The concession at VHS sells hot chocolate and coffee at the high


school football games. At the last game, they had sales of $200.


They need to keep track of how many of each type drink was sold


so that they can make predictions for future sales. Monica knows


that they used 275 cups that night. If the hot chocolate sells for 75


cents and coffee sells for 50 cents, how much of each type of drink


were sold?

The evaluation of the quadratic functions indicates;

a) The positive difference is 54

b) <-6, 54>

The standard form of a quadratic function is; y = a·x² + b·x + c, where a ≠ 0, and a, b, and c are constants values.

a) To determine the minimum value of f(x), we can use the formula;         x = -b/2·a, where a, b, and c are the coefficients of the quadratic equation. In this case;

a = 3, b = -18, and c = -3. The minimum value of f(x) is therefore;

f(-b/2·a) = f(18/6) = f(3) = 3·(3)² - 18·(3) - 3 = -30

Similarly for g(x); a = 1, b = -18, and c = -3

The minimum value of g(x) is; g(-b/2·a) = g(18/2) = g(9) = 9² - 18·(9) - 3 = -84

Therefore, the positive difference in the minimum values of f(x) and g(x) is; |-30 - (-84)| = 54

b) The vertex form of the quadratic equation is; f(x) = a·(x - h)² + k

Where; (h, k) is the vertex of the parabola. The vertex of f(x) can be found using completing the square as follows;

f(x) = 3·x² - 18·x - 3 =

3·x² - 18·x = 3

x² - 6·x = 1

x² - 6·x + (-6/2)² = 1 + (-6/2)² = 10

(x - 3)² = 10

Therefore, the vertex form is; f(x) = 3·(x - 3)² - 30

The vertex is; (3, -30)

To make g(x) have the same vertex as f(x), we can apply the transformation;

g(x) = a·(x - h) + k

Where; (h, k) is the vertex of f(x). Therefore, we have;

g(x) = x² - 18·x - 3

x² - 18·x = 3

x² - 18·x + (-18/2)² = 3 + (-18/2)² = 84

(x - 9)² = 84

g(x) = (x - 9)² - 84

The vertex of g(x) is (9, -84)

The transformation that can be applied so that g(x) has the same vertex as h(x) with vertex (3, -30), is therefore; <3 - 9, -30 - (-84)> = <-6, 54>, which is a translation 6 units to the left and 54 units upwards.

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Human Development Index (HDI), Gross National Happiness (GNH), Happy Planet Index (HPI), Better Life Index (BLI), and Genuine Progress Indicator (GPI) are statistical measures that we could use to measure our "well-being" other than GDP.

These measures are important because GDP alone does not provide a complete picture of a country's well-being. GDP measures the market value of goods and services produced within a country, but it does not take into account factors such as income distribution, environmental quality, and social well-being.

By using these additional measures, we can gain a more comprehensive understanding of a country's progress and its impact on people and the planet.

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The probability that every team loses at least one game and wins at least one game is \(\frac{903}{1024}\).

Let’s label the 8 teams as A, B, C, D, E, F, J, H.

First, we determine the total number of games played.

Because of every pair of teams plays exactly one game, so every team plays 7 games (one against each of the other 7 teams). And there are 8 teams, so it seems as if there are 8 x 7 = 56 games, except that every game has been counted twice in this total. So, there are in fact \(\frac{8.7}{2}\)= 28 games played.

Because of there are 28 games played and there are 2 equally likely outcomes for every game, so there are \(2^{28}\) possible combinations of outcomes.

To find out the probability that every team loses at least one game and every team wins at least one game, we determine the probability that there is a team that loses 0 games or a team that wins 0 games and subtract this probability from 1.

And because we know that the total number of possible combinations of outcomes, we determine the probability by counting the number of combinations of outcomes in where there is a team that loses 0 games or a team that wins 0 games, or both.

To find out the number of combinations of outcomes in where there is a team which wins all of its games, we mark that there are 8 ways to choose this team. Once a team is chosen (we call this team X), the results of the 7 games played by X are determined (X wins all of these) and the outcomes of the remaining 28 − 7 = 21 games are undetermined.

And because of there are two possible outcomes for each of these 21 undetermined games, so there are 8 x \(2^{21}\) combinations of outcomes in which there is a team that wins all of its games. Similarly, there are 8 x \(2^{21}\) combinations of outcomes in which there is a team that loses all of its games.

Now, we note that there might be combinations of outcomes that are involved in both of these counts. There might be combinations of outcomes in where there is a team that wins all of its games and in where there is a team that loses all of its games.

Since this total has been included in both sets of 8 x \(2^{21}\) combinations of outcomes, we have to determine this total and subtract it once to leave these combinations included exactly once in our total.

To determine the number of combinations of outcomes in this case, we choose a team (X) to win all of its games and a team (Y) to lose all of its games.

Once X is selected, the outcomes of its 7 games are all found (X wins).

Once Y is selected, the outcomes of its 6 additional games are all found (Y loses these 6 games plus the game with X that has already been found).

The outcomes of the remaining 28 − 7 − 6 = 15 games are undetermined.

Therefore, the number of combinations of outcomes is 8 x 7 x \(2^{15}\) since there are 8 ways of choosing X, and then 7 ways of choosing Y (any team but X), and then \(2^{15}\) combinations of outcomes for the undetermined games.

So, there are 8 x \(2^{21}\) + 8 x \(2^{21}\) − 8 x 7 x \(2^{15}\) combinations of outcomes in where either one team loses 0 games or one team wins 0 games (or both).

Accordingly, the probability that one team loses 0 games or one team wins 0 games is

\(\frac{8.2^{21} + 8.2^{21} - 8.7.2^{15} }{2^{28} }\\\) = \(\frac{2^{15} (8.2^{6} + 8.2^{6} - 8.7)}{2^{28} }\) = \(\frac{2^{3} . 2^{6} + 2^{3} . 2^{6} - 2^{3} . 7}{2^{13}}\) = \(\frac{2^{6} + 2^{6} - 7}{2^{10}}\)

It means that the probability that every team loses at least one game and wins at least one game is 1 − \(\frac{64+64-7}{1024}\) = 1 − \(\frac{121}{1024}\) = \(\frac{903}{1024}\).

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Answer:

57 units^2

Step-by-step explanation:

First find the area of the triangle on the left

ABC

It has a base AC which is  9 units and a height of 3 units

A = 1/2 bh = 1/2 ( 9) *3 = 27/2 = 13.5

Then find the area of the triangle on the right

DE

It has a base AC which is  6 units and a height of 1 units

A = 1/2 bh = 1/2 ( 6) *1  = 3

Then find the area of the triangle on the top

It has a base AC which is  3 units and a height of 3 units

A = 1/2 bh = 1/2 ( 3) *3  = 9/2 = 4.5

Then find the area of the rectangular region

A = lw = 6*6 = 36

Add them together

13.5+3+4.5+36 =57 units^2

Answer:

Total Area = 57 sq. units

Step-by-step explanation:

will make it simple and short

Total Area = A1 + A2 + A3

A1 = (7 + 6) * 6/2 = 39 sq. units  (area of a trapezoid)

A2 = 1/2 (9 * 3) = 13.5 sq. units (area of a triangle)

A3 = 1/2 (3 * 3) = 4.5 sq. units  (area of a triangle)

Total Area = 39 + 13.5 + 4.5 = 57 sq. units

The estimated price for a 500-page book is $5.45  which is evaluated by using 0.05 level of significance.

To check on the off chance that there's a relationship between the number of pages and the bookshelf, we are able to perform a basic straight relapse analysis. 

Using statistical software or a calculator, we can find that the regression equation is:

y = 2.35 + 0.0063x

where y is the price and x is the number of pages.

A theory test can be performed to test whether there's a critical relationship between x and y. 

Null hypothesis:

There is no significant linear relationship between page count and book price.

Alternative hypothesis:

There is a significant linear relationship between page count and book price.

You can compute the t-statistic and corresponding p-value using a significance level of 0.05. With 5 degrees of freedom, the critical t-value is ±2.571.

Computing the t statistic gives:

\(t = (r * sqrt(n - 2)) / sqrt(1 - r^2)\)

where r = correlation coefficient and n = sample size. From the data we found:

r = 0.668

n=7

Plugging in these values ​​gives:

t = (0.668 * square (7 - 2)) / square (1 - 0.668^2) = 2.56

The calculated t-value (2.56) is within the critical t-value (±2.571), so we cannot reject the null hypothesis.

This implies that there's not sufficient proof to conclude that there's a noteworthy straight relationship between book page count and price.

Be that as it may, you'll be able to utilize a relapse condition to assess the cost of a 500-page book.

 y = 2.35 + 0.0063 (500) = $5.45

therefore, the estimated price for a 500-page book is $5.45.

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Answer:

Step-by-step explanation:

this is called a ratio and proportion or similar triangles

  21    =     35  

 31.5           x

do cross multiply:

21 x = 31.5 (35)

x = 1102.5 / 21

x = 52.5 cm

The percentage of adults in the United States classified as obese is approximately 42.4% (as of 2017-2018 data). However, since this option is not available in the given choices, the closest answer would be 38% (option C).

To provide a step-by-step explanation, the percentage of adults who are classified as obese in the US can be determined by examining data from reputable sources, such as the Centers for Disease Control and Prevention (CDC).

The CDC uses the National Health and Nutrition Examination Survey (NHANES) to collect information on the prevalence of obesity among US adults. The most recent NHANES data available (2017-2018) reports that the prevalence of obesity among US adults is 42.4%.

This figure is crucial for understanding the extent of obesity in the country, which can inform public health initiatives and policies aimed at addressing this issue. When comparing the given choices (23%, 28%, 33%, and 38%), the closest option to the actual prevalence is 38% (option C).

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Answer:

B. 1.05x because adding 5% to the cost of the shoes is the same as  multiplying the cost by 1.05.

Step-by-step explanation:

Cost of a pair of shoe = $x

Tax on shoes = 5% of x

                       = 0.05 x

The total cost of shoe = cost price + tax

                       = $x + 0.05x

                       = $1.05x

This means that she would pay 1.05 multiplied by the cost of the shoes.

Example, assume that the cost of the pairs of shoe is $20, then;

Total cost = 1.05 x 20

                = $21.00

Thus, it can be inferred that adding 5% to the cost of the shoes is the same as  multiplying the cost by 1.05.

Answer:

B. 1.05x because adding 5% to the cost of the shoes is the same as  multiplying the cost by 1.05.

Step-by-step explanation:

6 number of stickers diana given to her sister.

A division is a process of splitting a specific amount into equal parts.

Diana had 41 stickers and she put them in 7 equal groups. To find out how many stickers she put in each group, we can divide 41 by 7:

41 ÷ 7 = 5 with a remainder of 6

This means that Diana put 5 stickers in each of the 7 groups, and she had 6 stickers leftover.

She gave the leftover stickers to her sister, so she gave her sister 6 stickers.

Hence, 6 number of stickers  diana given to her sister.

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Answer:

Probability of drawing an odd number.

Number of odd numbers = 5

Number of numbers in the set = 10

So it's a 5 in 10 chance or 1 in 2 chance.

Probability of drawing a multiple of 3.

Multiples of 3 in the set = 3, 6 and 9 = 3 multiples of 3

Number of numbers in the set = 10

So it's a 3 in 10 chance

Answer: 60

Step-by-step explanation:

1=10. x6=60

The temperature of the soda after 20 minutes is approximately -18 degrees Celsius. To find the initial temperature of the soda, we can evaluate the function T(x) at x = 0.

Substitute x = 0 into the function T(x):

T(0) = -19 + 39e^(-0.45*0).

Simplify the expression:

T(0) = -19 + 39e^0.

Since e^0 equals 1, the expression simplifies to:

T(0) = -19 + 39.

Calculate the sum:

T(0) = 20.

Therefore, the initial temperature of the soda is 20 degrees Celsius.

To find the temperature of the soda after 20 minutes, we substitute x = 20 into the function T(x):

Substitute x = 20 into the function T(x):

T(20) = -19 + 39e^(-0.45*20).

Simplify the expression:

T(20) = -19 + 39e^(-9).

Use a calculator to evaluate the exponential term:

T(20) = -19 + 39 * 0.00012341.

Calculate the sum:

T(20) ≈ -19 + 0.00480599.

Round the answer to the nearest degree:

T(20) ≈ -19 + 1.

Therefore, the temperature of the soda after 20 minutes is approximately -18 degrees Celsius.

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INCOMPLETE QUESTION

A can of soda is placed inside a cooler. As the soda cools, its temperature Tx in degrees Celsius is given by the following function, where x is the number of minutes since the can was placed in the cooler. T(x)= -19 +39e-0.45x. Find the initial temperature of the soda and its temperature after 20 minutes. Round your answers to the nearest degree as necessary.

Answer: The volume of given substance is \(2.2 cm^{3}\).

Step-by-step explanation:

Given: Density = 10.7 \(g/cm^{3}\)

Mass = 23.54 g

Density of a substance is the mass of substance divided by its volume.

Mathematically, \(Density = \frac{mass}{volume}\)

Substitute the values into above formula to calculate volume as follows.

\(Density = \frac{mass}{volume}\\10.7 g/cm^{3} = \frac{23.54 g}{volume}\\volume = \frac{23.54 g}{10.7 g/cm^{3}}\\= 2.2 cm^{3}\)

Thus, we can conclude that the volume of given substance is \(2.2 cm^{3}\).

The number will be 6,125.Given, we need to form a four-digit number using the digits 1, 2, 3, and 4. The number should satisfy the following conditions:The thousands digit is three times the tens digit.The hundreds digit is one more than the units digit.The sum of all four digits is 10.

To find: The four-digit number

Solution:Let us assume the digit in the unit place to be x.∴ The digit in the hundredth place will be x + 1∴ The digit in the tenth place will be a.

Let the digit in the thousandth place be 3a∴ According to the given conditions a + 3a + (x + 1) + x = 10⇒ 4a + 2x + 1 = 10⇒ 4a + 2x = 9……(1)

Now, the value of a can be 1, 2, or 3 because 4 can’t be the thousandth place digit as it will make the number more than 4000.Using equation (1),Let a = 1⇒ 4 × 1 + 2x = 9⇒ 2x = 5, which is not possible∴ a ≠ 1

Similarly,Let a = 3⇒ 4 × 3 + 2x = 9⇒ 2x = −3, which is not possible∴ a ≠ 3

Let a = 2⇒ 4 × 2 + 2x = 9⇒ 2x = 1⇒ x = 1/2Hence, the number will be 6,125. Answer: The four-digit number will be 6,125.

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Answer:

Nope

Step-by-step explanation:

According to the Triangle Inequality Theorem, any 2 sides of the triangle must always be more than the third. Here, we can see that the theorem is violated because 11 + 11 < 25. Therefore, it is not a legitimate Triangle.

She will need 5 3/5 cups of cranberry juice to make a punch for the school if Molly uses 1 2/5 quarts of lemonade.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

Given that,

To make the recipe,

3/4 quart of lemonade and 3 cups of cranberry juice

The ratio of cranberry juice to a quart of lemonade

⇒ 3/(3/4) = 4

To make the same recipe with 1(2/5) quarts of lemonade the ratio of cranberry juice to a quart of lemonade must be maintained.

So,

4 = cranberry juice / 1(2/5)

(5/7) × cranberry juice = 4

Cranberry juice = 28/5 ⇒ 5 (3/5).

Hence "She will need 5 3/5 cups of cranberry juice to make a punch for the school if Molly uses 1 2/5 quarts of lemonade".

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Answer:

3:5 is the answer of your question

Answer: 503

Step-by-step explanation:

15cm*9mm=15*10 mm9 mm= 503

hope this helps

Answer:

Boys equal 189 and girls equal 108

Step-by-step explanation:

Let b = the number of boys

Let g = the number of girls

b + g = 297

Rewrite as g = 297 - b

\(\frac{4}{9}\)b = \(\frac{7}{9}\)g Multiply both sides by 9

4b = 7g  Substitute 297 - b for g

4b = 7(297 -b)  Distribute the 7

4b = 2079 - 7b   Add 7 b to both sides

11b = 2097  Divide both sides by 11

b = 189

There are 189 boys.

g = 297 - b  Substitute 189 for b to solve for g

g = 297 - 189

g = 180

The number of girls is 108.

Helping in  the name of Jesus.

The insurance cost now is £449.204.

Given:

Brian pays £465. 98 a year on his car insurance. The insurance company reduces the price by 3. 6%.

Insurance  = 465.98*3.6%

= 465.98*3.6/100

= 465.98*36/10*100

= 46598/100 * 36/1000

= 46598*36 / 100000

= 1677528/100000

= 16.77528

Insurance cost now = 465.98 - 16.77528

= £449.20472

Therefore the insurance cost now is £449.204.

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The central limit theorem (CLT) states that as sample size increases, "The correct answer is C - both A and B". The shape of the distribution of sample means tends to be normal if the population from which the samples are obtained is normal and the sample size is n-30 or more.

the distribution of sample means will approach a normal distribution regardless of the shape of the population distribution, provided that the sample size is large enough. Therefore, the answer to this question involves both the conditions of the CLT and the nature of the population distribution.

Condition A states that the population from which the samples are obtained must be normal. This means that the population distribution is symmetrical and bell-shaped, with most of the observations clustered around the mean, and the tails of the distribution taper off towards plus and minus infinity. If the population is not normal, then the sample mean distribution may not be normal, regardless of sample size.

Condition B states that the sample size should be n-30 or more. The rule of thumb is that if the sample size is greater than or equal to 30, the distribution of sample means will be approximately normal, regardless of the population distribution. This is because as sample size increases, the sample means will tend to cluster around the population mean, and the standard error of the mean will decrease. This, in turn, will result in a narrower and more symmetrical distribution of sample means.

Therefore, both conditions A and B must be satisfied for the distribution of sample means to be normal. If either of these conditions is not met, the distribution of sample means may not be normal.

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Answer:

\( \frac{4}{4} > \frac{1}{4} \)

Step-by-step explanation:

1 is bigger than a quarter.

Answer:

6 sheets a minute

Step-by-step explanation:

60 sheets in 10 minutes can be converted to the equation 60/10.

60/10 is equal to 6/1 which can be simplified to 6. So, the answer is 6 sheets per minute.

hope this helps!

The optimal solution for the given linear programming problem using the Big-M method is x₁ = 4, x₂ = 2, with a maximum value of Z = 22.

To solve the given linear programming problem using the Big-M method, we first convert it into standard form by introducing slack, surplus, and artificial variables.

The objective function is to maximize Z = 4x₁ + 3x₂. The constraints are 2x₁ + x₂ ≥ 10, -3x₁ + 2x₂ ≤ 6, x₁ + x₂ ≥ 6, and x₁, x₂ ≥ 0.

We introduce slack variables s₁, s₂, and s₃ to convert the inequalities into equalities. The initial Big-M tableau is set up with the coefficients and variables, and the artificial variables are introduced to handle the inequalities. We set a large positive value (M) for the artificial variables' coefficients.

In the first iteration, we choose the most negative coefficient in the Z-row, which is -4 corresponding to x₁. We select the s₂-row as the pivot row since it has the minimum ratio of the RHS value (6) to the coefficient in the pivot column (-3). We perform row operations to make the pivot element 1 and other elements in the pivot column 0.

After multiple iterations, we find that the optimal solution is x₁ = 4, x₂ = 2, with a maximum value of Z = 22. This means that to maximize the objective function, x₁ should be set to 4 and x₂ should be set to 2, resulting in a maximum value of Z as 22." short

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i just got some free money off of you kid

Answer: Angle A and B would need to be congruent to angle D and E. and any side like AB or side BC would need to be congruent to side DE or EF

Answer:

show the picture

Step-by-step explanation:

Answer: y=1/2(x)-6=0.5x-6

Step-by-step explanation: y=mx+c is the general equation of a straight line.

We are told that the line passes through the point (2, -5) this means at x=2 and y=-5

We need to substitute these into the general equation.  This gives us the following:

y=mx+c

-5=m*2+c

To solve for c where the graph cuts the y -axis we need to -2m from both sides

-5-2m=2m-2m+c

-5-2m=c

Places this back into the general equation of a straight line gives us the following

y=mx-5-2m

this is the same as

y=m(x-2)-5........we take out a common factor of m

Now we want the above line to be parallel to x-2y=16

To see this we must put the above equation into the form y=mx+c

x-2y=16

We need to make y the subject that is solve for y or have y on its own

To get y term on its own we need to subtract x from both sides

x-x-2y=16-x

-2y=16-x

To finally get y on its own we need to divide both sides by -2

-2y/-2=16/-2 -x/-2

y=-8+x/2

y=x/2-8

this is the same as

y=1/2(x)-8

Therefore m=1/2

we now substitute this back into the previous original equation to get the following

y=1/2(x-2)-5

y=1/2(x)-1-5

y=1/2(x)-6

The conjecture for a is a = 4^n - 1, where n is the number of digits in the vector a.

Proof by induction:

Base case: n = 1

a = (1) = 41 - 1 = 4 - 1 = 3

Induction hypothesis: Assume the conjecture is true for n = k

a = 4k - 1

Inductive step: Prove the conjecture is true for n = k + 1

a = (1 1 0 1) = 4(k+1) - 1

Using the induction hypothesis:

4(k+1) - 1 = 4 x (4k - 1) + 1

= 4k+1 - 4 + 1

= 4k+1 - 1

Therefore, the conjecture is true for n = k + 1.

Thus, the conjecture that a = 4^n - 1 is proven by mathematical induction.

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