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Answer:

w = (4/35)

Step-by-step explanation:

-1/5 = -1/2w - 1/7

+1/7              +1/7

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

-2/35 = -1/2w

÷-1/2      ÷-1/2

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

4/35 = w

Extra:

-1(7)      1(5)

------- + -------

5(7)      7(5)

  -7        5          -2

------- + ------- = -------

 35        35        35

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

 -2         -1

------- ÷ -------

 35         2

 -2        -2          4

------- × ------- = -------

 35         1          35

I hope this helps!

we gotta know the conversion between cups and gallons

We know

1 cup (US) = 0.0625 gallons

So, 2 gallon would be 2/0.0625 = 32 cups

So, the problem in cups is:

32 cups = $23.36

17 cups = $20.06

Definitely 32 cups for 23.36 is better buy

2 gallons for $23.36 is the better buy

Note:

23.36/32 = $0.73 per cup

20.06/17 = $1.18 per cup

Answer:

-0.7 < -0.4

0.5 > -0.6

-0.8 < -0.7

0.6 > 0.4

Explanation:

The symbol < means less than and the symbol > means greater than.

On the other hand, if we identify each number on a number line, we get:

Therefore, the true statements are:

-0.7 < -0.4

0.5 > -0.6

-0.8 < -0.7

0.6 > 0.4

Because, for example, -0.7 is on the left of -0.4 which means that -0.7 is less than -0.4.

0.5 in on the right of -0.6 which means that 0.5 is greater than -0.6.

Answer:

Step-by-step explanation:

Let the amount invested at 9% be x.

Then the amount invested at 7% is 10000 - x.

The amount of interest after one year is $780.

Set up equation to represent this:

Amount invested at 7% is:

Answer:

Milan invested:

Step-by-step explanation:

Given information:

Let x be the amount invested in Account A.

Therefore, the amount invested in Account B is (10000 - x).

Simple Interest Formula

I = Prt

where:

Create two equations using the given information:

[tex]\begin{aligned}\textsf{Interest: Account A} &= x \cdot 0.09 \cdot 1\\& = 0.09x\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Interest: Account B} &= (10000 - x) \cdot 0.07 \cdot 1 \\& = 0.07(10000 - x)\\& = 700-0.07x\end{aligned}[/tex]

As the total interest earned was $780, set the sum of the two found equations to 780 and solve for x:

[tex]\begin{aligned}\implies 0.09x+700-0.07x&=780\\0.02x+700&=780\\0.02x&=80\\x&=4000\end{aligned}[/tex]

Therefore, Milan invested:

We have that:

Paul biked 7 miles on Saturday.

Paul bike 15 miles on Sunday.

The total distance, in miles, the Paul biked during Saturday and Sunday is:

The average price in 1992 and 2013 was given. It is required to find the percentage increase in the average price over these years.

Recall that the formula for Percentage Increase is:

Substitute initial price=12500 and final price= 22000 into the formula:

Hence, the percent increase in the average price is 76%.

Answer:

depends on whether or not the dealerships are scammers

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

Hakeem is the oldest of three siblings who ages are consecutive integers. If the sum of their ages are 69, find Hakeem age.

It should be noted that:

= 22 + 23 + 24

= 69

Hakeem's age is 24

Answer:

m/1 = 87

m/2 = 93

Step-by-step explanation:

m1 and m2 need to have an angle of 180

so 180-87 = 93

The factors of the given quadratic equations are [tex]\frac{-13+\sqrt{409} }{8}[/tex] and [tex]\frac{-13-\sqrt{409} }{8}[/tex]

What is factorization?

When we try to write the given equation in terms of linear values from which we calculate the roots of the given equation then we say that we have factorized them. Root of a equation means a value which satisfies a equation.

We are given a quadratic equation

[tex]4x^2+13x-15[/tex]

We use quadratic formula to compute the factor of the equation

[tex]x=\frac{-b}{2a}[/tex]±[tex]\frac{\sqrt{b^2-4ac} }{2a}[/tex]

[tex]x=\frac{-13}{8}[/tex]±[tex]\frac{\sqrt{169+240} }{8}[/tex]

[tex]x=\frac{-13}{8}[/tex]±[tex]\frac{\sqrt{409} }{8}[/tex]

Therefore the factors are [tex]\frac{-13+\sqrt{409} }{8}[/tex] and [tex]\frac{-13-\sqrt{409} }{8}[/tex]

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Answer: 0.125

Step-by-step explanation:

1 1/4 is equal to 5/4

5/4 is equal to 1.25

then you would do 1.25 divided by 10

once you do that you would get your answer of 0.125!

Answer:

11/4÷10 =

11/4 ×1/10=

11/40=

0.275

Step-by-step explanation:

you can ask questions for clarification

_______________

I'm reading your question

___________________

According to the Pythagorean theorem

Hypotenuse ^2 = Side 1 ^2 + Side 2 ^2

The hypotenuse is the case (Square 1 )

area of the sqaure= side of the square^2

________________________

That means the area of 1 is = area of square 2 + area fo square3 (J is false)

_______________________________

We are not sure about the relation between square 2 and 3 just the addition is the square 1 (F and H we have no certainty)

______________________________

G is true

______________________________

Answer

G

Answer:

??

Step-by-step explanation:

The distance between Ashely’s house and the public library is of 7.8 miles.

Suppose that we have two points with coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The shortest distance between these two points is given by the following rule:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

This formula is derived from the Pythagorean Theorem, as the points form a right triangle in the Cartesian plane, with the hypotenuse representing the distance between them.

In the context of this problem, the coordinates of her house and of the library are given as follows:

Hence the distance is calculated as follows:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]D = \sqrt{(10 - 4)^2+(7 - 2)^2}[/tex]

D = sqrt(61)

D = 7.8 miles, as each unit on the plane represents one mile.

The problem states that each unit on the plane represents one mile and the image gives their position on the plane.

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The equation relating to A to B is A = 45 + b and the amount is $66.

An equation is used to show the relationship between the variables that are illustrated.

In this case, Kala earns 45 dollars each week working part-time at a bookstore and she earns one additional dollar for each book that she sells.

Let the books be represented as b. The equation will be:.

A = 45 + 1b

A = 45 + b

where A = amount earned.

The amount earned when 21 books are sold will be:

A = 45 + b

A = 45 + 21

A = 66

The amount is $66.

This illustrates the concept of equations.

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Based on the yards of fabric used by Jan for the quilt squares, the total fabrics used by Jan was 1 ¹ / ₅₆ yards

The yards of fabric used by Jan were 7 / 8 of a yard and 1 / 7 of another yard.

The total yards used by Jan can be found by adding these fractions up. To add both fractions, you first need to find the common denominator of 8 and 7 which is 56.

Then the numerators can be found by dividing 56 by the denominator and then multiplying the numerator by the result.

Fraction 7 / 8 yards:

= 56 / 8 x 7

= 49 / 56

Fraction 1 / 7:

= 56 / 7 x 1

= 8 / 56

The total number of yards used is:
= 49 / 56 + 8 / 56

= 57 / 56

= 1 ¹ / ₅₆ yards

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The solution of 0.125x +1 -0.25x < -3 is x > 32

Difference between equality and inequality equations

Both mathematical phrases, equations and inequalities, are created   by connecting two expressions.The equal sign (=) indicates that two expressions in an equation are believed to be equivalent. The symbols show that the two expressions in an inequality are not always equal: >, <, ≤ or ≥. Or in simple words the equation which has '=' sign is an equality equation while the inequality equation has the signs are >, <, ≤ or ≥.

The given expression is,

0.125x +1 - 0.25x < -3

subract the x value,

0.125x  - 0.25x + 1 < -3

-0.125x + 1 < -3

-0.125x < -3 - 1

-0.125x < -4

Now, if on both the sides the signs are -ve then change the inequality sign, like this

x > 4 / 0.125

x > 32

Hence, The solution of 0.125x +1 -0.25x < -3 is x > 32

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The image of the point (-4, -1) after the translation is:

(-3, 1)

A translation:

Tᵃ'ᵇ applied to a point (x, y) gives:

Tᵃ'ᵇ(x, y) = (x + a, y + b).

In this case, we know that:

Tᵃᵇ(1, 1) = (1 + a, 1 + b) = (0, 3)

Then:

1 + a = 0

1 + b = 3

Solving these we get:

a = 1

b = 3 - 1 = 2

The translation is:

T¹'²

Applying this to the point (-4, -1) gives:

T¹'²(-4, -1) = (-4 + 1, -1 + 2) = (-3, 1)

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Answer:

B) x > 8

Step-by-step explanation:

1-Step: Combine like terms by subtracting 9 on both sides : 17-9 < X

8 < X

2- Step: flip the signs (Since 8 is less than X, Then X is greater than X)

X > 8

The statements The range of the distribution is around 60 cm and

the center of the distribution is around 180 cm are true.

Statistics is the study and manipulation of data, including ways to gather, review, analyze, and draw conclusions from data.

In the given statements

There are no outliers in this distribution.

The shape of the boxplot is fairly symmetric.

The range of the distribution is around 60 cm.

The center of the distribution is around 180 cm.

The statement "The range of the distribution is around 60 cm" is true.

The range is the spread of your data from the lowest to the highest value in the distribution.

In the given graph

Range=200-140

=60

So it is true.

The center of the distribution is around 180 cm is also true.

Hence the statements The range of the distribution is around 60 cm and

the center of the distribution is around 180 cm are true.

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Using the concept of Application of Derivatives(A.O.D),we got 4.79 inches will be the square size for making the volume of candy box maximum.

A candy box is made from a piece of a cardboard that measures 43 × 23 inches.

Let squares of equal size will be cut out of each corner with the measure of x inches.  

Therefore, measures of each side of the candy box will become

Length = (43 - 2x)

Width   = (23 - 2x)

Height  = x

Now we have to calculate the value of x for which volume of the box should be maximum.

Volume (V) = Length×Width×Height

 =>V = (43 -2x)×(23 - 2x)×(x)

 =>V= [(43)×(23) - 46x - 86x + 4x²]×x

 =>V= [989 - 132x + 4x²]×x

 =>V= 4x³- 132x² + 989x

Now we find the derivative of V and equate it to 0

[tex]\frac{dV}{dx}[/tex]= [tex]12x^{2} -264x+989[/tex]=0

Now we get values of x by quadratic formula

x=(264±[tex]\sqrt{264^{2}-4.12.989 }[/tex] )/24

=>x=(264±[tex]\sqrt{69696-47472}[/tex])/24

=>x=(264+√22224)/24, and x=(264-√22224)/24

=>x=(264+149.07)/24 and x=(264-149.07)/24

=>x=17.212                  and x=4.79

Now we test it by second derivative test for the maximum volume.

[tex]\frac{d^{n}V }{dx}[/tex]=24x-264

For x = 17.212

[tex]\frac{d^{n}V }{dx}[/tex]=(24×17.212)-264=413.088-264=149.088

This value is > 0 so volume will be minimum.

For x = 4.79

[tex]\frac{d^{n}V }{dx}[/tex]=(24×4.79)-264= -149.04

-149.04 < 0, so volume of the box will be maximum.

Therefore, for x = 4.79 inches volume of the box will be maximum.

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(Complete Question) is

A candy box is made from a piece of cardboard that measures 43 by 23 inches. Squares of equal size will be cut out from  each corner. The sides will then be folded up so that to form a rectangular box. What size square should be cut from each corner so that to obtain maximum​ volume?

-24-68i is solution of complex number.

What is the best definition of a complex number?

(4-6i)(6-8i)

= 24-32i-36i+48i²

= 24 + -68i - 48

= -24-68i

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The complete question is -

Multiply the following complex numbers (4-6i)(6-8i)

The fraction of oranges eaten by the family is 3/5

Given,

Number of oranges in a bag = 8 oranges

Number of bags sold to a family = 10 bags

Number of members in the family = 6 members

Number oranges ate by each member of the family = 6 oranges

We have to find the fraction of the oranges eaten by the family members;

Here,

8 oranges in 1 bag and 10 bags sold.

So, total number of oranges sold = 8 x 10 = 80 oranges

Each member ate 6 oranges and there are 8 members.

So, total number of oranges eaten by them = 6 x 8 = 48 oranges

Now,

The fraction of oranges eaten by the family = 48/80 = 6/10 = 3/5

That is,

3/5th of oranges were eaten by the family.

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Applying power rules, the equations that is true when x = 10 but false when x = -10 is given as follows:

x³ = 10000.

The behavior of the exponents of 10 is different for even and for odd exponents, as follows:

In this problem, we have two exponents, as follows:

We want different results for the power when x = 10 and when x = -10, hence the correct option will involve the odd exponent 3.

The third power of 10 is calculated as follows:

10³ = 10 x 10 x 10 = 100 x 10 = 1000.

Hence the equation that is true for x = 10 and false for x = -10 is:

x³ = 10000.

As when x = -10, the result is:

(-10)³ = (-10) x (-10) x (-10) = 100 x (-10) = -1000.

The options are given by the image at the end of the answer.

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Answer:

1/5

Step-by-step explanation:

I multiplied 2 * 7, which is 14. Then, I multiplied 7 * 10 which equals 70. Then, I divided 14/70 by 14. The answer is 1/5.

Answer:

y - 283 = 48

Step-by-step explanation:

y decreased by 283 means that 283 is subtracted from y. All set equal to 48.

The measure of the value of ∠j is 10°.

What are a few properties of a triangle considering its angles?
A triangle's outer angle is the sum of its internal angles' two opposite sides.
The sum of two linear angles is supplementary.

Given, the three angles of the triangle are measured as (5x - 3)°,
(4x - 2)° and j°.
Also, the exterior angle of the triangle is (10x - 20)°.
Following the literature established above, considering that a triangle's outer angle is the product of its internal angles' two opposite sides, we have: (5x - 3) + (4x - 2) = 10x - 20 ⇒ 9x - 5 = 10x - 20 ⇒ 10x - 9x = 20 - 5
⇒ x = 15 --(i)
Again, since the sum of two linear angles is supplementary, we have using (i):
j + (10x - 20) = 180 ⇒ j + 150 - 20 = 180 ⇒ j = 10°
Therefore, the measure of the value of ∠j is 10°.

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Answer: $0.2

Step-by-step explanation:

To find the answer you divide 6.52 by 40 which will get 0.163. To check the answer and make sure its correct you can multiply 0.163 by 40 to get 6.52 making the answer correct so 0.2 is the answer to the nearest cent. Hope this helps :)

Here is the answer again

Answer:

Concept:

Mean is just another name for average. To find the mean of a data set, add all the values together and divide by the number of values in the set. The result is your mean!

The values are given below as

The image below shows how to calculate the mean

By substituting values, we will have

Hence,

The mean = 10

To calculate the variance, we will use the formula below

Hence

The variance = 21

To calculate the standard deviation,

Hence,

The standard deviation is = 4.58

From the question, we are asked to find which is great between 12.5 or |-13|

recall:

|-13|

The absolute value is the distance between a number and zero. The distance between -13 and 0 is 13.

The absolute symbol makes any number positive.

So, |-13| is the greater because |-13| = 13.

So, between 12.5 and |-13|, |-13| is greater since it is same as 13.