The composition of functions

Answer:40

Step-by-step explanation: 15 bars to a box.

600 bars in total.

600/15= 40

40 boxes of granola bars

The relation is decreasing by a factor of 2 each time, so:

Therefore:

Answer:

-191

Answer:

Explanation:

Here, we want to convert from ounces to grams

Mathematically,we have it that:

7 ounces will be the product of 7 and this

Mathematically,we have this as;

To the nearest whole number, this is 198 g

You have:

sin 2A = -√7/4

In order to determine the value of sin A, first calculate the value of angle A by using sin⁻¹ over the previous equation, just as follow:

sin⁻¹(sin 2A) = sin⁻¹(-√7/4) In this way you cancel out the sin

2A = -41.41° divide by 2 both sides

A = -41.41°/2

A = -20.705°

however, take into account that angle A is in the third quadrant. Then, it is necessary to consider the result A=-20.705° is respect to the negative x-axis.

To obtain the angle respect the positive x-axis (the normal way), you simply sum 180° to 20.705°:

20.705 + 180° = 200.705°

Next, use calculator to calculate sinA:

sin(200.705°) = -0.3535

EXPLANATION

Savings account balance = $2,764

Desired amount = $5,000

Let's call x to the amount of money the family needs.

The inequality that could be used to determine the amount of money the family needs is the following:

2,764 + x ≥ 5,000

The measure of angle 1 is 71º, we can find this, because angle 1 and angle x form a straight line of 180º, so 180º - 109º = 71º

The measure of angle 2 is also 71º, we can use the vertical angles propierty, then m∠1 = m∠2

The measure of angle 3 is 109º, we can use again the vertical angles theorem to find that m∠x = m∠3

Themeasure of angle 7 is 109º. We need to use the alternating exterior angles theorem. Since angle x and angle 7 are not between the parallel lines they're exterior angles; and since they're on opposite sides of the transversal line, they're alternates. Then the theorem says that m∠x = m∠7

The measure of angle 6 is 71º, again we're using the fact that angle 7 and angle 6 forms a straight line, then m∠6 = 180º - 109º = 71º

Now we can find the lasts two measures using the vertical angles theorem.

The measure of angle 5 is 71º, because m∠6 = m∠5

The measure of angle 4 is 109º, because m∠7 = m∠4

ANSWER

EXPLANATION

Given;

The total number of marble is;

Recall, the probability of an event can be calculated by simply dividing the favorable number of outcomes by the total number of the possible outcome

Hence, the probability of selecting a red marble is;

The Pythagoras theorem gives the relation for the right-angle triangle between the perpendicular, base, and hypotenuse thus the perpendicular x will be 14.70.

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.

Triangle is a very common figure to deal with in our daily life.

In a triangle, the sum of all three angles is 180°

As per the given right-angle triangle,

Pythagoras' theorem states that in a right-angle triangle →

Hyp² = Perp² + Base²

In the given triangle Hyp = 21 , Base = 15 and Perp = x

So,

21² = x² + 15²

x² = 21² - 15²

x = √216 = 14.6993 ≈ 14.70

Hence "The value of x for the given right-angle triangle is 14.70 units".

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The expression has a value of -31 when a = 2 and b = –3

From the question, the expression is given as

5 – a(3² + (ab + 2)² – 7)

Also, we have the values of the variables to be

a = 2 and b = –3

Substitute a = 2 and b = –3 in the expression 5 – a(3² + (ab + 2)² – 7)

So, we have the following equation

5 – a(3² + (ab + 2)² – 7) = 5 – 2 * (3² + (2 * -3 + 2)² – 7)

Evaluate the expressions in the bracket

5 – a(3² + (ab + 2)² – 7) = 5 – 2 * (3² + (-4)² – 7)

Evaluate the exponents

5 – a(3² + (ab + 2)² – 7) = 5 – 2 * (9 + 16 – 7)

So, we have

5 – a(3² + (ab + 2)² – 7) = 5 – 2 * 18

This gives

5 – a(3² + (ab + 2)² – 7) = 5 – 36

Evaluate the difference

5 – a(3² + (ab + 2)² – 7) = -31

Hence, the value of the expression is -31

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A die can have 6 possible outcomes.

The probability of an event is calculated using the formula:

Therefore, the probability of rolling a 1 is gotten to be:

The probability is 1/6.

a) To convert to radical form, we follow this:

So:

b) The formula we have is for mass in Kilograms, so the first step is to convert the mass stated from lbs to kg.

1 lb -- 0.454 kg

160 lb -- m

Now, we can use this value in the formula:

a) To convert to radical form, we follow this:

So:

b) The formula we have is for mass in Kilograms, so the first step is to convert the mass stated from lbs to kg.

1 lb -- 0.454 kg

160 lb -- m

Now, we can use this value in the formula:

The equation for 'P', representing Madeline's total pay on a day on which she sells 'x' computers is → P = 80 + 20x.

Given, At an electronics store, Madeline sells computers as a salesperson. She receives a $80-per-day base salary in addition to a $20 commission for each computer she sells.

What is Equation Modelling?

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We can model the equation for Madeline's total pay as follows -

P = base pay + (number of sold computer) × (cost of 1 computer)

P = 80 + 20x

Therefore, the equation for 'P', representing Madeline's total pay on a day on which she sells 'x' computers is → P = 80 + 20x

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The ratio of boy to girl is 3:2. There are 15 boys on the team. The total number of players on the team can be calculated as follows.

Total players = 25

Let's begin by identifying key information given to us:

To know if the vertex is the maximum or minimum point, we will follow this below:

Hence, the answer is B.(0,4); minimum

Given:

1 counsellor for every 9 campers.

Lets' determine the type of variation and write the equation.

Here, we can see that for every 9 campers, there is one extra counsellor. This means that as the number of campers increase, the number of counsellors will also increase.

Since one variable as the other increases, this is a direct variation.

Hence, we have the equation which represents the direct variation below:

y = 9x

Where x represents the number of counsellors and y represents the number of campers.

ANSWER:

Direct variation.

y = 9x

Using some simple mathematical operations we can conclude that the new amount of budgeted total sales is (D) $66,250.

So, new amount of budgeted total sales for March:

So, we know that:

And 2350 is further:

Let's replace 800 with 1100.

Now, solve as follows:

Therefore, using some simple mathematical operations we can conclude that the new amount of budgeted total sales is (D) $66,250.

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Total number of defected radios is 18

Let the total number of defective radios be taken as y

If 0.024% of the total number of radios inspected are defective, i.e 0.024% of y

Solve for y, by cross multiplying

Hence, the number of radios inspected, y, is 75000

Question:

Solution:

Remember the following theorem: the ratio of the areas of two

similar triangles is equal to the ratio of the squares of their corresponding sides. Then, here A1 and A2 are areas of two similar triangles, and S1 and S2 are their corresponding sides respectively :

S1 : S2 = 5 : 8

then

now, A1 = 87.5. Thus, according to the theorem, we get the following equation:

this is equivalent to:

by cross-multiplication, this is equivalent to:

solving for A2, we get:

so that, we can conclude that the correct answer is:

The area of the larger triangle is

Given:

The angels and sides of the triangle are

A = 50°. B = 45°, and a=3

Aim:

We need to find the angle C and sides c and b.

Explanation:

Use sine law.

Substitute A = 50°. B = 45°, and a=3 in the equation.

Use the triangle sum property to find the angle C.

Substitute A = 50°. and B = 45° in the equation.

Substitute A = 50°. C= 85°, and a=3 in the equation.

Final answer:

Samantha, this is the solution to problem 5:

With the information given in the statement you can solve for k, where k is the center in y:

(x-h)^2 + (y-k)^2 = r^2

(6-3)^2 + (5-k)^2 = (√(13))^2

(3)^2 + (5-k)^2 = 13

9+(5-k)^2 = 13

(5-k)^2 = 4

√((5-k)^2) = √4

5-k = 2

-k = -3

k = 3

Then the equation of the circle will be

(x-3)^2 + (y-3)^2 = 13

The average profit of this group is B. -$100.

The average represents the total profits and losses generated by the group of friends, divided by the number in the group.

The average is the data set's mean after performing the mathematical operations of addition and division on the data values.

Friends    Profits

A                $120

B              -$230

C               $670

D              -$1020

E               $250

F               -$430

G               -$60

Total      -$700

Average profit = -$100 (-$700/7)

Thus, we can conclude that the friends generated an average profit of B. -$100 from gambling or a total loss of $700.

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Given data:

The given function is f(x)= x^2 +3x-10.

The given inequality is,

First, to find the inverse of a function, call the original function "x" and call call "x" in the original function as the inverse function:

Now, we solve for the inverse function:

To graph lines, we can find two points in it and draw a line that passes through both.

Let's pick x = 0 and x = 1 for the first equation:

So, we plot the points (0, 1) and (1, 6).

For the inverse, we can simply invet the coordinates, which is the same as picking x = 1 and x = 6:

Thus, we have the points (1, 0) and (6, 1).

The line y = x is jus the diagonal that passes though point (0, 0) and (1, 1), for example.

Putting these points and drawing the lines, we get:

The dimensions of new rectangular playing field are 183 yards and 44 yards, by the concept of perimeter of rectangle.

The whole distance that the sides or limits of a rectangle cover is known as its perimeter. Since a rectangle has four sides, its perimeter will be equal to the sum of those four sides. Given that the perimeter is a linear measurement, the rectangle's perimeter will be expressed in meters, centimeters, inches, feet, etc.

Formula, perimeter of rectangle =2× (length +width)

Given, perimeter of rectangular playing field = 454 yards (equation 1)

Let us assume, width =x

According to question length = 4x+7 (quadruple=4times)

By the above equations,

Perimeter=2×(4x+7+x)

2×(5x+7) =454 (by equation 1)

Dividing the above equation by 2 both the sides

(5x+7) =227

Subtracting the above equation by 7 both the sides

5x=220

Dividing the above equation by 5 both the sides

x=44

Therefore, the required width of new rectangular playing field is 44 yards and length of new rectangular playing field is 183 yards

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Solution

For this case the area is given by:

Then we can replace b = 5ft and h = 20 ft and we got:

Answer:

(8, 0)

Explanation:

Whenever a point (x,y) is reflected across the line y=x, the transformation rule is given below:

That is, the x-coordinate and y-coordinate change places.

Therefore, the image of the point (0,8) when reflected across the line y=x is:

The correct answer is (8,0).

The consumption is 355 billion  .

Given,

In the question:

Consumption and savings if real domestic output is $370 billion and planned investment is $15 billion.

Now, According to the question:

Based on the given condition,

Formulate;

Aggregate expenditure (consumption)= Output - Savings= Investment

370 - 15

Calculate the sum or difference

= 355billion

Hence, The consumption is 355 billion  .

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Given:

There is a function given as below

Required:

For what value of b the given function in decreasing

Explanation:

The given function is logarithm function

also written as

The base b is determines that if the function is increasing or decreasing

here

for

for

the given function is increasing

Final answer:

The sides of the triagle have lengths:

1.1 p + 9.5 q

4.5 p - 5.2 r

5.3 r + 5.4 q

Or:

1.1 p + 0 r + 9.5 q

4.5 p - 5.2 r + 0 q

0 p + 5.3 r + 5.4 q

If we want to calculate the perimeter of the triangle, we just need to sum the three lenghts:

(1.1 + 4.5) p + (-5.2 + 5.3) r + (9.5 + 5.4) q

= 5.6 p + 0.1 r + 14.9 q

Given: The function below

To Determine: If the function as a aximum or a minimum using the first principle

Solution

Let us determine the first derivative of the given function using the first principle

So,

So

Therefore,

Please note that at critical point the first derivative is equal to zero

Therefore

At critical point the range of value of x is 0 and 2

Let us test the points around critical points

The function given has both maximum and minimum point

Hence, the maximum point is (0,0)

And the minimum point is (2, 4)