If Meg walks 1/3 a mile in 1/9 of an hour, how many miles will she walk in one hour?

The unit rate of computers per day using the graph is that 12 computers are made per day.

The unit rate is how many units of quantity correspond to the single unit of another quantity. We say that when the denominator in rate is 1, it is called unit rate. Unit rates is said to be the amount of something in each unit or per unit.

To obtain the unit rate of computers sold per day using the graph, we need to obtain the slope of the graph, which is the change in y per change in x

So, it is given by:

\(\text{Slope} = \dfrac{\text{change in y}}{\text{change in x}}\)

\(\text{Slope} = \dfrac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}\)

\(\text{y}_2 = 60 , \ \text{y}_1 = 36 , \ \text{x}_2 = 5, \ \text{x}_1 = 3.\)

\(\text{Slope} = \dfrac{(60 - 36)}{(5 - 3)} = \dfrac{24}{2} = 12\)

\(\bold{Slope = 12}\)

Unit rate = 12 computers per day.

The attachment of the graph is given below.

Therefore, the unit rate of computers per day is 12.

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The amount of money used for scholarship and the fraction of the estate gotten by Miss Maple are :

The entire fraction of the estate = 1/1

Fraction given to children = 2/3

Fraction left = Total - fraction given to children

Fraction left = 1/1 - 2/3 = 1/3

For scholarship :

1/5 of fraction left :

1/5 of 1/3 = 1/5 × 1/3 = 1 /15

Fraction Given to grand children :

1/5 - 1/15 = 2/15

Amount of money used for scholarship :

1/15 × 8424000 = $561,600

B.)

Since There are four grand children and it was equally shared among them:

Miss Maple is one of the grand children:

Fraction each grandchild gets is :

2/15 ÷ 4

2/15 ÷ 4/1

2/15 × 1/4 = 2/60 = 1/30

Hence, miss Maple will get 1/30

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The area and perimeter of the parallelogram are: 56 square units and 30 units respectively

In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The parameters that will help us do the math are

base = 7

height = 8

Area = 8*7 = 56 square units

perimeter 2b + 2h

perimeter = 2*7 + 2*8

= 14 +16

P = 30 units

Therefore, the perimeter of the parallelogram and area are 30 units and 56 square units

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Answer:

=20

Step-by-step explanation:

18+g=38 so g=20

Answer:

63 m/s

Step-by-step explanation:

h(3) = 3(3)² + 36(3) + 300 = 435

h(6) = 3(6)² + 36(6) + 300 = 624

v = Δh/Δt = (624m - 435m) / (6s - 3s) = 63 m/s

I can't see the semi circle is that image. From what I see, the perimeter of the trapezoid is 41.

Answer:

360

Step-by-step explanation:

From the given figures

Since LH // KJ, then

GL = 6, LK = 30

GH = 3, HJ = y

Substitute them in the ratio above

By using cross multiplication

Divide both sides by 6

Since GJ = GH + HJ

The answer is 36

Answer:

Jessica put $4.88 into her savings account.

Step-by-step explanation:

First, you'll add up how kuch she has spent.

7.37 + 3.75 = 11.12

Secondly, you'll subtract 11.12 from 16.

16 - 11.12 = 4.88

Answer:

1.48 miles

Step-by-step explanation:

If the trail is 14.8 miles and Rita has hiked 1/10 of it. Then just multiply 14.8 by 1/10.

14.8 * 1/10 = 1.48 miles.

Answer:

1.48

Step-by-step explanation:

I know the answer is correct

The true statement about n is (a) The value of n is 1/5 because (⁵√2)⁵ = 2¹ and (2¹/⁵)⁵ = 1, so ⁵√2 = 2¹/⁵

From the question, we have the following parameters that can be used in our computation:

Expression =  ⁵√2

Also from the question, we understand that the expression is to be expressed as

2ⁿ

This means that

⁵√2 = 2ⁿ

Re-express ⁵√2 using the law of indices

2ⁿ = 2¹/⁵

By comparison, we have

n = 1/5

This means that the value of n is 1/5

Hence, the true statement is (a)

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Answer:

1236

Step-by-step explanation:

First, we will express each of these values to two decimal places;

6.20, 6.24, and 6.28 from the least to the greatest which corrresponds to:

It will take 15 days for the hair to grow from 12mm to 16.5mm

By "average rate" in this context, we mean the typical or usual amount of hair growth per unit of time, which is often measured in millimeters per day. This rate can vary slightly depending on factors such as age, gender, genetics, diet, and overall health.

Let's first find out how much the hair needs to grow by subtracting its initial length (12mm) from its target length (16.5mm):

16.5mm - 12mm = 4.5mm

Now we can divide this growth by the average rate of hair growth to find the number of days it will take to grow this much:

4.5mm ÷ 0.3mm/day = 15 days

Therefore, it will take 15 days for the hair to grow from 12mm to 16.5mm.

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The y-intercept of the function is given as (0, -4). This also shows that the value of y missing from the coordinate is -4

The y-intercept of a function is the point where the value of x is zero. Given the function below;

4x-9y=36

when the value of x is zero, hence;

4(0) - 9y = 36

Simplify to have:

0 - 9y = 36

-9y = 36

Divide both sides by -9 to have:

-9y/-9 = 36/-9

y = -4

Hence the y-intercept of the function is given as (0, -4). This also shows that the value of y missing from the coordinate is -4

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Answer:

20

Step-by-step explanation:

good luck!!

Answer:

24 or 20

Step-by-step explanation:

Answer:X=10

Step-by-step explanation:

The person is approximately 8.43 miles from home, and they need to walk in the direction of approximately 26.6 degrees east of north to head directly home.

To determine the distance from home, we can use the concept of vector addition. The person walks 4 miles west, which can be represented as a vector (-4, 0) in a coordinate plane. Then, they walk 5 miles southwest, which can be represented as a vector (-3.54, -3.54) since southwest is a combination of west and south. Adding these two vectors together gives us (-7.54, -3.54).

To find the magnitude or distance from home, we use the Pythagorean theorem. The distance is given by sqrt((-7.54)^2 + (-3.54)^2) = 8.43 miles (approximately).

To determine the direction to head directly home, we need to find the angle between the vector (-7.54, -3.54) and the positive x-axis. We can use trigonometry to find this angle. The tangent of the angle is given by the ratio of the y-coordinate to the x-coordinate, which is -3.54 / -7.54. Taking the inverse tangent of this value gives us approximately 26.6 degrees.

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No student took both calculus and physics out of the 30 students.

Given that, total number of students are 30. Out of which 18 took calculus and 12 took physics. Then, we have to calculate how many took both calculus and physics. So, by using venn diagram we have,

Total number of students = 30

Students who took calculus = P(A) = 18

Students who took physics = P(B) = 12

Students who took both calculus and physics = P(A∩B) = x

Students who took only physics = P(B)-x = (12-x)

Students who took only calculus = P(A)-x = (18-x)

From venn diagram, we get

(18-x)+x+(12-x) = 30

18-x+x+12-x = 30

⇒ x = 0

∴ P(A∩B) = 0

Therefore, No student took both physics and calculus.

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Using the cosine ratio, the distance between Dimitri and Sarah is calculated as approximately 12.4 m.

The cosine ratio is a trigonometric ratio that represents the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle. It is calculated by dividing the length of the adjacent side by the length of the hypotenuse.

Using the cosine ratio, we have:

Reference angle (∅) = 72 degrees

Hypotenuse length = 40 m

Adjacent length = distance between Dimitri and Sarah = x

Plug in the values:

cos 72 = x/40

x = cos 72 * 40

x ≈ 12.4 [to one decimal place]

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Given the expression:

Let's simplify the expression.

To simplify the expression, take the following steps:

Step 1:

Rewrite -48 as 48(-1)

Step 2:

Expand:

Step 3:

Where √-1 = i

Rewrite √-1 as i

Step 4:

Rewrite 48 into smaller factors

Therefore, the simplified expression is:

ANSWER: D)

Step-by-step explanation:

3:

h(x)=(-3x-15)/5

let y=(-3x-15)/5

interchanging role of x &y

x=(-3y-15)/5

5x+15=-3y

y=-(5x+15)/3

h-1(x)=-(5x+15)/3

not

equal to f(x)=(-3x-6)/4

Given function are not function of each other .

4:

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

let

y=2/3(x-1)

interchanging role of x &y

x=2/3(y-1)

3/2x+1=y

g-1(x)=3/2x+1

not equal to f(x)=½x+1

Given function are not function of each other .

Problem 1

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

Explanation:

One way to see if we have an inverse pair or not is to compute these two composite functions

If both result in x, and just that, then we have shown that they are inverses of one another.

f(x) = (2x)/3

f(x) = (2/3)x

f(g(x)) = (2/3)*g(x)

f(g(x)) = (2/3)*(3/2)x

f(g(x)) = x

The steps to show that g(f(x)) = x are very similar

g(x) = (3/2)x

g(f(x)) = (3/2)*f(x)

g(f(x)) = (3/2)*(2/3)*x

g(f(x)) = x

So this verifies that you have the correct answer.

======================================================

Problem 2

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

Explanation:

We'll use the same idea as problem 1

f(x) = 2 - (3/4)*x

f(g(x)) = 2 - (3/4)*( g(x) )

f(g(x)) = 2 - (3/4)*( (-4/3)x + 8/3 )

f(g(x)) = 2 - (3/4)*(-4/3)x  - (3/4)*(8/3)

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

f(g(x)) = x

So far so good, but we need to check the other way around as well

g(x) = (-4/3)x + 8/3

g(f(x)) = (-4/3)*( f(x) ) + 8/3

g(f(x)) = (-4/3)*( 2 - (3/4)*x ) + 8/3

g(f(x)) = (-4/3)*(2) + (-4/3)*(-3/4)*x + 8/3

g(f(x)) = -8/3 + x + 8/3

g(f(x)) = x

This verifies that f(x) and g(x) are inverses of each other.

Problems 3 and 4 will have similar steps.

Answer:

The animal farm should buy 1.775 bags of soybeans and 1.575 bags of oats

\(Cost = 51.275\)

Step-by-step explanation:

The given parameters can be summarized as:

\(\begin{array}{cccc}{} & {x} & {y} & {Total} & {Protein} & {70} & {21} & {168} &{Fats}& {9} & {7} & {27} & {Minerals} & {7} & {1} & {14}& {Cost} & {21} & {7} & {} \ \end{array}\)

Where: x = Soybeans and y = Oats.

So, the system of equations are:

\(70x + 21y = 168\)

\(9x +7y = 27\)

\(7x + y = 14\)

\(Cost = 21x + 7y\)

The best way to solve this, is using graph

Plot the following equations on a graph, and get the points of intersection:

\(70x + 21y = 168\)

\(9x +7y = 27\)

\(7x + y = 14\)

From the attached graph, we have:

\((x_1,y_1) = (1.636,2.545)\)

\((x_2,y_2) = (1.775,1.575)\)

\((x_3,y_3) = (2.023,1.256)\)

Substitute each of the values of x's and y's in the cost function to get the minimum cost:

\(Cost = 21x + 7y\)

\((x_1,y_1) = (1.636,2.545)\)

\(Cost = 21 * 1.636 + 7 * 2.545\)

\(Cost = 52.171\)

\((x_2,y_2) = (1.775,1.575)\)

\(Cost = 21 * 1.775 + 7 * 1.575\)

\(Cost = 48.3\)

\((x_3,y_3) = (2.023,1.256)\)

\(Cost = 21 * 2.023 + 7 * 1.256\)

\(Cost = 51.275\)

The values of x and y that gives the minimum cost is:

\((x_2,y_2) = (1.775,1.575)\)

and the minimum cost is:

\(Cost = 48.3\)

Hence, the animal farm should buy 1.775 bags of soybeans and 1.575 bags of oats

Answer:

This is the answer and I hope it helps. have a great time.

Answer:

wait is that a test if it is cheating

Step-by-step explanation:

well the first one go on the bottom 2 row secound one first row third first row but it is in happpy i am not reall good at math XD third last row forth very happy fifth on unhappy sixth very unhappy seven very unhappy eight on very happy i think i got it i did this before i just don't rembear but i tried

The minimum point on the graph is \((-6,25)\), which confirms that the function has a minimum at\(-6\).

In mathematics, a graph is a diagram that shows the relationship between different sets of data. It is made up of points, which are also called vertices or nodes, that are connected by lines or curves called edges or arcs.

In mathematics, a function is a relation between two sets of data, such that each input in the first set corresponds to exactly one output in the second set. In other words, a function maps each input value to exactly one output value.

According to given information:

Let's start by writing the quadratic function in factored form, given that it has zeros at \(-1\) and \(-11\):

\(f(x) = a(x- (-1))(x- (-11))\)

Simplifying, we get:

\(f(x) = a(x+1)(x+11)\)

To find the value of a, we need to use the fact that the function has a minimum at \(-5\). Since the vertex of the parabola is at the minimum point, we know that the x-coordinate of the vertex is \(-5\). Therefore, we can use this information to find the value of a as follows:

\(-5 = (-1+(-11))/2\\-5 = -6\)

This tells us that the axis of symmetry of the parabola is \(x =-5\). Since we know that the function has zeros at \(-1\) and \(-11\), we can deduce that the vertex must lie halfway between these two zeros, at\(x = -6\). Therefore, the value of a is:

\(f(-6) = a((-6)+1)(-6) +11) = a(5) (-1) = -5a\)

We also know that the function has a minimum at this point, so we can use this to find the value of a:

\(f(-6) = -5\\-5= -5a\\\\a = 1\)

Therefore, the quadratic function that satisfies these conditions is:

\(f(x) = (x+1) (x+11)\)

We can check that this function has zeros at \(-1\) and \(-11\), and that it has a minimum at\(x =-6\) by finding its vertex:

x-coordinate of vertex = \((-1 +(-11))/2 =-6\)

y-coordinate of vertex =\(f(-6) = (-6+1)(-6+11) = 25\)

Therefore, the minimum point on the graph is \((-6,25)\), which confirms that the function has a minimum at -6.

Which of the following function has zeros at \(-1\) and\(-11\) and a minimum of \(-5\) ?

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The better prediction for y, when x = 74, based on the scatter plot, can be found to be 57.

Looking at the scatter plot, the better prediction of y when the value of x is 74 can be found by looking for the values of y that have a value of x that is around 74.

From the scatter plot, we see that the value of x of 74, would correspond with the value of y of 57. We can therefore infer that y = 57 is the better prediction for x = 74.

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The matching word are as follows:- center of dilation - C,corresponding angles - D,dilation - E,scale factor (of a dilation) - A,similar polygons - B respectively.

Corresponding angles are a pair of angles that have the same relative position at the intersection of two lines when one line is crossed by a transversal.

They are located in corresponding (matching) positions in congruent or similar figures, and are congruent if the figures are similar.

center of dilation: C.The fixed point that is parallel to each point on the pre-image and the corresponding point on the picture during a dilatation

corresponding angles: D.a pair of angles in two congruent or similar figures that are in the same relative position

dilation: E. The transformation in which each point on the image lies on the same line as the corresponding point on pre-image and a fixed point called the center of dilation.

scale factor (of a dilation): in a dilation, the constant  rate between the distance from the center of dilation and a point on the image and the distance from the center of dilation and the  matching point on thepre-image

similar polygons: B.two or  further polygons in which corresponding angles are  harmonious and the lengths of corresponding sides are in proportion.

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The amount of ribbon needed to go around a package that had a length 2x² + 3x -5/(x² + x - 3) centimeters and width x² - x - 5 / (x² + x - 3) is

\(\frac{(2x^2+3x-5)(x^2-x-5)}{(x^2+x-3)^2}\)

An equation is an expression that shows the relationship between two or more number and variables.

The  length 2x² + 3x -5/(x² + x - 3) centimeters and width x² - x - 5 / (x² + x - 3) centimeters. Hence:

\(Area=\frac{2x^2+3x-5}{x^2+x-3} *\frac{x^2-x-5}{x^2+x-3} =\frac{(2x^2+3x-5)(x^2-x-5)}{(x^2+x-3)^2}\)

The amount of ribbon needed to go around a package that had a length 2x² + 3x -5/(x² + x - 3) centimeters and width x² - x - 5 / (x² + x - 3) is

\(\frac{(2x^2+3x-5)(x^2-x-5)}{(x^2+x-3)^2}\)

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