Amanda increased the amount of protein she eats every day from 48 g to 54 g. what percentage did Amanda increase the amount of protein she eats

Answer:

y=2x+12

Step-by-step explanation:

When one organism gains a benefit at the expense of a second organism and causes them harm is called:

A. Parasitism

B. Mutualism

C. Commensalism

D. Predation

Answer:

Step-by-step explanation:

a

Answer:

83in²

Step-by-step explanation:

This can also be expressed as;

Area of polygon=Area of ∆ABF +Area of rectangle BCDF + Area 0f ∆DEF

For ∆ABF;

Area of ∆ABO=∆AOF

Area of ∆ABF=2×Area of ∆ABO

Area of ∆ABO=1/2×Length×height

=1×4×7/2=28/2=14in

But area of ∆ABF=2×Area of ∆ABO

Area=2×14in=28in.

Area of rectangle;

Area=length×breadth

Area=5in×8in=40in.

Area of ∆DEF=2×Area of ∆EFG

Area=1/2× base× height

Area=1×2.5×6/2

Area=15/2=7.5in.

But area of ∆EFG=2×7.5in

=15in.

Area of polygon=28in+40in+15in=83in

Solving the quadratic equation we conclude that:

The height of the rocket is defined by the quadratic equation:

[tex]d = 90t - 5t^2[/tex]

The maximum height is what we get in the vertex of the quadratic equation, such that for this quadratic equation, the vertex is at:

[tex]t = -90/(2*-5) = 9[/tex]

So the maximum height is what we get when we evaluate in t = 9:

[tex]d = 90*9 - 5*9^2 = 45[/tex]

The maximum height is 45ft.

Now we need to solve the equation for the largest value of t:

[tex]d = 90*t - 5t^2 = 0[/tex]

Rewriting it, we get:

[tex]0 = 90*t - 5*t^2\\\\0 = t*(90 - t*5)[/tex]

The maximum solution is what we get when:

0 = 90 - t*5

t = 90/5 = 18

The rocket is 18 seconds in the air.

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A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.

A line plot can be defined as a type of graph that is used to graphically represent a data set above a number line, while using crosses, dots, or any other mathematical symbol.

A mean is also referred to as an arithmetic average and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.

Mathematically, the distance between the means of both classes A and B is given by:

Distance = Mean of class A - Mean of class B

Distance = 12 - 4

Distance = 8.

The mean absolute deviation (MAD) for class A is given by:

MAD A = 1/9[2(9 - 12) + (10 - 12) + (11 - 12) + (12 - 12) + (13 - 12) + (14 - 12) + 2(15 - 12)]

MAD A = 1/9[2(3) + (2) + (1) + 0 + (1) + (2) + (1) + 2(3)]

MAD A = 1/9[6 + 2 + 1 + 1 + 2 + 1 + 6]

MAD A = 1/9 × [18]

MAD A = 18/9

MAD A = 2.

Also, the mean absolute deviation (MAD) for class B is given by:

MAD B = 1/9[2(1 - 4) + (2 - 4) + (3 - 4) + (4 - 4) + (5 - 4) + (6 - 4) + 2(7 - 4)]

MAD B = 1/9[2(3) + 2(2) + (1) + (0) + (1) + (2) + 2(3)]

MAD B = 1/9[6 + 4 + 1 + 0 + 1 + 2 + 6]

MAD B = 1/9 × [18]

MAD B = 18/9

MAD B = 2.

Therefore, distance between the means = four (4) times the MAD.

Distance = Means × MAD

8 = 4 × 2.

In conclusion, we can infer and logically deduce that there is no overlap and the distance between the means of both players A and B is between one (1) times the MAD and five (5) times the MAD.

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The P(B|A) expressed in the simplest form will be (B) 2/7.

To find the P(B|A) expressed in the simplest form:

Given -

Total possible numbers = 2,3,4,5,6,7,8,9

Let the value of the number be AB.

Therefore, the P(B|A) expressed in the simplest form will be (B) 2/7.

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The complete question is given below:
A locker combination consists of two non-zero digits. The digits in a combination are not repeated and range from 2 through 9.

Event a = a first digit is an odd number

Event b = the second digit is an odd number

If a combination is picked at random with each possible locker combination being equally likely, what is P(B/A) expressed in the simplest form?

A.1/4

B.2/7

C.4/9

D.1/2

Answer:

  triangle angle sum theorem

Step-by-step explanation:

The missing statement is one that justifies the sum of the angles in a triangle being 180°.

That justification is provided by the ...

  triangle angle sum theorem

the equation that represents the new graph is:

g(x) = √(x - 3) - 2

Here we start with the function:

y = f(x) = √x

First, we shift it 2 units down, then the new equation will be:

g(x) = f(x) - 2

Now we apply a horizontal shift, this time we shift the graph 3 units to the left, then the new equation is:

g(x) = f(x - 3) - 2

Now we replace f(x) = √x to get:

g(x) = √(x - 3) - 2

That is the equation that represents the new graph.

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The least common multiple of two or more natural numbers is the least common multiple of all of them. This concept has historically been linked to natural numbers, but can be used for negative integers or complex numbers.

We calculate the least common multiple, by simultaneous decomposition, this method consists of extracting the common and non-common prime factors, therefore

L.c.m.(12,15,18)= 2² × 3² × 5 = 180 min

The least common multiple of 12, 15, and 18 is 180.

Convert the minutes to hours, for this we apply the rule of 3:

As the bells all together ring at 6 am, so we add

Answer: The bells are rung together again at 9 in the morning.

Answer:

n = 2

Step-by-step explanation:

cross multiply

-5 times -4 = 20

10n = 20

n = 2

[tex]\bf{Move \ the \ negative \ symbol \ to \ the \ left. }[/tex]

[tex]\boldsymbol{\sf{-\dfrac{10n}{5}=-4 \ \ \longmapsto \ \ [Split] }}[/tex]

[tex]\boldsymbol{\sf{-2n=-4 }}[/tex]

[tex]\bf{Divide \ both \ sides \ by \ -2. }[/tex]

[tex]\boldsymbol{\sf{n=\dfrac{-4}{-2} }}[/tex]

[tex]\bf{Two \ negatives \ make \ a \ positive. }[/tex]

[tex]\boldsymbol{\sf{n=\dfrac{4}{2} \ \ \longmapsto \ \ [Split] }}[/tex]

[tex]\blue{\boxed{\boldsymbol{\sf{Answer \ \ \longmapsto \ \underline{n=2}}}}}[/tex]

Step-by-step explanation:

g(x) is also called y. the functional result value for an input value x is shown in the y direction above or below that x value on the x axis.

so, when it says g(x) = c, the solution is to find the values of x for which b the function g delivers c as result.

now, we look at the graphic.

for example, g(x) = 0 (c = 0) has actually 3 solutions, as the function crosses the x-axis (and that means y or g(x) = 0) 3 times. so, there are 3 different values of x that create g(x) = 0.

but we are looking for a c that has only one solution (one value of x to create that result).

c = 1 ?

let's imagine a horizontal line through y = 1.

we see, it cuts the function also 3 times. 3 solutions.

c = -1 ?

a similar horizontal line through y = -1 cuts the function also 3 times. 3 solutions

but c = 3 !

a horizontal line through y = 3 stays above all the waves of the function and then cuts the function only one time at the very right. 1 solution !

and that is therefore our answer.

We know that there are (3 + 1/2) groups, such that each group fill one bus.

2/5 of the students are boys, then the number of groups that we can make only with boys is:

(2/5)*(3 + 1/2) = 6/5 + 1/5 = 7/5 = 5/5 + 2/5 = 1 + 2/5

Then you can make one and a little less than a half of a group, which means that you need 1 and 2/5 of a buss to transport the boys, rounding that to the a whole number, you will need 2 busses to only transport the boys.

The original distance is:

D = (2 + 3/4) miles.

But Mark only covers 2/3 of that distance, then we have:

d = (2/3)*D = (2/3)*(2 + 3/4) miles = (4/3 + 2/4) miles

d = (4/3 + 1/2) miles = (8/6 + 3/6) miles = (1 + 5/6) miles

Mark is at (1 + 5/6) miles of his house.

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The distance from Sang to Jazmin is 101 yards.

From the discussion in the question, we can see that the positions of Sang and Jazmin can be construed to give a rectangle. We know that the rectangle is a four sided figure.

The diagonal is a line that is drawn from one side of the four sided figure to another. Hence we can be able to apply the Pythagoras theorem to obtain the distance from Sang to Jazmin.

From;

c^2 = a^2 + b^2

c = √a^2 + b^2

c = √(20)^2 + (99)^2

c = 101 yards.

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Answer:

  -3√11

Step-by-step explanation:

If the coefficients of a polynomial are rational, any irrational root will have a conjugate that is also a root.

The root 3√11 is irrational, so its conjugate, -3√11, will also be a root.

__

Additional comments

The conjugate of a root of the form a+√b or a+bi will be the same form with the sign changed: a-√b or a-bi.

The conjugate of 3√11 = 0 +√99 will be 0 -√99 = -3√11.

__

A quadratic with rational coefficients can only have irrational roots of the form a±√b, where 'a' and 'b' may be any rational number.

3 - √11  also be a root of f(x).

A polynomial function is a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc.

Get the conjugate of any irrational zero if you want rational coefficients.

The conjugate of 3 + √11  is  3 - √11

x = 3 +√ 11

Subtract 3 on both sides

x minus 3 = 3 + √11 - 3

x - 3 = √11

By squaring on both sides

(x - 3)² =√ 11

Now subtract 11 on both sides

(x - 3)² - 11 = 0

To factor use the difference of squares

u² minus v² = (u minus v) (u plus v)

[(x - 3) - 11][(x - 3) + 11] = 0

We get,

(x - 3) - 1 = 0 or (x - 3) + 11 = 0

Solve for x - 3 and x

Add √11 on both sides of first equation and subtract √11 on both sides of second equation

x minus 3 = √11 or x minus 3 = - √11

By adding 3 on both sides

x = 3 + √11 or x = 3 - √11

As a result,

the root of 3 - √11 must likewise be f(x).

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By definitions of volume and flow rate, it will take a time of 10 minutes to fill the tank to a height of 50 centimeters.

Herein we find the case of a rectangular tank being filled with water at constant flow are, which is dimensionally speaking, volume by time. We know that dimensions of the tank are described in centimeters, whereas flow rate is described in liters per minute. Please notice that a liter is equal to 1000 cubic centimeters:

t = [(80 cm) · (60 cm) · (50 cm) · (1 L / 1000 cm³)] / (24 L / min)

t = 10 min

By definitions of volume and flow rate, it will take a time of 10 minutes to fill the tank to a height of 50 centimeters.

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The y-intercept of the linear equation that models the data indicates that:

There was 1 inch of water on the tub when the water was turned on.

A linear function is modeled by:

y = mx + b

In which:

In this problem, when x changes by 1, y changes by 2, hence the slope is of 2. Hence, since when x = 1, y = 3, when x = 0, y = 3 - 2 = 1, which means that the y-intercept is of 1, and the correct interpretation is:

There was 1 inch of water on the tub when the water was turned on.

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Carries two brothers each ate 4 pieces, the rest of carries family ate 14 pieces and there were 14 pieces remaining given that Carries family broke a package of graham crackers into 32 pieces. carries two brothers each ate 1/8 of the pieces and the rest of the family ate 7/16 of the pieces. This can be obtained by multiplying the fractions given with the total number.

From the question it is given that,

Carries family broke a package of graham crackers into 32 pieces.

Therefore total number of pieces will be 32 pieces.

carries two brothers each ate 1/8 of the pieces

This means that out of 32, 1/8 of the pieces were ate by the two brothers.

1/8 of 32 = 1/8 × 32 = 4 pieces

⇒ Carries two brothers each ate 4 pieces

the rest of the family ate 7/16 of the pieces

This means that out of 32, 7/16 of the pieces were ate by the rest of the family

7/16 of 32 = 7/16 × 32 = 14 pieces

⇒ the rest of carries family ate 14 pieces

remaining pieces = 32 - (4 + 14) = 32 - 18 = 14 pieces

⇒ there were 14 pieces remaining

Hence Carries two brothers each ate 4 pieces, the rest of carries family ate 14 pieces and there were 14 pieces remaining given that Carries family broke a package of graham crackers into 32 pieces.

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Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Question: Carries family broke a package of graham crackers into 32 pieces. carries two brothers each ate 1/8 of the pieces and the rest of the family ate 7/16 of the pieces.

carries two brothers each ate ____ pieces

the rest of carries family ate ____ pieces

there were ____ pieces remaining

He has thrown 425 free throws if he missed 17

The given parameters are:

Proportion of free throw missed, p = 4%

Number of free throw missed, n = 17

Let the total number of throws be N.

So we have

n = p * N

Substitute the known values in the above equation

17 = 4% * N

Divide both sides by 4%

N = 425

Hence, he has thrown 425 free throws if he missed 17

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To estimate the volume of the chord of wood, since the wood exists cut into equal lengths and stacked evenly in a rack then we can use a cylinder as a model.

In mathematics, a cylinder exists as a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance. These bases exist normally circular (like a circle) and the center of the two bases exists joined by a line segment, which exists named the axis.

A cylinder exists as a closed solid that contains two parallel circular bases joined by a curved surface.

To calculate the volume of the chord of wood, since the wood exists cut into equal lengths and stacked evenly in a rack then we can use a cylinder as a model.

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a3=9

assuming the pattern is constant, a3 is right in the middle of a1 and a5 so the answer would be right in the middle of 6 and 12. the average of 6 and 12 is 9, so a3=9.

hope this helps!

Answer:

11/24 ths each

Step-by-step explanation:

Add the portions left...then divide by the five of them

3/4 + 5/8 + 11/12  = ?      must find common denominator (24) and convert

(18 + 15+22) / 24 = 55/24  now divide by 5 (which is the same as mult by 1/5)

55/24 * 1/5 = 55/120     now simplify to 11/24

∠KJI≅ZJX is the additional information.

What are the AAS congruency criteria?

⇒ AAS stands for Angle-Angle-Side. When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent

We have been given that

⇒ kJ=ZJ

⇒∠KJI=∠ZJX (vertically opposite angle)

And we require one more angle which can't be on the non-included side

so we have only one angle that can satisfy this  

⇒∠JIK=∠JXZ

⇒ Now we can say that △KJI ≅ △ZJX is congruent with AAS congruency criteria

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(i) The measures of the angles are m ∠ TCM = m ∠ TCQ = m ∠ CMQ = 90°.

(ii) The lengths of sides CM and CQ are 2 cm and 2√2 cm, respectively.

(iii) The angle between the side face and the base is equal to θ = cos⁻¹ (2 / MT) and the angle between the slant edge and the base is θ = cos⁻¹ [2√2 / √(4 + MT²)].

In this problem we have a right pyramid as line segment TC is perpendicular to the base PQRS, which means that any line coplanar with PQRS is perpendicular to line segment TC. i) the measures of the angles are m ∠ TCM = m ∠ TCQ = 90°.

Besides, the base PQRS is a square, which is equivalent to four right triangles with angles 45° - 45° - 90° and each triangle can be divided into two right triangles. Hence, the measure of the angle CMQ is 90°.

ii) The length of the sides can be found by the 45-45-90 theorem, which states that the length of the hypotenuse is √2 times the length of any of the legs:

CQ = (√2 / 2) · PQ

CQ = (√2 / 2) · (4 cm)

CQ = 2√2 cm

CM = (√2 / 2) · (2 √2 cm)

CM = 2 cm

iii)  The angle between the side face, one of them contains the line segment MT and the base can be found by the following inverse trigonometric relation: (value of the pyramid height is missing)

θ = cos⁻¹ (CM / MT)

θ = cos⁻¹ (2 / MT)            (1)

Similarly, the angle between the slant edge and the base is found by Pythagorean theorem and inverse trigonometric relation: (value of the pyramid height is missing)

θ = cos⁻¹ (CQ / TQ)

θ = cos⁻¹ [2√2 / √(QM² + MT²)]

θ = cos⁻¹ [2√2 / √(4 + MT²)]          (2)

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The scale factor of the given dilation transformation is calculated as; 1/2

We know that from transformation that  a dilation is a non - rigid transformation that produces similar figures.

If two lines are similar, then the lines are parallel and parallel lines always have the same slope.

Thus;

Line A has the formula; 2y = x + 8

Writing it in slope intercept form gives us;

y = 0.5x + 4   ------(1)

Thus;

slope of the line A is m = 0.5

y-intercept of the line A is b = 4

Line B has the equation;

y - ¹/₂x = 2

Rearranging in Slope Intercept form gives us;

y = ¹/₂x + 2

Thus;

slope of the line B is m = 0.5

y-intercept of the line B is b = 2

Now, it should be noted that the y-intercept of line A multiplied by the scale factor k must be equal to the y-intercept of line B. Thus;

4k = 2

k = 2/4

k =  ¹/₂

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Answer:

The frame will be 4 inches in width

Step-by-step explanation:

The length of the outside is 24+2x

The width of the outside is 20+2x

(24+2x)(20+2x) - 20(24) = 416

480 + 40x + 48x + 4x2 - 480 = 416

4x2 + 88x - 416 = 0

x2 + 22x - 104 = 0

(x+26)(x-4) = 0

x = -26 or x=4

The frame will be 4 inches in width

The correct  option (D).

There are infinitely many intersection points.

a two-variable equation that, when plotted on a graph, results in a straight line.

The term "point of intersection" refers to the intersection of two lines.

Russ is attempting to solve an equation whose two sides are both linear expressions.

He graphs the system and finds that they are on the same line after setting the expressions to y.

Since both lines are the same, there are an endless number of junction places.

Russ should therefore consider the outcome to be option (D) There are a limitless number of intersections.

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I understand that the question you are looking for is:

Russ is solving an equation where both sides are linear expressions. He sets the expressions equal to y and graphs the system finding that they are the same line. How should Russ interpret this outcome? There are no intersection points. There is exactly one intersection point. There are exactly two intersection points. There are infinitely many intersection points.Russ is solving an equation where both sides are linear expressions. He sets the expressions equal to y and graphs the system finding that they are the same line. How should Russ interpret this outcome?

A. There are no intersection points.

B. There is exactly one intersection point.

C. There are exactly two intersection points.

D. There are infinitely many intersection points

The solution to the system and the solution that fills the blank space is (6, 1)

This are also known as a set of simultaneous equations, also known as a system of equations which is a finite set of equations for which common solutions

Given the following system of equations

2y − x = 8, and

y − 2x = −5.

From equation 2;

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

Substitute equation 2 into equation 1 to have:

2(-5+2x) - x = 8

Expand to have:

-10 +4x -x = 8

-10 + 3x = 8

3x = 8 + 10

3x = 18

Divide both sides

by 3

3x/3 = 18/3

x = 6

Substitute x = 6 into equation 3

y = -5 + 2x

y = -5 + 2(3)

y = -5 + 6

y = 1

Hence the solution to the system and the solution that fills the blank space is (6, 1)

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Answer:

Its D (6,7)

Step-by-step explanation:

We have:

√32x + 1 = 9x - 2

<=> √32x - 9x = -2 - 1

<=> (√32 - 9)x = -3

<=> x = -3/(√32 - 9) = (27+12√2)/49

ANSWER: x = (27+12√2)/49

P/s: i'm not pretty sure

Ok done. Thank to me :3

The resulting equation on completing the square is (x+19/2)^2 = 39 + (19/2)^2

Quadratic equation are equations that has a leading degree of 2. Most quadratic equations have 3 terms.

Given the quadratic equation x^2-19x-39 = 0

Add 39 to both sides to have:

x^2 - 19x - 39 + 39 = 0 + 39

x^2 -19x = 39

Complete the square of the resulting

x^2-19x+(19/2)^2 = 39 + (19/2)^2
(x+19/2)^2 = 39 + (19/2)^2

x + 19/2 = ±√39 + (19/2)^2

x = ±√39 + (19/2)^2 - 19/2

Hence the resulting equation on completing the square is (x+19/2)^2 = 39 + (19/2)^2

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[tex]-16=r^3\implies \sqrt[3]{-16}=\sqrt[3]{r^3}\implies \sqrt[3]{-16}=r\implies \sqrt[3]{-2^4}=r \\\\\\ \sqrt[3]{(-2)^3\cdot 2^1}=r\implies -2\sqrt[3]{2^1}=r\implies -2\sqrt[3]{2}=r[/tex]