For a party, Ashley wants to make 12 hamburgers. If she has 2.964
pounds of meat, how much would each patty weigh? _________ pounds

The area of the poster in inches is,

⇒ A = 4 inches²

We have to given that;

A rectangular poster is 50 centimeters long and 25 centimeters wide.

Here, 1 centimeter is approximately 0.4 inches

Hence, Lenght = 50 cm

Lenght = 50 x 0.4

            = 2 inches

Width = 25 cm

          = 25 x 0.4

           = 1 inches

Thus, The area of the poster in inches is,

⇒ A = 1 x 4

⇒ A = 4 inches²

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The calculated measure of the angle D is (c) 32 degrees

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

The triangles ABC and DEF

The triangles are similar triangles

This means that the corresponding angles are equal

Given that

A = 32 degrees

And the corresponding angle is D

We have

D = 32 degrees

Hence, the measure of the angle is (c) 32 degrees

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Given the first term, a1=20

Common ratio, r=0.5*1/2=0.25

A geometric sequence is represented by the following expression:

We want to find the 15th term:

a) The probability that exactly one of them will be a girl = 0.3407

b) The probability that at least one of them will like the football = 0.7672

a) If we select three students then the probability that exactly one of them will be a girl

From the attached two way table we can observe that the total number of girls = 22

the total number of boys = 18

and the total number of students = 40

The possible outcomes for selecting 3 students from 40 would be,

⁴⁰C₃

Using combination formula,

⁴⁰C₃ = 40! / (3! × (40 - 3)!)

      = 9880

If there is exactly one girl then other two must be boys in the set of 3 selected students.

So, the required probability would be,

P = (²²C₁ × ¹⁸C₂) / ⁴⁰C₃

P = (22 × 153)/9880

P = 0.3407

b) The number of students like the football = 15

and the number of students who don't like the football are 40 - 15 = 25

The probability that at least one of them will like the football would be,

P = (¹⁵C₃ × ²⁵C₀ + ¹⁵C₂ × ²⁵C₁ + ¹⁵C₁ × ²⁵C₂) / ⁴⁰C₃

P = ((455 × 1) + (105 × 25) + (15 × 300)) / 9880

P = 0.7672

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Answer:

Step-by-step explanation:

g(f(x)) = x2  -1 + 2 = x2 + 1

The expression sin²x/(1+cosx) can be simplified to 1-cosθ

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Recall that sin²x = 1 - cos²x. Thus, we have:

sin²x/(1+cosx) = (1-cos²x) / (1+cosx)

                      = (1²-cos²x) / (1+cosx)

                      = (1+cosx)(1-cosx) / (1+cosx)

                      = 1-cosx

                      = 1-cosθ        (If x = θ)

Note: Using difference of two squares, 1²-cos²x = (1+cosx)(1-cosx)

Therefore, the expression sin²x/(1+cosx) can be simplified to 1-cosθ

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The function is increasing when the slope is positive so:

The function is decreasing when the slope is negative so:

and the range are the posible values of y so in this case is:

Answer:(-(3x^(3)-x-1))/((x^(2)+1)^(2))

Answer:

83 kilometres per hour =

51.574 miles per hour

Solution:

Note that:

Simplify the equation to find the word per minute.

The word per minute is 170/9 words per minute.

Typist = \(1700\)

words = 1 hour \(30\) minutes

Lets, find the word per minute :

\(1700\) words = \(1hour 30\) minutes

\(1700\) words = \(90\) minutes

\(\frac{170}{9}\) words = \(1\) minute

The word per minute is \(\frac{170}{9}\) words per minute.

Answer:

IR= 12/7

Step-by-step explanation:

Answer:

  x = 10

Step-by-step explanation:

You want the value of x in triangle RST with angle bisector UT dividing RS into parts RU=3x and US=x+2, while RT=40 and ST=16.

The angle bisector divides the sides of the triangle proportionally;

  3x/40 = (x +2)/16

  6x = 5x +10 . . . . . . . multiply by 80

  x = 10 . . . . . . . . . subtract 5x

The value of x is 10.

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The present value (PV) of the investment today is approximately $2,965.05.

To find the present value (PV) of the investment today, we need to calculate the present value of each individual contribution and then sum them up. We can use the formula for the present value of an annuity to do this calculation.

The formula for the present value of an annuity is given by:

PV = C * [(1 - (1 + r)^(-n)) / r]

Where:

PV = Present Value

C = Cash flow per period

r = Interest rate per period

n = Number of periods

In this case, the cash flow per period (C) is $500, the interest rate per period (r) is 10.5% (or 0.105), and the number of periods (n) is 20 years.

Let's plug in these values into the formula and calculate the present value (PV):

PV = $500 * [(1 - (1 + 0.105)^(-20)) / 0.105]

Using a calculator, we can evaluate the expression inside the brackets:

PV = $500 * [(1 - 0.376889) / 0.105]

Simplifying further:

PV = $500 * [0.623111 / 0.105]

PV = $500 * 5.930105

PV = $2,965.05

Therefore, the present value (PV) of the investment today is approximately $2,965.05.

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Answer:

1) 9

2) 27

3) Read explanation below!

Step-by-step explanation:

1) Use the Pythagorean theorem to find AD. Show your working

To find '?' we first have to expand the indices...

Now work out '?'

2) Find AC. Show your working

We have found out that AD is 9 and to find AC we have to add 18!

3) Is ΔABC a right triangle? Explain

We can that ΔABC is not a right angle as none of the angles in the triangle are 90°!  If it was a right angled triangle we would see the ∟sign on one of the angles. Even though there are two of those in the middle it does not count as the question is asking about ΔABC!!

Have a lovely day :)

Answer:

100

Step-by-step explanation:

<x is congruent to the angle that measures 100°.

x = 100

Answer:

100 degrees

Step-by-step explanation:

The lines under the angles show that they are congruent angles

Answer:

x = 21

Step-by-step explanation:

Adding numbers:

3x+ 18 + 4x + 15 = 180

3x + 33 + 4x = 180

Combine Like terms:

3x + 33 + 4x = 180

7x + 33 = 180

Subtract:

7x + 33 - 33 = 180-33

7x = 147

Divide:

On solving the provided question, we can say that - the range \(|x + 1| = 0\) \(x + 1 = 0 = > x = -1\) and \(y = 3\)

Finding the variable's greatest observed value (maximum) and deducting the least observed value will yield the range (minimum). Limits of variation or potential range: a variety of steel costs; several styles; The size or scope of an action or operation: insight. how far a weapon's projectile can or will travel. The number in a list or set between the lowest and maximum is referred to as a range. Line up all the numbers before locating the region. After that, take away (get rid of) the lowest number from the greatest number. The solution provides the list's range.

The regions where the absolute values are zero are known as the vertex points of an absolute value function.

\(|x + 1| = 0\\x + 1 = 0\\x = -1\)

\(y = |-1 + 1| + 3\\y= 0 + 3\\y = 3\)

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Answer:

f(5) = 16.5

Step-by-step explanation:

Substitute x = 2.5 into f(x) , that is

f(2.5) = 6(2.5) + 1.5 = 15 + 1.5 = 16.5

Answer:

16.5

Step-by-step explanation:

Answer:

769

Step-by-step explanation:

Answer:

109

Step-by-step explanation:

Answer:hi

Step-by-step explanation:

There are 23 quaters in the container in first 6 days and there are 44 quaters in the container on 13th day.

given that

on first day Jake was saved 5 quarters in the container.

Then he adds 3 quaters each day.

now find the how many quarters will he have for the first 6 days.

from the question

5 + (3 X 6) = 5 + 18 = 23

so, there are 23 quaters in the container in first 6 days.

now find how many quaters will he have on the 13th day.

from the question

5 + (3 X 13) = 5 + 39 = 44

so,there are 44 quaters in the container on 13th day.

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Answer: The quotient is 3y² + 2y - 1.

Step-by-step explanation:

You can use long division to solve this expression by setting the dividend under the roof and the divisor outside as you would normally do when dividing numbers.

1) Look at the first term of the dividend, 15y³, and the first term of the divisor, 5y. Determine what value multiplied by 5y would give you 15y³. The answer is 3y², and given the number, you multiply it by the WHOLE divisor.

3y²(5y + 6) = 15y³ + 18y² <-- subtract this from the dividend.

2) Continue this process and make sure to drag down the next term for each new value you form after subtracting. Keep in mind of any negative values! When you reach up to -5y, determine what value multiplied by 5y would give you the value of -5y, which would be -1.

3) You should be left with a remainder of 0, leaving you with a quotient of 3y² + 2y - 1.

Answer:

How do you do synthetic division fast?

Synthetic division is another way to divide a polynomial by the binomial x - c , where c is a constant.

Step-by-step explanation:

g(x) = 2x^2

for g(- 4), you just plug in - 4 for x

g(- 4) = 2(- 4)^2

g(- 4) = 2(16)

g(- 4) = 32

Answer:

g(-4) = 32

Step-by-step explanation:

Given the quadratic function, g(x) = 2x², finding the output value given g(-4) involves substituting the value of the input, x = -4, into the function.

g(x) = 2x²

g(-4) = 2(-4)² = 2(-4)(-4)

g(-4) = 2(16)  

g(-4) = 32

Therefore, g(-4) = 32.

Note that in the prompt above, the value of x is given as: 16°

To answer the issue, we will first name all of the points supplied to us on the isosceles triangle, then identify O, and last discover the value of x. See the attached image.

As a result, an isosceles triangle has two equal sides and two equal angles. The term is derived from the Greek words iso (same) and skelos (skull) (leg). An equilateral triangle has all of its sides equal, whereas a scalene triangle has none of its sides equal.

In ΔAOB

OA =  OB = R, the radius of the circle O,

therefore, the ΔAOB is an isosceles triangle, with OA, OB as the congruent sides and AB as the base of the triangle.

Thus, ∠OAB = ∠OBA = 53°

Sum of all the angles of a triangle = 180°

∠O + ∠AOB + ∠OBA = 180°

We know ∠AOB = ∠OBA, therefore,

∠O + 2(∠AOB) = 180°

∠O + 2(53°) = 180°
∠O = 180 - 106

∠O = 74°

In ΔOBC,

BC is the tangent to the circle O, therefore,

∠OBC = 90°

Sum of all the angles of a triangle = 180°

∠O + ∠OBC + ∠OCB = 180°

74° + 90° + ∠OCB = 180°

∠OCB = 180° - 74° - 90°

∠OCB = 16°

Hence, the value of x is 16°.

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Answer:

What is a linear function? A linear function is a function whose graph is a straight line. The rate of change of a linear function is constant. The function shown in the graph below, y = x + 2, is an example of a linear function.

Graph of linear function

Graph of linear function

A linear function has a constant rate of change. The rate of change is the slope of the linear function. In the linear function shown above, the rate of change is 1. For every increase of one in the independent variable, x, there is a corresponding increase of one in the dependent variable, y. This gives a slope of 1/1 = 1.

A linear function is typically given in the form y = mx + b, where m is equal to the slope, or constant rate of change.

Examples of linear functions include:

If a person drives at a constant speed, the relationship between the time spent driving (independent variable) and the distance traveled (dependent variable) will remain constant.

Assuming no change in price, the relationship between the number of pounds of bananas a person buys (independent variable) and the total cost of the bananas (dependent variable) will remain constant.

If a person earns an hourly wage at their job, the relationship between the time spent working (independent variable) and the amount earned (dependent variable) will remain constant.

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Exponential Functions

What is an exponential function? An exponential function is a function that involves exponents and whose graph is a smooth curve. The rate of change in an exponential function is not constant. The functions shown in the graph below, y = 0.5x and y = 2x, are examples of exponential functions.

Graphs of exponential functions

Graphs of exponential functions

An exponential function does not have a constant rate of change. The rate of change in an exponential function is the value of the independent variable, x. As the value of x increases or decreases, the rate of change increases or decreases as well. Rather than a constant change, as in the linear function, there is a percent change.

An exponential function is typically given in the form y = (1 + r)x, where r represents the percent change.

Examples of exponential functions include:

Step-by-step explanation: