your school wants to maximize their profit, P, from the sales of tickets, T, to the homecoming football game. They determine the function, P(t)=60t^2+420t-440 models the profit they can earn in hundreds of dollars in terms of price per ticket, in dollars.

There are 73,701 different 6-card hands (from a standard deck) with at least 3 kings.

To calculate the number of 6-card hands with at least 3 K's, the problem can be divided into:

Case 1:

Exactly 3 Kings

There are 4 ways to choose 3 kings to put in the hand, then there are 48 cards left to choose the remaining 3 cards (because we used 3 cards in a 52-card deck). Therefore, the number of 6-card hands with exactly 3 kings is:

4 * (48 choose 3) = 4 * 17,296 = 69,184

Case 2:

Exactly 4 Kings

There are 4 ways to choose 4 kings to put in the hand, then there are 48 cards left to choose the remaining 2 cards. Therefore, the number of 6-card hands with exactly 4 kings is:

4 * (48 choose 2) = 4 * 1.128 = 4.512

Case 3:

Exactly 5 kings

There are 4 ways to choose the 5 kings in the hand, then there is only one card left to choose from (because we used 5 of the 52 cards in the deck of cards). Therefore, the number of 6-card hands with exactly 5 kings is:

4*1=4

Case 4:

6 cards are king

There is only one way to choose all 6 cards as king.

Therefore, the total number of 6-card hands with at least 3 kings is:

69,184 + 4,512 + 4 + 1 = 73.701

So there are 73,701 different 6-card hands with at least 3 kings.  

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Answer:

[tex]c + 15 > 24[/tex]

[tex]c > 9[/tex]

The additional amount will be more than $9.

The sine function that describes the child's apparent distance from the center of the merry-go-round is d(t) = 5.3 sin(2π/15 * t)

To write a sine function that describes the child's apparent distance from the center of the merry-go-round as a function of time t, we can start by finding the amplitude, period, and phase shift of the motion.

Amplitude:

The amplitude of the motion is half the diameter of the merry-go-round, which is 10.6/2 = 5.3 feet. This is because the child moves back and forth across the diameter of the merry-go-round.

Period:

The period of the motion is the time it takes for the child to complete one full cycle of back-and-forth motion, which is equal to the time it takes for the merry-go-round to complete one full rotation.

From the given information, the child completes 8 rotations in 120 seconds, so the period is T = 120/8 = 15 seconds.

Phase shift:

The phase shift of the motion is the amount of time by which the sine function is shifted horizontally (to the right or left).

In this case, the child starts at one end of the diameter and moves to the other end, so the sine function starts at its maximum value when t = 0. Thus, the phase shift is 0.

With these values, we can write the sine function that describes the child's apparent distance from the center of the merry-go-round as:

d(t) = 5.3 sin(2π/15 * t)

where d is the child's distance from the center of the merry-go-round in feet, and t is the time in seconds. The factor 2π/15 is the angular frequency of the motion, which is equal to 2π/T.

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Answer:

Set your calculator to degree mode.

[tex] \tan(39) = \frac{12}{x} [/tex]

[tex]x \tan(39) = 12[/tex]

[tex]x = \frac{12}{ \tan(39) } = 14.818766[/tex]

So the area of this triangle is

(1/2)(14.818766)(12) = 88.91 (B)

To reduce the width of a confidence interval, you can use a smaller sample size and decrease the level of confidence, or use a larger sample size and decrease the level of confidence.

What are the factors?

what are factorsIn mathematics, a factor is a number that divides another number without leaving a remainder.

The combination of factors that would definitely cause the confidence interval to become wider is to use a larger sample and increase the level of confidence or to use a smaller sample and increase the level of confidence.

When using a larger sample size, the standard error of the mean decreases, and the interval will become narrower. Conversely, when using a smaller sample size, the standard error of the mean increases, and the interval will become wider. However, increasing the level of confidence will also increase the width of the interval as a wider interval is required to capture the true population parameter with a higher level of confidence.

Therefore, to reduce the width of a confidence interval, you can use a smaller sample size and decrease the level of confidence, or use a larger sample size and decrease the level of confidence.

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The length of the third side between 2.1 inches and 8.3 inches (exclusive) could be a valid length for the third side of the triangle.

In a triangle, the length of any side must be less than the sum of the lengths of the other two sides and greater than the difference between the lengths of the other two sides.

We can apply this rule to find the possible lengths of the third side of the triangle, given that the lengths of the two sides are 5.2 inches and 3.1 inches.

Here we have

The lengths of two sides of a triangle are 5.2 inches and 3.1 inches

Let's denote the length of the third side as x. Then, we have:

3.1 + 5.2 > x > 5.2 - 3.1

8.3 > x > 2.1

Therefore, the length of the third side x must be greater than 2.1 inches and less than 8.3 inches.

We can write this as an inequality:

2.1 < x < 8.3

Therefore,

The length of the third side between 2.1 inches and 8.3 inches (exclusive) could be a valid length for the third side of the triangle.

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Answer:

The perimeter of this trapezoid is

7 + 5 + 3 + 7 + 4 = 26 cm

rectangle, A = lw, 4 × 7 = 28 square cm

triangle, A = (1/2)bh, (1/2) × 3 × 4 =

6 square cm

(1/2)(4)(7 + 10) = (1/2)(4)(17) = 34 square cm = 28 square cm + 6 square cm

Based on the given information, we can set up the following hypotheses for the hypothesis test:

Null Hypothesis (H0): The actual proportion of people taking the cruise within 1 year is equal to the believed proportion of 5%.

Alternative Hypothesis (H1): The actual proportion of people taking the cruise within 1 year is not equal to the believed proportion of 5%.

Let p be the proportion of people taking the cruise within 1 year. We can use the sample proportion, denoted as p-hat, which is calculated as the ratio of the number of people who took the cruise within 1 year (3 in this case) to the total number of people who requested the brochures (100 in this case).

Given that the significance level is 0.05, we can use a z-test to compare the sample proportion with the believed proportion of 5%. The z-test statistic is calculated as:

z = (p-hat - p) / sqrt(p * (1 - p) / n)

where n is the sample size, which is 100 in this case.

Now we can calculate the z-test statistic and compare it with the critical value for a two-tailed test at a significance level of 0.05. If the calculated z-test statistic falls outside the critical value, we would reject the null hypothesis; otherwise, we would fail to reject the null hypothesis.

Since the sample proportion p-hat is 3/100 = 0.03, and the believed proportion p is 0.05, we can substitute these values into the z-test formula:

z = (0.03 - 0.05) / sqrt(0.05 * (1 - 0.05) / 100)

Calculating the above expression, we get the value of z. We can then compare this value with the critical value for a two-tailed test at a significance level of 0.05 from a standard normal distribution table or using a statistical calculator.

If the calculated z-test statistic falls outside the critical value, we would reject the null hypothesis and conclude that the actual proportion of people taking the cruise within 1 year is different from the believed proportion of 5%. If the calculated z-test statistic falls within the critical value, we would fail to reject the null hypothesis and not conclude that the actual proportion is different from the believed proportion.

Without the actual values of the calculated z-test statistic and the critical value, we cannot provide a specific decision for this hypothesis test. Please note that hypothesis testing requires careful consideration of the sample size, significance level, and other relevant factors, and should be conducted with caution and in consultation with a qualified statistician or expert in statistical analysis.

Answer:

mean: 101 (add all the numbers then divide by 7)

mode: 102 (the most frequent number in the set)

median: 102 (the number in the middle of the set)

range: 20 (the difference between the largest and smallest number)

Mean = 101

Mode = 102

Median = 102

Range = 20

MEAN: Add up all the numbers, then divide by how many numbers there are.

102 + 107 + 99 + 102 + 111 + 95 + 91 = 707

707 ÷ 7 = 101

MODE: Arrange all numbers in order from lowest to highest or highest to lowest and then count how many times each number appears in the set. The one that appears the most is the mode.

91,95,99,102,102,107,111

MEDIAN: Arrange the numbers from smallest to largest. If the amount of numbers is odd, the median is the middle number. If it is even, the median is the average of the two middle numbers in the list.

91,95,99,102,102,107,111

RANGE: Subtract the lowest number from the highest number

111 - 91 = 20

The statement which  is true for the quadrilateral is B.

To dilate a figure by a scale factor of 2, each point of the original figure is multiplied by 2.

So the coordinates of each vertex of A'B'C'D' are twice the coordinates of the corresponding vertex of ABCD.

The coordinates of A' are (4,10), B' are (4,4), C' are (8,6), and D' are (8,12).

To determine which statements are true, we can compare the angles and side lengths of the two quadrilaterals:

A) None of the answers apply. This may be a valid answer, but we should check the other options before concluding that none of them apply.

B) The angles of Quadrilateral ABCD and Quadrilateral A'B'C'D' are the same. This is true because dilation does not change angles. The corresponding angles of the two quadrilaterals are congruent.

C) The side lengths of Quadrilateral ABCD and Quadrilateral A'B'C'D' are not the same. We can see this by calculating the length of each side of both quadrilaterals.

Therefore, the correct answer is B.

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Answer:

[tex]f(x) = 500( {.89}^{x} )[/tex]

Answer: The answer is A.

Step-by-step explanation: Because I am smart don't underestimate me.

Answer:

C

Step-by-step explanation: (look at attachment)

3x + 4 = -2x -2

By looking at the y-intercepts, you automatically know the answer is C.

The y-intercept of the pink line is 4 because of 3x + 4.

The y-intercept of the blue line is -2, because of -2x - 2.

The 21st term of the sequence 3, 8, 13, 18, .. is 103

To find the indicated term in the sequence, we first need to identify the pattern followed by the sequence. It appears that each term is obtained by adding 5 to the previous term. So, we can write the general formula for the nth term of the arithmetic sequence as

a(n) = a(1) + (n-1)d

where a(1) is the first term of the sequence, d is the common difference, and n is the term number.

In this case, we have:

a(1) = 3 (the first term)

d = 5 (the common difference)

To find the 21st term, we substitute n = 21 in the formula:

a(21) = a(1) + (21-1)d

a(21) = 3 + 20(5)

a(21) = 103

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The measure of angle A and B is 29° and 61° respectively

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

sin(tetha) = opp/hyp

tan(tetha) = opp/adj

cos(tetha) = adj/hyp

The opposite is 6 and the adjascent = 11

Therefore tan (tetha) = 11/6 = 1.833

tetha = tan^-1( 1.833)

= 61°( nearest degree)

The sum of angle in a triangle is 180°

therefore,

angle A = 180-( 61+90)

= 180-151

= 29°

therefore the measure of angle A and B is 29° and 61° respectively.

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fraction wise, a whole is always simplified to 1, so

[tex]\cfrac{4}{4}\implies \cfrac{1000}{1000}\implies \cfrac{9999}{9999}\implies \cfrac{17}{17}\implies \text{\LARGE 1} ~~ whole[/tex]

so, we can say the whole of the players, namely all of them, expressed in fourth is well, 4/4, that's the whole lot,  and we also know that 3/4 of that is 12, the guys who chose the bottle of water

[tex]\begin{array}{ccll} fraction&value\\ \cline{1-2} \frac{4}{4}&p\\[1em] \frac{3}{4}&12 \end{array}\implies \cfrac{~~ \frac{4 }{4 } ~~}{\frac{3}{4}}~~ = ~~\cfrac{p}{12}\implies \cfrac{~~ 1 ~~}{\frac{3}{4}} = \cfrac{p}{12}\implies \cfrac{4}{3}=\cfrac{p}{12} \\\\\\ (4)(12)=3p\implies \cfrac{(4)(12)}{3}=p\implies 16=p[/tex]

The simplified expression is 4(x - 3y).

logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = logb n. For example, 23 = 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log2 8.

Using the following logarithmic identities:

log a (bc) = log a (b) + log a (c)

log a (b/c) = log a (b) - log a (c)

We can simplify the expression as follows:

2㏒4 x - 6 log4 y = 2(㏒4) x - 6(㏒4) y

= 2(㏒4) x - 2(㏒4)3 y

= 2(㏒4)(x - 3y)

Now, we can simplify further by using the fact that ㏒4 = 2:

2(㏒4)(x - 3y) = 2(2)(x - 3y) = 4(x - 3y)

Therefore, the simplified expression is 4(x - 3y).

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To find the inverse of a function, we need to swap the positions of x and y and then solve for y. In other words, we replace f(x) with y and then solve for x.

x = 5y - 6

Next, we'll solve this equation for y:

x + 6 = 5y

y = (x + 6)/5

According to the information, he test statistic for this sample is 5.

To calculate the test statistic for the Wilcoxon signed-rank test, we need to calculate the differences between the "before" and "after" engagement ratings and rank them in order of their absolute values.

Student Before After Difference Absolute Difference Rank

1 30 40 10 10 1

2 20 40 20 20 2

3 32 37 5 5 3

4 43 46 3 3 4

5 48 44 -4 4 5

The sum of the ranks for the positive differences is 1 + 2 + 3 + 4 = 10, and the sum of the ranks for the negative differences is 5.

The smaller of the two sums (in this case, the sum of the ranks for the negative differences) is the test statistic for the Wilcoxon signed-rank test.

Therefore, the test statistic for this sample is 5.

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Answer:

x = 4√5 ≈ 8.94 (2 d.p.)

y = 8√5 ≈ 17.89 (2 d.p.)

Step-by-step explanation:

To find the values of x and y, use the Geometric Mean Theorem (Leg Rule).

The altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments. The ratio of the hypotenuse to one leg is equal to the ratio of the same leg and the segment directly opposite the leg.

[tex]\boxed{\sf \dfrac{Hypotenuse}{Leg\:1}=\dfrac{Leg\:1}{Segment\;1}}\quad \sf and \quad \boxed{\sf \dfrac{Hypotenuse}{Leg\:2}=\dfrac{Leg\:2}{Segment\;2}}[/tex]

From inspection of the given right triangle RST:

Substitute the values into the formulas:

[tex]\boxed{\dfrac{20}{y}=\dfrac{y}{16}}\quad \sf and \quad \boxed{\dfrac{20}{x}=\dfrac{x}{4}}[/tex]

Solve the equation for x:

[tex]\implies \dfrac{20}{x}=\dfrac{x}{4}[/tex]

[tex]\implies 4x \cdot \dfrac{20}{x}=4x \cdot \dfrac{x}{4}[/tex]

[tex]\implies 80=x^2[/tex]

[tex]\implies \sqrt{x^2}=\sqrt{80}[/tex]

[tex]\implies x=\sqrt{80}[/tex]

[tex]\implies x=\sqrt{4^2\cdot 5}[/tex]

[tex]\implies x=\sqrt{4^2}\sqrt{5}[/tex]

[tex]\implies x=4\sqrt{5}[/tex]

Solve the equation for y:

[tex]\implies \dfrac{20}{y}=\dfrac{y}{16}[/tex]

[tex]\implies 16y \cdot \dfrac{20}{y}=16y \cdot \dfrac{y}{16}[/tex]

[tex]\implies 320=y^2[/tex]

[tex]\implies \sqrt{y^2}=\sqrt{320}[/tex]

[tex]\implies y=\sqrt{320}[/tex]

[tex]\implies y=\sqrt{8^2\cdot 5}[/tex]

[tex]\implies y=\sqrt{8^2}\sqrt{5}[/tex]

[tex]\implies y=8\sqrt{5}[/tex]

Answer:

The answer is 3

Step-by-step explanation:

x×108=y

x×2²×3³=y

3×108=324

Arun is not correct - he has just under $5 in total, not just over.

Let's start by finding out how many 5-cent and 10-cent coins Arun has.

Let the number of 5-cent coins be 5x and the number of 10-cent coins be 3x (since the coins are in the ratio 5:3).

Then the total value of the 5-cent coins is 5x0.05 = 0.25x dollars, and the total value of the 10-cent coins is 3x0.1 = 0.3x dollars.

So the total value of all the coins is 0.25x + 0.3x = 0.55x dollars.

Since Arun has 72 coins, we know that 5x + 3x = 72, or 8x = 72, or x = 9.

Therefore, Arun has 5x = 59 = 45 5-cent coins and 3x = 39 = 27 10-cent coins.

The total value of these coins is 450.05 + 270.1 = 2.25 + 2.7 = 4.95 dollars.

So Arun is not correct - he has just under $5 in total, not just over.

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The analysis of the bank statement thus, given below. Since the result is negative, this means that Andre would still have a negative balance after depositing $100, and therefore would still be in debt.

1. If we put withdrawals and deposits in the same column, they can be represented as positive and negative values in a single column. Deposits would be represented with positive values, and withdrawals would be represented with negative values.

2. Andre's new balance would be $16.37. We can calculate this by subtracting $40 (the withdrawal) from his previous balance of $56.37:

$56.37 - $40 = $16.37

3. If Andre deposits $100 in this account, he will no longer be in debt. We can calculate his new balance by adding his previous balance and the deposit, and then subtracting any withdrawals:

$56.37 + $100 = $156.37 (balance after the deposit)

$156.37 - $28.50 - $37.91 - $16.43 - $42.00 - $72.50 - $45.00 - $50.00 - $10.03 - $62.47 = -$49.47

Since the result is negative, this means that Andre would still have a negative balance after depositing $100, and therefore would still be in debt.

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Answer:

A

Step-by-step explanation:

Equation of a line is:    y = mx + b    where  m = slope    b = y axis intercept

      To find the slope between any two of the given points :

  say   18, 100   and     27, 85

    m = slope =  (y1-y2) / (x1-x2) = (85-100) / ( 27-18)  = -15/12 = -5/3  

so now you have

   y = - 5/3 x   + b       we still need to find the value of b

                                        use any point to calculate b

                              say    15, 106

     106 = - 5/3 (15) + b    

          b = ~ 131

the equation is then     y = - 5/3 x + 131     closest  to answer 'A'

Step-by-step explanation:

x = -4     ( the value of the x-coordinate of the vertex is the axis of symmetry for normal up or down opening parabolas)

Answer:  a. In this context, d(5) = 0.25 means that 5 minutes after 7:00 a.m., Tyler is 0.25 miles away from his house. This is because the function d(t) gives the distance of Tyler from his house t minutes after 7:00 a.m.

b. If d(5) = 0.25, then we know that 5 minutes after 7:00 a.m., Tyler is 0.25 miles away from his house. If there is a 120-minute delayed start time, then Tyler will walk for 20 + 120 = 140 minutes to reach his school. We want to find the corresponding point on the function s, which gives Tyler's distance from home t minutes after 7:00 a.m. with a 120-minute delayed start time. Since Tyler walks the same distance regardless of the delayed start time, we can use the same function for s as we did for d. Therefore, s(145) = 1.25, since Tyler is 1 mile away from his house after walking for 140 minutes and then an additional 5 minutes to account for the delayed start time.

c. Since Tyler walks the same distance regardless of the delayed start time, we can express s(t) in terms of d(t) by adding 120 minutes to the time t. Therefore, s(t) = d(t + 120).

d. The function n(t) = d(t + 60) gives Tyler's distance from his house t minutes after 8:00 a.m. This is because adding 60 minutes to t corresponds to adding one hour to the time, which means that Tyler leaves his house at 8:00 a.m. instead of 7:00 a.m. Therefore, n(t) gives Tyler's distance from school one hour after he leaves his house.

Step-by-step explanation:

The probability that the mean of a sample of 77 computers would be greater than 82.59 months, assuming the population mean is 80 months and the variance is 64, is approximately 0.0606

The situation described can be modeled using a normal distribution, with a mean of 80 months and a standard deviation of the square root of the variance, which is 8 months (since variance = standard deviation squared).

To find the probability that the mean of a sample of 77 computers would be greater than 82.59 months, we need to standardize the sample mean using the formula

z = (x - μ) / (σ / √n)

where

x is the sample mean

μ is the population mean (believed to be 80 months)

σ is the population standard deviation (8 months)

n is the sample size (77)

Plugging in the values, we get

z = (82.59 - 80) / (8 / √77) ≈ 1.55

To find the probability of a z-score being greater than 1.55, we can use a standard normal distribution table or calculator. From the table, we find that the probability of z being greater than 1.55 is approximately 0.0606.

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The decimal that represents the fraction of the $30.00 Maggie spent is 0.6.

Now, let's talk about decimals. Decimals are a way of expressing parts of a whole number in a fraction of 10. For example, 0.5 is the same as 1/2. In your situation, Maggie spent $18.00 out of $30.00. To figure out what decimal represents the fraction of the $30.00 Maggie spent, we need to divide the amount she spent by the total amount she had.

So, we can write this as a fraction:

$18.00 / $30.00

To turn this fraction into a decimal, we divide the numerator (top number) by the denominator (bottom number) using long division or a calculator.

$18.00 / $30.00 = 0.6

Another way to say this is that Maggie spent 60% of the money she had in her wallet.

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When x is 2, the value of the expression is 9.

An algebraic expression is a mathematical phrase that contains one or more variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It can also contain exponents, roots, and trigonometric functions.

Algebraic expressions are used to represent mathematical relationships and solve problems in a wide range of fields, including physics, engineering, finance, and statistics. They can be used to model real-world phenomena and to make predictions based on data.

Algebraic expressions can be simplified by combining like terms and using mathematical rules and properties. They can also be evaluated by substituting values for the variables and simplifying the expression. Solving equations involving algebraic expressions often involves manipulating the expression to isolate a variable and find its value.

When x is 2, the value of the expression 12/4+3(8−x)-12 can be found by substituting 2 for x and simplifying the expression:

12/4 + 3(8 - 2) - 12

= 3 + 3(6) - 12

= 3 + 18 - 12

= 9

Therefore, when x is 2, the value of the expression is 9.

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The complete question is :

When x is 2, what is the value of the expression 12/4+3(8−x)-12?

Answer:

Same equation just using the assocaitive property

Step-by-step explanation:

For example, 8 + (2 + 3) = (8 + 2) + 3 = 13

Hope this helps! =D

Answer:

Step-by-step explanation:

Let A be the area of the surface of the cube.

When the side length changes from s to 4s, the new area A' can be calculated as:

A' = 6(4s)^2 = 96s^2

The change in area is then:

ΔA = A' - A = 96s^2 - 6s^2 = 90s^2

To find the integral that quantifies the change in area, we can integrate the expression for ΔA with respect to s, from s to 4s:

∫(90s^2)ds from s to 4s

= [30s^3] from s to 4s

= 30(4s)^3 - 30s^3

= 1920s^3 - 30s^3

= 1890s^3

Therefore, the integral that quantifies the change in area of the surface of a cube when its side length quadruples from s units to 4s units is:

∫(90s^2)ds from s to 4s

= 1890s^3 from s to 4s

= 1890(4s)^3 - 1890s^3

= 477,840s^3 - 1890s^3