Marianna went running and had 1/6 of a bottle of water left when she stopped to rest. She went to a water fountain and filled it until it was 2/3 full.

How much water (as a fraction of a bottle) did Marianna put in her bottle at the water fountain?

answer:

7

explanation:

7+14=21

21/3=7

Answer:

Step-by-step explanation:

3x = 7 + 14

3x = 21 (7 + 14 = 21)

x = 7 (divide 3 from both sides) (3x / 3 = x and 21 / 3 = 7)

Answer:

a ) mean = 1.8

b ) new mean = 11.8

c ) new mean = 23.6

hope this helps

Answer:

P(17.4 < X < 22.6) = P((X-20)/2.6 < (22.6-20)/2.6) = P(Z < 1.38)

From a standard normal table, we find that P(Z < 1.38) = 0.9128

Step-by-step explanation:

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Answer:

x=8

Step-by-step explanation:

multiply both sides of the equation by 8

combine like terms

divide both sides of the equation by -5

The ΔXYZ is an Right Angled triangle.

Pythagoras Theorem states that the sum square of two sides of triangle is equal to the  square of longest side.

Distance Formula is used to calculate distance between two points A(a,b) and B(c,d)

denoted by [tex]d=\sqrt{(c-a)^{2} +(d-b)^{2} }[/tex]

In the given question , first calculate the length of each side of the triangle.

given X(3,1),Y(3,7),Z(11,1)

using distance formula

XY=[tex]\sqrt{(3-3)^{2} +(7-1)^{2} } =\sqrt{36} =6[/tex]

YZ=[tex]\sqrt{(11-3)^{2} +(1-7)^{2} } =\sqrt{8^{2}+(-6)^{2} } =\sqrt{64+36}= \sqrt{100} =10[/tex]

XZ=[tex]\sqrt{(11-3)^{2}+(1-1)^{2} } =\sqrt{8^{2} } =\sqrt{64} =8[/tex]

The longest side is 10 and other two sides are 8,6.

by using Pythagoras Theorem

[tex]hypotnuse^{2} =base^{2} +perpendicular^{2}[/tex]

[tex]YZ^{2} =XY^{2} +XZ^{2} \\ \\ 10^{2} =8^{2} +6^{2} \\ \\ 100=64+36\\ \\ 100=100[/tex]

Since Pythagoras Theorem is satisfied It is a right  angled triangle.

Therefore ,  The ΔXYZ is an Right Angled triangle.

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The length of the fence around the triangular land is equal to 180 meters.

The perimeter of a figure is the sum of the side lengths of the figure. Triangles have three sides and we need to determine the perimeter of the triangular land. If we know that l₁ = 55 meters, l₂ = 60 meters and l₃ = 65 meters, then the perimeter of the figure is:

p = l₁ + l₂ + l₃

p = 55 m + 60 m + 65 m

p = 180 m

The length of the fence around the triangular land is equal to 180 meters.

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Answer:

5x - 6y + 126 = 0

Step-by-step explanation:

y-y1=m(x-x1)

y - 6 = 5/6 (x - (-18))

6y - 36 = 5x + 90

5x - 6y + 126 = 0

Answer:

[tex]p= \dfrac{1}{2}[/tex]

Step-by-step explanation:

Given equation:

[tex]p^3=\dfrac{1}{8}[/tex]

Cube root both sides:

[tex]\implies \sqrt[3]{p^3}= \sqrt[3]{\dfrac{1}{8}}[/tex]

[tex]\implies p= \sqrt[3]{\dfrac{1}{8}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]

[tex]\implies p= \left(\dfrac{1}{8}\right)^{\frac{1}{3}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \left(\dfrac{a}{b}\right)^c=\dfrac{a^c}{b^c}:[/tex]

[tex]\implies p= \dfrac{1^{\frac{1}{3}}}{8^{\frac{1}{3}}}[/tex]

[tex]\textsf{Apply exponent rule} \quad 1^a=1:[/tex]

[tex]\implies p= \dfrac{1}{8^{\frac{1}{3}}}[/tex]

Rewrite 8 as 2³:

[tex]\implies p= \dfrac{1}{(2^3)^{\frac{1}{3}}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies p= \dfrac{1}{2^{(3 \cdot \frac{1}{3})}}[/tex]

Simplify:

[tex]\implies p= \dfrac{1}{2^{\frac{3}{3}}}[/tex]

[tex]\implies p= \dfrac{1}{2^{1}}[/tex]

[tex]\implies p= \dfrac{1}{2}[/tex]

Mr. Shaw can use 70 shelves with 2 books each.

or

Mr. Shaw can use 35 shelves with 4 books each.

or

Mr. Shaw can use 28 shelves with 5 books each.

or

Mr. Shaw can use 20 shelves with 7 books each.

or

Mr. Shaw can use 14 shelves with 10 books each.

Mr. Shaw has 140 books in his library.

Divisibility rule of 2:

A number is always entirely divisible by 2 if it is even or has an even last digits, such as 2,4,6,8, or 0.

The last digit of 140 is 0 which is an even number. So, 140 is divisible by 2.

Therefore,

Number of shelves = 140/2 = 70

Divisibility rule of 4:

An integer is divisible by 4 if its last two digits are also divisible by 4. A number is divisible by 4 if its last two digits are zeros since 4 divides 100.

The last two digits of 140 are 4 and 0.

Now, 40/ 2 = 20. Hence, 140 is divisible by 4.

Therefore,

Number of shelves = 140/4 = 35

Divisibility rule of 5:

If the last digit of a given integer is either 5 or 0, then the number is divisible by 5 according to the divisibility rule of five.

Since the last digit of the number 140 is 0. Hence 140 is divisible by 5.

Therefore,

Shelves = 140 / 5 = 28

Now,

Divisibility rule of 7:

According to the divisibility rule of 7, if a number is divisible by seven, then "the difference between twice the unit digit of the provided number and the remaining part of the given number should be a multiple of seven or it should be equal to zero."

140 = 14 - 2 × 0 = 14

Since 14 is divisible by 7. Hence 140 is divisible by 7.

Therefore,

Number of shelves = 140 / 7 = 20

Similarly,

Divisibility rule of 10:

The divisibility rule for 10 states that any number whose last digit is 0, is divisible by 10.

As the last digit of 140 is 0, hence 140 is divisible by 10.

Therefore,

Number of shelves = 140/10 = 14

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Answer: 48x⁸y⁶

Step-by-step explanation:

[tex]6x^2y^3(2x^2y)^3=\\6x^2y^32^3(x^2)&^3y^3=\\(6)(8)(x^2)(x^{(2)(3)}})(y^{3+3})=\\48(x^2)(x^6)y^6=\\48x^{2+6}y^6=\\48x^8y^6[/tex]

Answer:

[tex]48 {x}^{8} y^{6} [/tex]

Step-by-step explanation:

[tex]1. \: 6 {x}^{2} y {}^{3} \times 2 {}^{3}( {x}^{2}) {}^{3} y {}^{3} \\ 2. \: 6x {}^{2} y {}^{3} \times 8( {x}^{2} ) {}^{3} y {}^{3} \\ 3. \: 6x {}^{2} y {}^{3} \times 8x {}^{6} y {}^{3} \\ 4. \: (6 \times 8)x {}^{2}x {}^{6} y {}^{3} y {}^{3} \\ 5. \: 48 {x}^{2} x {}^{6} y {}^{3} y {}^{3} \\ 6. \: 48x {}^{2 + 6} y {}^{3 + 3} \\ 7. \: 48x {}^{8} y {}^{3 + 3} \\ 8. \: 48x {}^{8} y {}^{6} [/tex]

Answer:

Inverse Property of Addition

Step-by-step explanation:

Most table tops are square, rectangular, or circular.

The solution to the system of equations is (2.5, -2)

The system of equations is given as:

2x + y = 3

2x - 5y = 15

Subtract the equations to eliminate the variable x

This is represented as

2x - 2x + y - -5y = 3 - 15

Evaluate the like terms in the above equation

So, we have

y + 5y = 3 - 15

Evaluate the like terms in the above equation

So, we have

6y = -12

Divide both sides of the above equation by 6

So, we have

y = -2

Substitute y = -2 in 2x + y = 3

2x - 2 = 3

This gives

2x = 5

Divide by 2

x = 2.5

Hence, the solution to the system of equations is (2.5, -2)

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Answer:

2.5, -2

Step-by-step explanation:

The coordinates of one point in the solution set are (2, 0)

The system of inequality is given as

-7x + 3y < 3

5x + 7y ≥ -7

The graph that completes the question is added as an attachment

From the question, we also have the graph that represents the inequalities in the above system of inequality

As a general rule, the shaded region in a system of inequality represents the solution set

From the attached graph, the point (2, 0) is in the shaded region

Hence, the coordinates of one point in the solution set are (2, 0)

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Answer:

Step-by-step explanation:

has 25 sections of seating

Solution of polynomial 4/2a = 5/a +6 is , [tex]a=-\frac{1}{2}[/tex]

In mathematics, polynomial function can be defined as the equation which consist of coefficient, variables and exponents. A polynomial equation has positive numbers as their exponent which is also known as its degree. All the equations such as monomials, quadratic equation, cubic equation, linear equation of one degree, two degree and more  which has non  negative number as their powers all are part of polynomial equation and can be taken as types of the polynomial equations.

Some examples of polynomial equation are :

According to question,

[tex]\frac{4}{2a} = \frac{5}{a} +6\\\\= > \frac{2}{a} = \frac{5}{a} +6\\\\= > 5 + 6a =2\\ \\= > 6a = -3\\\\= > a = -\frac{3}{6} =-\frac{1}{2}[/tex]

Thus a = -1/2

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The 46th term of a Arithmetic Progression (AP) is (a₄₆ = 95.)

The difference between the two numerical orders is a constant value in Arithmetic Progression (AP). Another name for it is Arithmetic Sequence.

We'd end up coming across a few key words in AP, which were denoted as:

The AP can also be defined in terms of common differences, as shown below.

Now, in the question, the given sequence is;  3,5,7, ...........

Assume the first term is'a₁' = 3

Assume 'a₂' = 5 is the second term.

Assume the third term is 'a₃' = 7

Find the common difference;

d = a₂ - a₁  

Substitute the values in the above equation;

d = 5 - 3 = 2

Now, to calculate the value of the 46th term use the formula of nth term.

an = a + (n − 1) × d , n = total number of terms = 46.

Substitute all the values;

a₄₆ = 5 + (46 - 1) × 2

a₄₆ = 5 + 45 × 2

a₄₆ = 5 + 90

a₄₆ = 95

Therefore, the value of the 46th term is estimated as 95.

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Will they have enough money for their trip?Yes.They will have $1407.35

If not, how much more do they need?

Given:

a1 = $125

r = 1.25

n = 6(march-august)

[tex]S_n=\frac{a(1-r^{n})}{1-r} \\\\S_6=\frac{125(1-(1.25)^{6})}{1-1.25}\\\\S_6=1407.35[/tex]

The family will have $1407.35 after making the final deposit in August.

So, they will have enough money for their trip.

They have an additional amount of $32.35 ($1407.35-$ 1375)

What is a geometric sequence?

The complete question is:

In March, a family starts saving for a vacation they are planning for the end of August. The family expects the vacation to cost $ 1375 . They start with $125 . Each month they plan to deposit 25% more than the previous month. Will they have enough money for their trip? If not, how much more do they need?

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In Δ SZU, UJ = 9, VI = 3 , and ZT = 18 then the value of SV = 9.

The triangle's centroid is the point where the three medians intersect. According to the centroid theorem, the centroid is 23 times the distance from each vertex to the midpoint of the opposite side.

The centroid has the unique property that the distance from a vertex to the centroid is twice that of the distance from the centroid to the midpoint of the side opposite that vertex for each median. In addition, the three medians of a triangle divide the triangle into six equal-area regions.

Given: In Δ SZU, UJ = 9, VI = 3 , and ZT = 18 .

Since ZV ≅ VU, Y is the midpoint of UZ and SV is a median of Δ ZSU. Similarly, points Y and T are also midpoints of SZ and SU, respectively, so YU and ZT are also medians. Therefore, point J is the centroid of

Δ ZSU and, according to the Centroid Theorem, SJ is 2/3 of SV.

SJ = 2/3 (SV)

= 2/3 (SJ + VJ)

simplifying the above equation, we get

(3SJ/2) - SJ = VJ

SJ/2 = 3

SJ = 4.5

Therefore, to find SV, we can now add SJ and VJ

SV = SJ + VJ

= 6 + 3

= 9

Therefore, the value of SV = 9.

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Using it's concept, the domain of function m is given as follows:

-∞ < x < ∞.

The domain of a function is the set that contains all the values of the input. In a graph, it is the set that contains all values of x of function.

In this problem, the function is defined for all real values of x, as it keeps increasing to left and right, hence the domain of function m is given as follows:

-∞ < x < ∞.

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Based on the table of the number of species in the United States, the probability that a randomly selected endangered species is a bird is 17.1%

The probability that a randomly selected mammal is endangered is 81.4%.

The probability that when an endangered species is selected randomly, it is a bird can be found as:

= Number of endangered birds / Number of endangered species

= 80 / (70 + 80 + 318)

= 17.1%

The probability that should a randomly selected mammal be picked, the mammal is endangered is:
= Number of endangered mammals / Number of mammals

= 70 / (70 + 16)

= 81.4%

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Using integer addition, the total profit from the Spanish Club's bake sale is $270.

Integer refers to whole numbers(non-fractional numbers) that can either be positive or negative, and zero.

Adding positive integers will result to a positive integer while adding negative integers will result to a negative integer. But, adding a negative integer to a positive integer is the same as subtracting its positive.

If the income from the Spanish Club's bake sale was $300 and the expenses for the sale is $30, the total profit will be:

income = +$300

expenses = -$30

Using integer addition,

profit = income + expenses

profit = +$300 + (-$30)

profit = $300 - $30

profit = $270

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Answer: 175

Step-by-step explanation:

By using logarithim quotient rule the given lograthimic expression log₅ x - 1/5 log₅ y can be written as log₅ (x/y^(1/5)).

According to the given question.

We have lograthimic expression.

log₅ x - 1/5 log₅ y

As we know that, a logarithmic expression is an expression that involves the logarithm of an expression containing a variable.

Also according to the logratimic quotient rule we know that

[tex]log_{b} (\frac{m}{n} ) = logm - logn[/tex]

Thereofore,by using logarithim quotient rule the given lograthimic expression log₅ x - 1/5 log₅ y can be written as

log₅ x - 1/5 log₅ y

= log₅ x - log₅ (y^(1/5))

= log₅ (x/y^(1/5))

Hence, by using logarithim quotient rule the given lograthimic expression log₅ x - 1/5 log₅ y can be written as log₅ (x/y^(1/5)).

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The length of BD is 4.29

BF is the radius of circle and CE is the chord. BF perpendicularly bisects the chord into two equal halves. Thus, we can say that -

CD = 1/2CE

Keep the values in equation to find the value of CD

CD = 1/2×13.5

CD = 6.75

Now, taking BCD as right angled triangle, we can say -

BC is hypotenuse, CD is base and BD is perpendicular. Using Pythagoras theorem to find the length of BD.

BC² = CD² + BD²

8² = 6.75²  + BD²

BD² = 64 - 45.5625

BD² = 18.4375

BD = √ 18.4375

BD = 4.29

Hence, the length of BD is 4.29

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The complete question is attached in the image below.

Using Pythagorean theorem, the student walked 53.58 meters more compared to the total displacement from the starting point.

If a student walks 100 meters north, then 100 meters west, then the path he travels resembles the sides of a right triangle (see attached photo).

Using Pythagorean theorem, we can solve for the total displacement from the starting point to the end point.

c^2 = a^2 + b^2

where c is the total displacement from the starting point to the end point

a is the distance he walks up north

b is the distance he walks to the west

c^2 = 100^2 + 100^2

c^2 = 10,000 + 10,000

c^2 = 20,000

c = 141.42 meters

Comparing the total distance the student walked and the total displacement from the starting point to the end point by subtraction.

100 meters + 100 meters - 141.42 meters = 53.58 meters

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