How many combinations are possible if you select one flavor of ice cream and one
topping?
Flavors Toppings
vanilla
chocolate
strawberry
fudge
marshmallow
caramel

Answer: I THINK 250

Step-by-step explanation: 125 is half and 125 times 2 is 250.

Answer:

The number of license plates that can be made is 1,757,600

Step-by-step explanation:

Here, we want to calculate the number of possible license plates

We do not have any restrictions here.

the number of digits is 0-9 making 10

Alphabets A-Z making 26

For two letters, one digit , one letter , one digit

1st letter

Number of choices is 26

second letter 26 too

1st digit 10 choices

third letter = 26 choices

last digit = 10 choices

Total number of choices will be;

26 * 26 * 10 * 26 * 10 = 1,757,600

Answer:

C

Step-by-step explanation:

i just did that question and got it right!!

The third side cannot connect to complete the triangle, we can conclude that the side lengths 6, 6, and 14 do not form a triangle.

What is the triangle inequality theorem?

The triangle inequality theorem states that the sum of the length of two sides must be greater than the length of the third side of that triangle.

No, the side lengths 6, 6, and 14 do not form a triangle.

To see why, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, if we add the two shorter sides 6 and 6, we get 12, which is less than the length of the longest side 14.

Therefore, the three side lengths cannot form a triangle.

We can also visualize this by trying to draw a triangle with sides of length 6, 6, and 14.

If we draw two equal-length sides of 6 units each and try to connect them with a third side of length 14 units, we will see that the third side is too long and cannot connect to form a triangle.

See the following diagram for an illustration in the attached image.

Hence, the third side cannot connect to complete the triangle, we can conclude that the side lengths 6, 6, and 14 do not form a triangle.

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The Calf weigh about 75 kg.

Given data :

The total weight of a giraffe and her calf is 904 kilograms.

Weight of the giraffe is 829 kg

So the weight of the calf = Total weight - weight of giraffe

                                         =  904 - 829 = 75

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Research Report:

Title: The Number of Coins Carried by Teachers

Introduction:

This research report aims to investigate the number of coins carried by teachers. The study seeks to understand the reasons behind carrying coins and whether there are any patterns or correlations between the number of coins and certain factors such as age, gender, and occupation.

The data was collected through a survey distributed among teachers from various educational institutions. The findings of this study provide insights into teachers' habits and preferences when it comes to carrying coins.

Results and Analysis:

A total of 300 teachers participated in the survey. The data revealed that the majority of teachers (60%) carry less than 5 coins, while 25% carry between 5 and 10 coins. Only a small percentage (15%) reported carrying more than 10 coins.

Further analysis based on demographic factors indicated that age and occupation had a significant influence on the number of coins carried. Older teachers were more likely to carry fewer coins, with 70% of teachers above the age of 50 carrying less than 5 coins.

Additionally, primary school teachers tended to carry more coins compared to secondary school teachers.

Discussion and Interpretation:

The findings suggest that the number of coins carried by teachers is influenced by various factors.

Teachers may carry coins for a range of reasons, such as purchasing small items, providing change for students, or utilizing vending machines.

The lower number of coins carried by older teachers could be attributed to a shift towards digital payment methods or a preference for carrying minimal cash.

The discrepancy between primary and secondary school teachers could be due to differences in daily activities and responsibilities.

This research provides valuable insights into the habits and preferences of teachers regarding the number of coins they carry.

Understanding these patterns can assist in designing more efficient payment systems within educational institutions and potentially guide the development of tailored financial solutions for teachers.

Further research could explore the reasons behind carrying coins in more depth and investigate how the digitalization of payments affects teachers' behavior in different educational contexts.

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The tangent to the curve at a point P (x, y) has slope dy/dx at that point. By the chain rule,

dy/dx = (dy/dθ) / (dx/dθ)

We're in polar coordinates, so

y (θ) = r (θ) sin(θ)   ==>   dy/dθ = dr/dθ sin(θ) + r (θ) cos(θ)

x (θ) = r (θ) cos(θ)   ==>   dx/dθ = dr/dθ cos(θ) - r (θ) sin(θ)

We're given r (θ) = 1 - sin(θ), so that

dr/dθ = -cos(θ)

Then the slope of the tangent to the curve at P is

dy/dx = (dr/dθ sin(θ) + r (θ) cos(θ)) / (dr/dθ cos(θ) - r (θ) sin(θ))

dy/dx = (-cos(θ) sin(θ) + (1 - sin(θ)) cos(θ)) / (-cos²(θ) - (1 - sin(θ)) sin(θ))

dy/dx = - (cos(θ) - sin(2θ)) / (sin(θ) + cos(2θ))

The tangent is horizontal if dy/dx = 0 (or when the numerator vanishes):

cos(θ) - sin(2θ) = 0

cos(θ) - 2 sin(θ) cos(θ) = 0

cos(θ) (1 - 2 sin(θ)) = 0

cos(θ) = 0   or   1 - 2 sin(θ) = 0

cos(θ) = 0   or   sin(θ) = 1/2

[θ = π/2 + 2nπ   or   θ = 3π/2 + 2nπ]   or   [θ = π/6 + 2nπ   or   θ = 5π/6 + 2nπ]

where n is any integer.

In the interval 0 ≤ θ ≤ 2π, we get solutions of θ = π/6, θ = 5π/6, and θ = 3π/2. (We omit π/2 because the denominator is zero at that point and makes dy/dx undefined.) So the points where the tangent is horizontal are themselves (√3/4, 1/4), (-√3/4, 1/4), and (0, -2), respectively.

The tangent is vertical if 1/(dy/dx) = 0 (or when the denominator vanishes):

sin(θ) + cos(2θ) = 0

sin(θ) + (1 - 2 sin²(θ)) = 0

2 sin²(θ) - sin(θ) - 1 = 0

(2 sin(θ) + 1) (sin(θ) - 1) = 0

2 sin(θ) + 1 = 0   or   sin(θ) - 1 = 0

sin(θ) = -1/2   or   sin(θ) = 1

[θ = 7π/6 + 2nπ   or   θ = 11π/6 + 2nπ]   or   [θ = π/2 + 2nπ]

Then for 0 ≤ θ ≤ 2π, the tangent will be vertical for θ = 7π/6 and θ = 11π/6, which correspond respectively to the points (-3√3/4, -3/4) and (3√3/4, -3/4). (Again, we omit π/2 because this makes dy/dx non-existent.)

Answer:

  x = 3

Step-by-step explanation:

Maybe you want the value of x such that ...

  4(6^x) = 864

Dividing by 4 gives ...

  6^x = 216

You may know that 216 = 6^3. Using that, we can equate exponents:

  6^x = 6^3

  x = 3

Alternatively, we can use logarithms to find x. Taking logs gives ...

  x·log(6) = log(216)

  x = log(216)/log(6) = 3

Answer:

1) P(1,0)Q(-2,3)R(-3,3)S(3,2)

2) (3,4)

3) (0,-4)

4) (1,2)

Step-by-step explanation:

Answer:

8 ounces

Step-by-step explanation:

Since there was 1 pint left, that means the mug had 1/2 pints of coffee.

Now, convert this to ounces. There are 16 ounces in a pint, so we can find how many ounces there were by multiplying 16 by 1/2

16(1/2)

= 8

So, there were 8 ounces of coffee in the mug

Answer:(2I3O-9247)

Step-by-step explanation:

1 times 2 is equal to 2.

Multiplication is a mathematical operation that combines two numbers (known as "factors") to produce a third number (known as the "product"). It is represented using the symbol "x" or the asterisk (*).

For example, consider the multiplication of the numbers 2 and 3:

2 x 3 = 6

Here, 2 and 3 are the factors, and 6 is the product. Multiplication is a type of arithmetic operation that can be used to find the total number of items in a set, the area of a rectangle, the volume of a rectangular prism, and many other quantities.

In summary, multiplication is a mathematical operation that combines two numbers to produce a third number, and it is represented using the symbol "x" or the asterisk (*). It is an important operation in mathematics, used to find the total number of items in a set, the area of a rectangle, the volume of a rectangular prism, and many other quantities.

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Answer:

10

Step-by-step explanation:

Distance formula:

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Let \((x_1,y_1)\) = (-4, 2)

Let \((x_2,y_2)\) = (2, -6)

Substituting given points into the formula:

\(\implies d=\sqrt{(2-(-4))^2+(-6-2)^2}\)

\(\implies d=\sqrt{(6)^2+(-8)^2}\)

\(\implies d=\sqrt{36+64}\)

\(\implies d=\sqrt{100}\)

\(\implies d=10\)

Answer:

0

Step-by-step explanation:

x² + 26 = 0 ( subtract 26 from both sides )

x² = - 26 ( take square root of both sides )

x = ± \(\sqrt{-26}\)

\(\sqrt{-26}\) ← has no real solutions

Answer:

0

Step-by-step explanation:

Look above goofy, have a good day!

Answer: 14,605 pieces.

Step-by-step explanation:

In the second quarter, the company produced 795 pieces more than in the first quarter.

So, the total pieces produced in the second quarter can be calculated as:

6905 + 795 = 7700

The total pieces produced in the first semester (two quarters) can be calculated as:

6905 + 7700 = 14,605

Therefore, the company produced 14,605 pieces in the first semester.

The number of pieces the company produced in the first semester was 14,605 pieces.

The question asks to calculate how many pieces a company produced in the first semester, considering the production of two quarters.

In the first quarter, the company produced 6,905 pieces, as indicated in the question.

Already in the second quarter, the company produced 795 more pieces than in the first quarter, which means that the production in the second quarter was:

6,905 + 795 = 7,700 pieces.

To know the company's total production in the first semester, just add the productions of the two quarters:

6,905 + 7,700 = 14,605 pieces

The angle measures for this problem are given as follows:

The sum of the measures of the internal angles of a triangle is of 180º.

The triangle in this problem is ABC, hence the measure of a is obtained as follows:

a + 68 + 50 = 180

a = 180 - (68 + 50)

a = 62º.

c and d are corresponding angles to angle a, as they are on the same position relative to parallel lines, hence their measures are given as follows:

Angle b is a corresponding interior angle with angle a, hence they are supplementary and it's measure is given as follows:

a + b = 180

62 + b = 180

b = 118º.

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Answer:

82

Step-by-step explanation:

6^3/(2x6)+64=?

216/12+64=82

Answer:

82

Step-by-step explanation:

6^3÷2 X 6 + 64= 216/12 + 64 = 18 + 64 = 82

To rewrite the expression -2(n-7) using the distributive property, we need to distribute the -2 to both terms inside the parentheses. The distributive property states that for any numbers a, b, and c:

a(b + c) = ab + ac

Applying this property to the given expression:

-2(n-7) = -2 * n + (-2) * (-7)

Simplifying further:

-2(n-7) = -2n + 14

Therefore, the rewritten expression is -2n + 14.

Answer:

2(17)+8

Step-by-step explanation:

answer: 2(17+8)

explanation: 17+8=  25

25 times 2= 50

34+16=50

:)

Answer:

Let's start by assigning a variable to Susan's present age. Let's call it "x".

According to the problem, in seven years, Susan will be "x + 7" years old.

Three years ago, Susan was "x - 3" years old.

The problem tells us that Susan will be 2 times as old in seven years as she was 3 years ago. So we can set up the following equation:

x + 7 = 2(x - 3)

Now we can solve for x:

x + 7 = 2x - 6

x = 13

Therefore, Susan's present age is 13 years old.

Let's assume Susan's present age is "x" years. According to the information provided, "Susan will be 2 times old in seven years as she was 3 years ago."

Seven years from now, Susan's age would be x + 7, and three years ago, her age would have been x - 3. According to the given statement, her age in seven years will be two times her age three years ago:

x + 7 = 2(x - 3)

Let's solve this equation to find Susan's present age:

x + 7 = 2x - 6

Subtracting x from both sides:

7 = x - 6

Adding 6 to both sides:

13 = x

Therefore, Susan's present age is 13 years.

Answer:

Step-by-step explanation:

You want to identify the x-intercepts on the graph.

An "x-intercept" is a point where the graph crosses or touches (intercepts) the x-axis. The y-value there is always 0.

The given graph crosses the x-axis where x = -2 and x = 3. This means the x-intercept points are ...

  (-2, 0) and (3, 0)

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Answer:

man's age = 54

daughter's age = 18

Step-by-step explanation:

x = man's age

y = daughters age

x = 3y

x - y = 36

substitute for x:

3y -y = 36

2y = 36

y = 18

x = 54

If a man has a daughter who is three times his age. The father and daughter will be 54 and 18, respectively, assuming their ages are 36 years distant.

Equations are statements that affirm the equivalence of two expressions that are joined by the equals symbol "=". An equal sign ("=") links two expressions together to form an equation. The two expressions on each side of the equals sign are referred to as the "left-hand side" and "right-hand side" of the equation.

It is given that, A man is three times as old as his daughter. If the difference in their ages is 36 years,

We have to find the ages of the father and daughter.

Suppose the age of the father and daughter will be x and y respectively.

If the man is three times as old as his daughter,

x = 3y

If the difference in their ages is 36 years

x - y = 36

Put the value of x as,

3y -y = 36

2y = 36

y = 18

x = 54

Thus, if a man has a daughter who is three times his age. The father and daughter will be 54 and 18, respectively, assuming their ages are 36 years distant.

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Answer:8

Step-by-step explanation:8x1=8

Answer:

1.L=4;W=3;P=14

2.L=6;W=2;P=16

3.L=12;W=1;P=26

Step-by-step explanation:

because i know

Note that the longest segment in the shapes shown is DC (Option B).

The longest side of a triangle is opposite to greatest angle.

To determine the longest side in a triangle, compare the lengths of all three sides. The side with the greatest length is the longest side.

You can use a ruler or a measuring tool to measure the lengths of the sides or compare the numerical values if they are provided.

In this case,

∠A = ∠DBA = 60°

So ∠ ABD is an equilateral triangle.

So, AB = BD = AD

Since

AB = BC

Then

∠BDC = ∠C ∠ 38°

so ∠DBC > 90°

This means that DC is the longest side.

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1: y=8, (-2,8)

2: y=6, (-1,6)

3: y=0, (2,0)

Step-by-step explanation:

Insert the x value into each equation then see what value of y that you need to get 4 on the right hand side of the equation.

The graph of the system of the inequalities is attached.

To graph the inequalities y < -x - 4 and y ≥ (3/5)x + 4, we can start by graphing the corresponding equations and then shade the appropriate regions based on the inequality signs.

Let's begin with the equation y = -x - 4:

Choose a range of x-values to plot.

For simplicity, let's use x-values from -10 to 10.

Substitute different x-values into the equation to find corresponding y-values.

For example:

When x = -10, y = -(-10) - 4 = 10 - 4 = 6.

When x = 0, y = -(0) - 4 = -4.

When x = 10, y = -(10) - 4 = -10 - 4 = -14.

Plot these points on the coordinate plane and draw a straight line passing through them.

This line represents the equation y = -x - 4.

Next, let's graph the equation y = (3/5)x + 4:

Again, choose a range of x-values to plot. Let's use the same range of -10 to 10.

Substitute different x-values into the equation to find corresponding y-values. For example:

When x = -10, y = (3/5)(-10) + 4 = -6 + 4 = -2.

When x = 0, y = (3/5)(0) + 4 = 0 + 4 = 4.

When x = 10, y = (3/5)(10) + 4 = 6 + 4 = 10.

Plot these points on the coordinate plane and draw a straight line passing through them.

This line represents the equation y = (3/5)x + 4.

Now, let's shade the regions based on the inequalities:

For y < -x - 4, we need to shade the region below the line y = -x - 4.

For y ≥ (3/5)x + 4, we need to shade the region above or on the line y = (3/5)x + 4.

Hence, the region where the shaded regions overlap represents the solution to both inequalities.

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Answer:

\((a)\) \(P(x) = 0.02x^2 +50x - 100\)

\((b)\) \(Average = 0.02x + 50 - \frac{100}{x}\) and \(Marginal = 0.04x + 50\)

\((c)\) \(Average = 59.8\) and \(Marginal = 70\)

(d) See Explanation

Step-by-step explanation:

Given

\(p(x) = 100\)

\(C(x) = -0.02x^2 +50x +100\)

Solving (a) Profit function; P(x)

\(P(x) = xp(x) - C(x)\)

This gives:

\(P(x) = x*100 - (-0.02x^2 + 50x + 100)\)

\(P(x) = 100x + 0.02x^2 - 50x - 100\)

Collect like terms

\(P(x) = 0.02x^2 - 50x +100x - 100\)

\(P(x) = 0.02x^2 +50x - 100\)

Solving (b): Average profit function and Marginal profit function

\(Average = \frac{P(x)}{x}\)

This gives:

\(Average = \frac{0.02x^2 + 50x - 100}{x}\)

Break down the fraction

\(Average = \frac{0.02x^2}{x} + \frac{50x}{x} - \frac{100}{x}\)

\(Average = 0.02x + 50 - \frac{100}{x}\)

\(Marginal = \frac{dP}{dx}\)

\(P(x) = 0.02x^2 +50x - 100\)

Differentiate

\(\frac{dP}{dx} = 2 * 0.02x + 50 - 0\)

\(\frac{dP}{dx} = 0.04x + 50\)

Hence:

\(Marginal = 0.04x + 50\)

Solving (c): Average profit and Marginal profit if x = a

\(a = 500\)

So:

\(x =500\)

Substitute 500 for x

\(Average = 0.02x + 50 - \frac{100}{x}\)

\(Average = 0.02 * 500 + 50 - \frac{100}{500}\)

\(Average = 59.8\)

\(Marginal = 0.04x + 50\)

\(Marginal = 0.04*500 + 50\)

\(Marginal = 70\)

Solving (d): Interpret the values in (c)

\(Average = 59.8\)

They make a profit of 59.8 for the first 500 items

\(Marginal = 70\)

From the 501st item, the profit is 70

Answer:

If you have to do the sliders problem the answeres in order are, set a to -3, set b to 2 and keep c at 0.

Step-by-step explanation:

the correct answer is y=-3 sin(2x) and the equation from the sliders should match the answer.

y=-3 sin(2x) is the equation has a maximum at (0, –1) and a minimum at ( pi Over 3, negative 5)

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given,

We need to use the sliders to change the values of a, b, c, and d in the cosine function.

We need to find the equation which has maximum at (0, –1) and a minimum at (pi Over 3, negative 5)).

While doing slider problems we have to set the values as set a to -3, set b to 2 and keep c at 0.

y=-3 sin(2x) is the answer and the equation from the sliders should match the answer.

Hence y=-3 sin(2x) is the equation has a maximum at (0, –1) and a minimum at ( pi Over 3, negative 5)

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