A student wants to compare the amount of money that two local movie theaters make over a two-week period for the last nightly showing of a particular movie. The following box plots show the data for the amount of money each theater makes over the period. Compare the median of each box plot.

The actions that have more than 4 possible outcomes are:

- Selecting an 8 or 9 card of any color (each set has 2 cards for a total of 8 possible outcomes)

- Selecting a yellow card greater than 4² (there are 7 yellow cards that meet this criteria)

- Selecting a blue card that is a multiple of 3 (there are 5 blue cards that meet this criteria)

Therefore, only three of the given actions have more than 4 possible outcomes.

Thus, Cost of making 1  solid aluminium ball is found as  $211.95.

Something spherical is similar to a sphere in three dimensions in that it is round, or somewhat round. Even though they are never exactly round, oranges and apples are both spherical. Since an asteroid is frequently spheroidal—nearly round but lumpy—it has an approximately spherical form.

radius of solid aluminium balls r = 7.5 in.

Cost of of aluminium = $0.12 per cu. in.

Volume of sphere = 4/3 * π * r³

Volume of sphere = 4/3 * 3.14 * 7.5³

Volume of sphere = 1766.25 cu. in.

Cost of making 1  solid aluminium ball = 0.12 * 1766.25

Cost of making 1  solid aluminium ball = $211.95.

Thus, Cost of making 1  solid aluminium ball is found as  $211.95.

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Proportionately, if $170,500 profits in the second year of operation represent 576% of the company's first-year profits, the first-year profits will be $29,600.

A proportion describes two ratios equated to each other.

Proportion is a fractional value that compares one value or quantity to another.

The profits for the second year of operation = $170,500

Let the profits for the first year of operation = x

Proportionately, if $170,500 is 576% of x, x = $29,600 ($170,500 ÷ 576%)

Using equations, 5.76x = $170,500

x = $29,600 ($170,500  ÷ 5.76)

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The equation that models the amount of water in the tank after x minutes is:

y = -3x + 9

We know that the tank contains 9 liters of water, and it loses water at a constant rate of 3 liters per minute.

Then we can model the amount of water y in the tank after x minutes with a linear equation where the y-intercept is 9 and the rate of change is -3 (the amount it loses per unit of x)

Then the equation is:

y = -3x + 9

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Answer:

x+y=9

5x+8y=66

Step-by-step explanation:

A sample of at least 433 individuals would need to be taken to estimate the population mean with 98% confidence to within $100.

To estimate the sample size needed to estimate the population mean with 98% confidence to within $100, we can use the formula:

n = (z * σ / E)²

where:

n = sample size

z = z-score for the desired level of confidence (98% in this case), which can be found using a standard normal distribution table or calculator. For 98% confidence, the z-score is approximately 2.33.

σ = population standard deviation ($800 in this case)

E = margin of error ($100 in this case)

Plugging in the values, we get:

n = (2.33 * 800 / 100)²

n ≈ 432.64

Rounding up to the nearest whole number, we get a sample size of 433. Therefore, a sample of at least 433 individuals would need to be taken to estimate the population mean with 98% confidence to within $100.

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Answer:

1/8

Step-by-step explanation:

The absolute value of positive numbers (decimals, fractions, etc.) is the same number. The absolute value of negative numbers (decimals, fractions, etc.) is the same, but positive.

What is Absolute value?

Absolute value is a set of lines that if any number is placed in it, the number would be positive

Absolute signs: | |

Examples:

|-6|= 6 (Absolute value of -6 is 6)

|9|=9 (Absolute value of 9  is 9) (Because 9 is already positive)

Your Question

Since 1/8 is already positive, the absolute value of it would just be 1/8

Please feel free to ask questions

Answer:

m = 3

Step-by-step explanation:

Given:

[tex]2^{m-3}[/tex] = 1

Take the logarithm of both sides (logarithm of 1 is 0):

m - 3 = 0

Add 3 to both sides:

m - 3 + 3 = 0 + 3

m = 3

Hence, m = 3.

Logarithm is the power to which a number must be raised in order to get some other number. For example:

Answer:

Step-by-step explanation:

c

Answer: No

Step-by-step explanation: They are not perpendicular due to the slopes. Perpendicular will have the same slopes value wise, but one is negative and one positive.

The point (3,b) can lie on the circle with radius 8 and center (-2,-1) for values of b equal to -1 + √39 and -1 - √39.

We know that the circle with radius 8 and center (-2,-1) has the equation:

(x + 2)² + (y + 1)² = 8²

Substituting x = 3 and y = b, we get:

(3 + 2)² + (b + 1)² = 8²

Simplifying, we get:

25 + (b + 1)² = 64

(b + 1)² = 39

Taking the square root of both sides, we get:

b + 1 = ± √39

Therefore, the possible values of b are:

b = -1 ± √39

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Answer: x=3

Step-by-step explanation:

shaded part is 5/6 of the full circle, so just make an equation.

5/6 pi r^2(formula to find area)=15/2 pi(area given)

cancel out pi and simplify

r^2=9

r=+-3 but cant be negative so r=3

The coordinates of Y' are (6, 4) and the coordinates of Z' are (5, -1).

To find the coordinates of Y' and Z', we need to apply the same translation that maps X to X'.

We know that the vector that connects X to X' is (3 - (-1), 1 - 0) = (4, 1).

So, to translate Y to Y', we add the vector (4, 1) to the coordinates of Y:

Y' = Y + (4, 1)

= (2, 3) + (4, 1)

= (6, 4)

Similarly, to translate Z to Z', we add the vector (4, 1) to the coordinates of Z:

Z' = Z + (4, 1)

= (1, -2) + (4, 1)

= (5, -1)

Therefore, the coordinates of Y' are (6, 4) and the coordinates of Z' are (5, -1).

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From the discrete distribution given, the standard deviation is of 0.83 children.

The distribution is:

P(X=1) =0.5

P(X=2) =0.25

P(X=3) =0.25

The mean is 1.75.

The standard deviation is the square root of the sum of the difference squared between each value and the mean, multiplied by it's respective probability.

Hence:

The standard deviation is 0.83 children.

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After substituting the values as x=3 and y=7, the value of the expression "2x²-y¹+3x⁰" is 14.

In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that can be simplified or evaluated to a numerical value.

To evaluate the expression 2x²-y¹+3x⁰ for x=3 and y=7, we substitute the given values, which are x=3 and y=7 into the expression and simplify:

On substituting the values,

We get,

= 2x² - y¹ + 3x⁰

= 2(3)² - 7¹ + 3(1)

= 2(9) - 7 + 3

= 18 - 7 + 3

= 14

Therefore, when x=3 and y=7, the value of the expression 2x²-y¹+3x⁰ is 14.

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Answer:

Step-by-step explanation:

It seems like you have provided multiple measurements for the radius of the circle. I'm sorry, but a circle can only have one radius, so I am not able to calculate its area with the given information.

Please provide the correct measurement for the radius of the circle, and I will be happy to help you calculate its area.

The Slope of x = -3 is undefined; 6x-3y=18 is 2; (4,-2) and (1,7) is -3; and (7,5) and (8,5) is 0.

Slope of a line (m) = rise/run = change in y / change in x

Note that the slope of vertical lines are always undefined.

Therefore, we have the following:

x = -3 represents the equation of a vertical line, therefore, the slope is undefined.

6x - 3y = 18 is rewritten as y = 2x - 6 in slope-intercept form. The slope is 2.

For (4,-2) and (1,7):

Slope (m) = (7 -(-2))/(1 - 4) = 9/-3 = -3

For (7,5) and (8,5):

Slope (m) = 5 - 5/8 - 7 = 0/1 = 0

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The zeros of the quadratic profit function are explained as:

x = 6, x = 44; The zeros represent the number of monthly memberships where no profit is made

The quadratic function is given as:

f(x) = −x² + 50x − 264

The general form of expression of a quadratic function is:

f(x) = ax² + bx + c

The quadratic formula to find the zeros is:

x = [-b ± √(b² - 4ac)]/2a

Thus, we have the zeros as:

x = [-50 ± √((-50)² - 4(-1 * -264))]/2(-1)

x = 6 and x = 44

This represents number of monthly memberships where no profit is made.

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The probability that none of the four adults is very confident in the nutritional information on the restaurant menus is 0.208 or approximately 20.8%. 

Ready to approach this issue by utilizing the hypergeometric conveyance, since we are examining without substitution from a limited populace of two sorts (those who are exceptionally sure and those who are not exceptionally sure).

Let X be the number of grown-ups in a sample of 4 who are not exceptionally sure about the wholesome data on eatery menus.

At that point, X takes after a hypergeometric dissemination with parameters N = 1000, n = 4, and K = 850 (since 850 grown-ups are not exceptionally certain).

The likelihood that none of the 4 grown-ups are exceptionally certain can be communicated as:

P(X = 4) = (K select 4) / (N select 4)

where (K select 4) speaks to the number of ways to select 4 grown-ups from the population of 850 who are not exceptionally sure,

and (N select 4) speaks to the entire number of ways to select 4 grown-ups from the populace of 1000.

Utilizing the equation for binomial coefficients, ready to disentangle this expression as:

P(X = 4) = [(850*849*848*847) / (4*3*2*1)] / [(1000*999*998*997) / (4*3*2*1)]

= 0.208

Hence, the likelihood that none of the four grown-ups are exceptionally certain within the wholesome data on eatery menus is 0.208 or approximately 20.8%. 

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Answer:

Step-by-step explanation:

You want the tangent and secant of the angle θ the line x-3y=0 makes with the negative x-axis.

The relations between the angle and its trig functions are ...

  Tan = Opposite/Adjacent

  Sec = Hypotenuse/Adjacent

We have shown the angle of interest in a unit circle with the "adjacent" side equal to the radius of the circle (1). Then the values of interest are ...

  tan(θ) = opposite side = 1/3 . . . . . . . equal to the slope of the line

  sec(θ) = hypotenuse = √(1 +(1/3)²) = √(10/9) = (√10)/3

The tangent is 1/3; the secant is (√10)/3.

__

Additional comment

A third-quadrant angle measured from the +x axis has a negative secant. The tangent is positive there.

Since this angle is measured from the -x axis, it isn't clear whether it is supposed to be considered a 3rd-quadrant angle or not. For the given acute angle θ shown, the trig functions are both positive. YMMV

The expanded form of log y^10 is either 10 log y or 10 ln y

Assuming that the base of the logarithm is not specified, we can use the change of base formula to expand the logarithm:

log y^10 = log (y^10) / log (base)

Using base 10:

log y^10 = log (y^10) / log 10

= 10 log y / 1

= 10 log y

Using natural logarithm:

log y^10 = log (y^10) / log e

= 10 log y / 1

= 10 ln y

Therefore, the expanded form of log y^10 is either 10 log y or 10 ln y, depending on the base used.

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Answer:

52 is the  least common dominator

Answer:

52/65

Step-by-step explanation:

The same fraction we can express in many different forms. If the numerator and denominator ratio is the same, the fractions represent the same rational number.

The least common denominator of a set of fractions is the least number that is a multiple of all the denominators: their least common multiple

The method of calculating the LCD is the same as the calculation least common multiple of fractions denominators.

The simple method for common computing denominators (not least at all) is to multiply all denominators.

To solve for x in terms of y in the equation 23x + 15y = 2, we can start by isolating the term with x on one side of the equation. We can do this by subtracting 15y from both sides of the equation to get 23x + 15y - 15y = 2 - 15y, which simplifies to 23x = 2 - 15y.

Next, we can solve for x by dividing both sides of the equation by 23 to get 23x/23 = (2 - 15y)/23, which simplifies to x = (2 - 15y)/23.

Therefore, the solution for x in terms of y is x = (2 - 15y)/23.

Answer:

r=4

center: (-2,4)

Step-by-step explanation:

The equation of a circle is:

(x-h)²+(y-k)²=r²

(h,k) would be the center of the circle and r would be length of the radius

To find r, we simply take the square root of 16, which would be 4

And the center is given in the equation

Answer:

Step-by-step explanation:

same goes 4 him i though he loved me but 10 =5x2

Answer: C

Step-by-step explanation: Rise/run so 1/1=1 but it's going down so it negative. -1

The statements that are true are ;

1. tan(tetha) = -√3

2. the measure of the reference angle is 60°

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

The value of each angle depends on the quadrant it falls on.

First quadrant = 0-90°

second quadrant = 91° -180°

third quadrant = 181-270°

fourth quadrant = 271° - 360°

pi is measurement of angle in radians which is equivalent to 180°

therefore;

2π/3 = 2 × 180/3 = 360/3

= 120°

120 falls on the second quadrant,

tan60 = √3

tan 120 = -√3

the reference angle is 60° i.e

180-120 = 60°

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234 2/5 is equivalent to 1172/5.

234 2/5 is a mixed number, which means it is a combination of a whole number and a fraction.

To convert it to an improper fraction, we need to multiply the whole number by the denominator of the fraction and add the numerator.

The result becomes the new numerator, and the denominator stays the same.

In this case, we have:

234 2/5 = (234 x 5 + 2) / 5

= 1172/5

Therefore, 234 2/5 is equivalent to 1172/5 as an improper fraction.

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