at a coffee shop, they offer 10 different drinks and four different desserts. how many ways can two people order the same drink but a different dessert. Show your work

Always check the quantity in each package to determine the appropriate number of hotdog bun packages needed for the given number of hotdog packages.
The dependent variable in this situation is the number of packages of hotdog buns needed, as it relies on the number of packages of hotdogs (the independent variable).

We want to know the dependent variable when considering the number of packages of hotdog buns needed for a certain number of packages of hotdogs.

Let me explain this relationship:
First, let's define the terms involved.

The dependent variable is the variable that depends on another variable (called the independent variable).

In this case, we are examining the relationship between the number of packages of hotdogs and the number of packages of hotdog buns needed.
The independent variable is the number of packages of hotdogs.

This is because the number of hotdog buns needed depends on the number of hotdogs you have.
The dependent variable, in this case, is the number of packages of hotdog buns needed.

This variable depends on the number of packages of hotdogs, as you need a certain amount of buns to accommodate the hotdogs.

To determine the relationship between these two variables, we would likely use a proportion or a ratio.

For example, if one package of hotdogs contains 10 hotdogs and one package of hotdog buns contains 10 buns, then the ratio is 1:1, meaning you need one package of hotdog buns for every package of hotdogs.
This relationship may vary depending on the number of hotdogs and buns in each package.

Remember to examine the proportion between the two variables to ensure you have the correct amount of buns for the hotdogs.

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the third side must be greater than 8 and less than 16.

To determine the range of possible lengths for the third side of the triangle, we can use the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side.

So, for a triangle with sides of 4 and 12, the third side must satisfy:

12 - 4 < third side < 12 + 4

which simplifies to:

8 < third side < 16

what is triangle?

A triangle is a geometric shape with three sides and three angles. It is formed by connecting three non-collinear points in a plane. The sum of the interior angles of a triangle is always 180 degrees, and there are various types of triangles based on their side lengths and angle measures.

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Answer:

Team Blue

Step-by-step explanation:

The reason this is, is because for each day that passes, they make 5 more light bulbs. This is in relation to the days that pass.

Answer:12

Step-by-step explanation:

3x+3x+x+x=16

8x=16 so x =2

2*3=6 6*2=12

Answer:

12 sq ft

Step-by-step explanation:

let w = width

let 3w = length

w + w + 3w + 3w = 16

8w = 16

x = 2

Area = 3(2) x 2

A = 6 x 2

Let's calculate the products and check if they indeed have the same value:

Product of 32 and 46:

32 * 46 = 1,472

Reverse the digits of 23 and 64:

23 * 64 = 1,472

As you mentioned, the products are the same. This phenomenon is not unique to this particular pair of numbers. In fact, it occurs with any pair of two-digit numbers whose digits, when reversed, are the same as the product of the original numbers.

To find two other pairs of two-digit numbers that have this property, we can explore a few examples:

Product of 13 and 62:

13 * 62 = 806

Reversed digits: 31 * 26 = 806

Product of 17 and 83:

17 * 83 = 1,411

Reversed digits: 71 * 38 = 1,411

As for determining if a given pair of two-digit numbers will have this property without actually performing the multiplication, there is a simple rule. For any pair of two-digit numbers (AB and CD), if the sum of A and D equals the sum of B and C, then the products of the original and reversed digits will be the same.

For example, let's consider the pair 25 and 79:

A = 2, B = 5, C = 7, D = 9

The sum of A and D is 2 + 9 = 11, and the sum of B and C is 5 + 7 = 12. Since the sums are not equal (11 ≠ 12), we can determine that the products of the original and reversed digits will not be the same for this pair.

Therefore, by checking the sums of the digits in the two-digit numbers, we can determine whether they will have the property of the products being the same when digits are reversed.

Answer:

x = 5 ± \(\sqrt{17}\)

Step-by-step explanation:

Given

x² - 10x + 25 = 17 ← left side is a perfect square, thus

(x - 5)² = 17 ( take the square root of both sides )

x - 5 = ± \(\sqrt{17}\) ( add 5 to both sides )

x = 5 ± \(\sqrt{17}\)

Thus

x = 5 - \(\sqrt{17}\)

x = 5 + \(\sqrt{17}\)

The arc length of the circle with radius 16m and central angle 50 degrees is 13.9m

According to the given question.

The radius of the circle = 16m

Central angle, θ = 50 degrees

As, we know that the arc length of the circle, s with the radius r and central angle θ by using the formula

s = θ × (π /180)r

Therefore, the arc length of the circle with radius 16m and central angle 50 degrees is given by

s = 50 × ( 3.14/180) 16

⇒ s = 50 × 0.0174 × 16

⇒ s = 13.9 m

Hence, the arc length of the circle with radius 16m and central angle 50 degrees is 13.9m.

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Answer:

\(\mathrm{18.84\ sq.\ miles}\)

Step-by-step explanation:

\(\mathrm{Solution,}\\\mathrm{We\ have,}\\\mathrm{diameter\ of\ the\ circle(d)=6\ miles}\\\mathrm{So,\ radius(r)=\frac{d}{2}=6\div 2=3}\\\mathrm{Now,}\\\mathrm{Circumference\ of\ circle=2\pi r=2(3.14)(3)=18.84\ square\ miles}\)

The circumference of the circle is :

Solution:

To find the circumference of the circle, we will use the formula :

\(\sf{C=\pi d}\)

I plug in the data

\(\sf{C=3.14\times6}\)

\(\sf{C=18.84\:miles}\)

When k is o doesn't satisfy the equation.

Value of \($\mathrm{k}=(?)$\), equation \($\mathrm{kx}(\mathrm{x}-2)+6=0$\) has equal roots.

\(& \Rightarrow \mathrm{kx}(\mathrm{x}-2)+6=0 \\\)

\(& \mathrm{kx} x^2-2 \mathrm{kx}+6=0 \\\)

two roots of quadratic equation

\(& \alpha, \beta= \frac{-\mathrm{b} \pm \sqrt{\mathrm{b}^2-4 \mathrm{ac}}}{2 \mathrm{a}} \\\)

\(& \alpha, \beta= \frac{+2 \mathrm{k} \pm \sqrt{(-2 \mathrm{k})^2-4 \times 6 \times \mathrm{k}}}{2 \times \mathrm{k}} \\\)

\(& \alpha, \beta=2 \mathrm{k} \frac{\pm \sqrt{4 \mathrm{k}^2-24 \mathrm{k}}}{2 \mathrm{k}} \\\)

\(\alpha=\beta \\\) The roots are qual

\(& \Rightarrow \frac{2 \mathrm{k}+\sqrt{4 \mathrm{k}^2-24 \mathrm{k}}}{2 \mathrm{k}}=\frac{2 \mathrm{k}-\sqrt{4 \mathrm{k}^2-24 \mathrm{k}}}{2 \mathrm{k}} \\\)

\(& \Rightarrow 2 \sqrt{4 \mathrm{k}^2-24 \mathrm{k}}=0 \\\)

\(& \Rightarrow 4 \mathrm{k}^2-24 \mathrm{k}=0 \\\)

\(& \Rightarrow 4 \mathrm{k}(\mathrm{k}-6)=0 \\\)

\(& \Rightarrow \mathrm{k}=0 \text { or } \mathrm{k}=6\)

\($\Rightarrow \mathrm{k}=6[\because \mathrm{k} \equiv 0]$\) as\($\mathrm{k}=0$\)  doesn't satisfy the equation.

The complete question is,

For what value of \($\mathrm{k}$\), are the roots of the quadratic equation, \($\mathrm{kx}(\mathrm{x}-2)+6=0$\) equal?

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Answer: The difference between sum of first 20032003 even numbers and sum of first 20032003 odd numbers is “-20032003”.

Step-by-step explanation:

The sum of first 20032003 even numbers:

\(Summation E=E_{1}+E_{2}+E_{3}+ . . . . . +E_{20032003}\)

The sum of first 20032003 odd numbers:

\(Summation O=O_{1}+O_{2}+O_{3}+ . . . . . +O_{20032003}\)

Difference between the sum of first 20032003 even numbers and the sum of first 20032003 odd numbers:

\(Difference=Summation E - Summation O=(E_{1}+E_{2}+E_{3}+ . . . . . . . +E_{20032003})-(O_{1}+O_{2}+O_{3}+ . . . . . . . +O_{20032003})\)

\(Difference=(E_{1}-O_{1})+(E_{2}-O_{2})+(E_{3}-O_{3})+ . . . . . . . +(E_{20032003}-O_{20032003})\)

Even numbers start as 0, 2, 4, 6…. While odd numbers start as 1, 3, 5, 7…..

(assuming that we are taking non-negative even/odd numbers into account only)

As we know, every nth even number is one behind their respective odd number (i.e. 0 lags 1, 2 lags 3, 4 lags 5 and so on)

Thus, our equation of difference becomes,

\(Difference=(-1)_{1}+(-1)_{2}+(-1)_{3}+ . . . . . . . +(-1)_{20032003} =(-1)*20032003=-20032003\)

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Answer:

find the value of the inequality on the number line

Step-by-step explanation:

do open circle for greater or less than

do closed circle for equal to

draw line left or right based on greater or less than

Answer:

Step-by-step explanation:find the value of the inequality on the number line

The roots of the given equation x² + 4x + 29 = 0 are -2 + 5i and -2 - 5i in simplest a + bi form

Given, the quadratic equation is x² + 4x + 29 = 0

We can find the roots of this quadratic equation using the quadratic formula, that is,

x = [-b ± √(b² - 4ac)] / 2a

where a, b and c are the coefficients of x², x, and the constant term, respectively.

So, comparing the given equation with the general form of quadratic equation ax² + bx + c = 0,

we have a = 1, b = 4 and c = 29

Now, substituting these values in the quadratic formula, we have the roots as:

x = [-4 ± √(4² - 4(1)(29))] / 2(1)

x = [-4 ± √(16 - 116)] / 2

x = [-4 ± √(-100)] / 2

x = [-4 ± 10i] / 2

x = (-4/2) ± (10i/2)x = -2 ± 5i

Therefore, the roots of the given equation x² + 4x + 29 = 0 are -2 + 5i and -2 - 5i in simplest a + bi form.

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Since the p-value is greater than the commonly used significance level of 0.05, we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that union efforts to organize have increased union membership.

We can use a one-sample proportion test to determine if the proportion of union members in the sample is significantly different from the population proportion of 11.3%.

The null hypothesis is that the population proportion is equal to 11.3%:

H0: p = 0.113

The alternative hypothesis is that the population proportion is greater than 11.3%:

Ha: p > 0.113

The sample proportion is P = 58/400

= 0.145

The standard error of the sample proportion is:

SE = √(p*(1-p)/n)

= √(0.113*(1-0.113)/400)

= 0.0197

The test statistic is:

z = (P - p) / SE

= (0.145 - 0.113) / 0.0197

= 1.6244

The p-value for this test is the probability of getting a z-score of 1.6244 or greater, assuming the null hypothesis is true:

p-value = P(Z > 1.6244)

= 0.0515 (using a standard normal distribution table)

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A correlation coefficient between average temperature and coat sales exists most likely to be between 0 and -1.

The correlation coefficient exists as the exact measure that quantifies the power of the linear relationship between two variables in a correlation analysis. A correlation coefficient between average temperature and coat sales exists most likely to be between 0 and -1.

A negative correlation suggests two variables that tend to move in opposite directions. A correlation coefficient of -0.8 or lower displays a strong negative relationship, while a coefficient of -0.3 or lower signifies a very weak one.

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Answer:

0 and -1

Step-by-step explanation:

Got it right on the test.

Applying the knowledge of algebraic equations, we have:

21. x = -5

23. x = -2

24. 35, 37, 39

27. W = V/LH

28.  B = (A - PH)/2

In algebra, to solve for any variable, we have to make the variable the subject of the formula by isolating the variable to one side of the algebraic equation.

21. Let the unknown number = x. The algebraic equation that would be used to find x is:

x - 6 = -11

Solve for x

x = -11 + 6

x = -5

23. Let the unknown number = x. Thus, the algebraic equation to be created to find x would be:

5x - 1 = -11

Solve for x

5x = -11 + 1

5x = -10

x = -10/5

x = -2

24. Odd numbers cannot be divided by 2 without a remainder, so, the consecutive odd numbers that have a sum of 111 are: 35, 37, 39

27. V = LWH

Solve for W

V/LH = W

W = V/LH

28.  A = PH + 2B

Solve for B in the equation

A - PH = PH + 2B - PH

A - PH = 2B

Divide both sides by 2

(A - PH)/2 = B

B = (A - PH)/2

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Answer:

21:x=17

23:x=-2

24:35,37,39

27:V/LH

28:B=(A-PH)/2

Step-by-step explanation:

21: To find the difference between 6 and -11, you can do 6-(-11). Since the two negatives cancel out into positive, it will become 6+11 which is 17.

23: So we know that -11 is 1 added to 5 times a number. Let's just use x for the number. So we have 5x+(-1)=-11 or 5x -1=-11. So we move the negative 1 to the other side and make the sign in front of it a positive. It would look like this: 5x=-11+1, which is also 5x=-10, so x=10/5 or -2.

24: You first do 111/3 which is 37. Then on the left side, you take away to from 37 since it wants it to be odd, and on the right side, you add 2 to get 39. So, it will look like: 35,37,39.

27: V=LWH, W=V/LH.

28: A - PH = PH + 2B - PH, A - PH = 2B, (A - PH)/2 = 2B/2, B = (A - PH)/2.

Answer:

30+20w=250

w=11

Step-by-step explanation:

To do this, write this equation because 30 is what she had and 20w is the weeks. We don't know the weeks so use w. Finally, put=250

30+20w=250

To solve this, do 250-30=220

So 20w=220

Divide 220/20

W=11

Answer:

11 weeks

Step-by-step explanation:

The equation would be 20w + 30 = 250

so, we need to solve w.

20w + 30 = 250

- 30 - 30

20w = 220

___ ____

20 20

w = 11

Answer:

D. 130 ft

Step-by-step explanation:

bob walks from his school 50 feet north and then walls 120 feet east. what is the shortest distance bob is from the school

A 170ft

B 165 ft

C 70 ft

D130 ft

Bob in his path forms a right angle, so the shortest distance for the school is the hypotenuse, and we solve it with the Pythagorean theorem.

√(120²+50²) =

√(14400 + 2500) =

√16900 =

130 ft

Answer:

2/3

Step-by-step explanation:

You arrived at 1:00 and longer than 10 minutes would be at 1:20 and 1:30

that is 2 chances of you waiting longer than 10 minute

By identifying type of sequence we got that recursive definition for the sequence -6, -10, -14, -18... is  

A sequence is collection of numbers with a particular pattern.

Here given sequence is

-6, -10, -14, -18...

\(a_1=-6\)

\(a_2=-10\)

\(a_3=-14\)

\(a_4=-18\)

\(a_2-a_1=-6+-10=-16\)

\(a_3-a_2=-14+-10=-24\)

\(a_4-a_3=-18+-14=-32\)

Hence this is an AP with a = -1 and d = -18

So general term of this AP can be written as

So difference of any consecutive terms is equal to -18

\(a_n-a_{n-1}=-18\)

\(a_n-a_{n-1}+-18\)

By identifying type of sequence we got that recursive definition for the sequence -6, -10, -14, -18... is \(a_n-a_{n-1}+-18\)

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Answer: variability between means increases relative to the variability within groups

Step-by-step explanation:

The formula to calculate F-ratio : variance between groups divided by variance within groups

Here, F-ratio \(\propto\) is proportional to variance between groups but inversely proportional to variance within groups .

So, F-ratio increases when variability between means increases relative to the variability within groups.

Answer:

The main branches of mathematics are algebra, number theory, geometry and arithmetic.

Answer:

The main branches of mathematics are algebra, number theory, geometry and arithmetic. Based on these branches, other branches have been discovered.

Answer:

a)139°

Step-by-step explanation:

two co interior angles make one opposite exterior angle

49+90=139°

It is an unlike term

Step-by-step explanation:

hope this helps you

By analyzing the graph's features, you can determine which rational function it represents.

A rational function is a fraction of two polynomial functions, where the denominator is not zero. Rational functions can have vertical asymptotes, where the denominator equals zero and the function is undefined.

They can also have horizontal asymptotes, where the degree of the numerator and denominator functions is equal and the coordinates of the leading term are the same. The graph of a rational function can also have slant asymptotes if the degree of the numerator is one greater than the degree of the denominator.

To determine which rational function is graphed, you need to compare the graph to the standard forms of rational functions. For example, the graph of a rational function y=1/x would have a vertical asymptote at x=0 and would approach the x-axis as it goes to positive and negative infinity. By analyzing the graph's features, you can determine which rational function it represents.

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Hypergeometric distribution refers to a discrete probability distribution where the probability of success changes in trials. In other words, the probability of success is determined by the previous successes as well as failures. The formula to calculate the expectation of a hypergeometric distribution is as follows:

The expectation of a hypergeometric distribution can be determined by finding the average value or mean of all the possible outcomes. In order to calculate the expectation for a hypergeometric distribution, we can use the formula

E(X) = n * (a/N).Here, E(X) represents the expectation of the hypergeometric distribution, n refers to the total number of trials, a refers to the number of successful outcomes, and N represents the total number of possible outcomes.It is important to note that the hypergeometric distribution is different from the binomial distribution since it does not assume that the probability of success remains constant throughout the trials. Instead, the hypergeometric distribution takes into account the changes in the probability of success as each trial is conducted.

The formula that could be used to calculate the expectation for a hypergeometric distribution is E(X) = n * (a/N).

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So, on solving the provided question, we can say that coefficient of the variable in the expression 2 − 5x − 4 8 is 5

A coefficient in mathematics is a polynomial, a series, or the multiplicative coefficient of a particular term in an expression. Typically numeric, however any expression is permitted. The term "parameter" can also refer to the coefficients themselves if they are variables. A number times a variable equals a coefficient. Coefficient examples include:  The coefficient is 14 in phrase 14c 14c 14c. The coefficient is 1 for word g. multiplies the variable by this amount. example  Given that "z" is a variable and that 6z is the definition of the term, the coefficient is 6. One is the coefficient of the square of x.

here,

coefficient of the variable in the expression 2 − 5x − 4 8 is 5

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Definition- any transformation, as a translation or rotation, of a set such that the distance between points is preserved.

Types- translation , rotation, reflection, and glide reflection.

Tn the rigid motion, the distance between any two internal points stays the same as the body moves.

Given is the rigid motion.

Rigid motion is a motion in which the distance between any two internal points stays the same as an idealized solid body moves around.

Rigid Body motion is one of three types mentioned below -

Therefore, in the rigid motion, the distance between any two internal points stays the same as the body moves.

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