfrac{4*sin(120)}{sin(30)} = \text{PC}[/tex]

4*0.866/0.5 = PC

Answer

PC= 6.928

ANSWER 1

Note that,

[tex]f(u)=tan^{-1}(u)[/tex]

is the same as

[tex]f(u)=arctan(u)[/tex]

We apply the product rule.

[tex]f(x)=x^2tan^{-1}(x)[/tex]

So we keep the second function and differentiate the first,plus we keep the first function and differentiate the second.

[tex]f'(x)=(x^2)'tan^{-1}(x)+x^2(tan^{-1}(x))' [/tex]

Recall that,

If

[tex]f(u)=tan^{-1}(u)[/tex]

Then,

[tex]f'(u)=\frac{1}{1+u^2}} \times u'[/tex]

This implies that,

[tex]f'(x)=2xtan^{-1}(x)+\frac{x^2}{x^2+1} [/tex]

ANSWER 2

We apply the product rule and the chain rules of differentiation here.

[tex]f(x)=xsin^{-1}(1-x^2)[/tex]

[tex]f'(x)=x'sin^{-1}(1-x^2)+x(sin^{-1}(1-x^2))' [/tex]

Recall that,

If

[tex]f(u)=sin^{-1}(u)[/tex]

Then,

[tex]f'(u)=\frac{1}{\sqrt{1-u^2}} \times u'[/tex]

This implies that,

[tex]f'(x)=sin^{-1}(1-x^2)+x \times \frac{1}{\sqrt{1-(1-x^2)^2}}\times (-2x) [/tex]

[tex]f'(x)=sin^{-1}(1-x^2)-\frac{2x^2}{\sqrt{1-(1-2x^2+x^4)}} [/tex]

[tex]f'(x)=sin^{-1}(1-x^2)-\frac{2x^2}{\sqrt{1-1+2x^2-x^4}}[/tex]

[tex]f'(x)=sin^{-1}(1-x^2)-\frac{2x^2}{\sqrt{2x^2-x^4}}[/tex]

If you want to simplify this, you can add the coefficients of like terms.

... = x²(2+2) +x(4+4) +(-3-3)

... = 4x² +8x -6

_____

Since both of the parts of the sum are the same, this expression can be rewritten using the distributive property:

... = 2(2x² +4x =3)

_____

The sum can also be rewritten to vertex form.

... = 4(x² +2x) -6

... = 4(x² +2x +1) -6 -4(1)

... = 4(x +1)² -10

This is an expression describing a parabola with vertex (-1, -10) and a vertical scale factor of 4. It has roots (x-intercepts) at -1±√2.5.

(1) QS bisecting <PQR implies <PQS = <SQR

(2) <PQS=45 deg and (1) imply <SQR also = 45 deg

(3) from (2) it follows that <PQR = <PQS + <SQR = 45 + 45 deg = 90 deg and therefore the triangle is right-angled

N = 10.79

isolate N by adding 6.47 to both sides of the equation

N = 4.32 + 6.47 = 10.79

The unknown number N in the equation N - 6.47 = 4.32 is found to be 10.79 when we add 6.47 to both sides of the equation.

To solve for the unknown number N in the equation N - 6.47 = 4.32, we must isolate the variable N on one side of the equation. We do this by adding 6.47 to both sides of the equation:

N - 6.47 + 6.47 = 4.32 + 6.47

This simplifies to:

N = 10.79

The unknown number N is therefore 10.79. When providing the final answer, we must make sure that it is reported with the correct number of significant figures, which in this case are three significant figures.

Let's form the difference of the two expressions and see what we can learn.

(2y -x) -(2x -y) = 2y -x -2x +y = 3y -3x = 3(y -x)

Since y > x, this is positive, so 2y -x is greater than 2x -y.

IQR = 6

First locate the median [tex]Q_{2}[/tex] at the centre of the data arranged in ascending order. Then locate the lower and upper quartiles [tex]Q_{1}[/tex] and [tex]Q_{3}[/tex] located at the centre of the data to the left and right of the median.

Note that if any of the above are not whole values then they are the average of the values either side of the centre.

rearrange data in ascending order

15 16 ↓17 17 18 21 22 ↓23 25

                     ↑

[tex]Q_{2}[/tex] = 18

[tex]Q_{1}[/tex] = [tex]\frac{16+17}{2}[/tex] = 16.5

[tex]Q_{3}[/tex] = [tex]\frac{22+23}{2}[/tex] = 22.5

IQR = [tex]Q_{3}[/tex] - [tex]Q_{1}[/tex] = 22.5 - 16.5 = 6

Final answer:

The interquartile range (IQR) for the given data set is calculated by first arranging the data in ascending order, finding the first and third quartiles (Q1 and Q3), and subtracting Q1 from Q3. The correct IQR for this data set, following this methodology, is 6, not the mistakenly provided 7.

Explanation:

The question asks about calculating the interquartile range (IQR) of a given data set. The IQR is important because it measures the middle 50% spread of data, pinpointing where the bulk of values lie, and helps in identifying potential outliers. To compute the IQR, we first need to organize the data in ascending order, then find the first quartile (Q1) and the third quartile (Q3), and finally subtract Q1 from Q3 (IQR = Q3 - Q1).

For the provided data set: 17, 16, 21, 15, 25, 22, 18, 23, 17:

Arrange data in ascending order: 15, 16, 17, 17, 18, 21, 22, 23, 25.

Find the median (Q2), which is 18 in this case as it's the middle value.

Q1 is the median of the first half (excluding the middle value if odd number of data), so Q1 = 16.5.

Q3 is the median of the second half, hence Q3 = 22.5.

Therefore, IQR = Q3 - Q1 = 22.5 - 16.5 = 6.

Contrary to the mistaken calculation of IQR as 9 - 2 = 7 provided in the reference, the computed IQR for this data set, following the correct methodology, is 6.