Huan has $100 to spend on video games. If each video game is $40 and he pays $5 in tax, how much money does Huan have left over?

Answer:

Step-by-step explanation:
To find the average number of days it takes for the sun to rotate once, we can add the three rotation periods and divide by 3:

Average rotation period = (24.5 + 24.8 + 34.3) / 3

Average rotation period = 83.6 / 3

Average rotation period = 27.87 days (rounded to two decimal places)

Therefore, the average number of days it takes for the sun to rotate once based on the given information is approximately 27.87 days.

The best measure of central tendency for this data is the mode, which is the most frequently occurring value in a dataset.

In this case, the grilled ribeye is the most popular selling dinner item with 2,021 portions sold, making it the mode of the data. While the mean and median are also measures of central tendency, they may not be as appropriate for this data since the counts for the grilled ribeye are much higher than the other two items.

Using the mean would give too much weight to the grilled ribeye, and using the median would not accurately represent the most popular item. Therefore, the mode is the best choice for this data.

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Answer:

The first one

Step-by-step explanation:

Use the pythagoras theorem=a ^2+b^2 =c^2

Use a is 9 b is 40 because the largest value is always the hypotenuse and the hypotenuse is always c.

so you do 9 squared add 40 squared to find c squared.

Square root the answer and you get 41 so it is a pythagoras triple

Since Shay's sibling is 7 years younger than twice her age, Shay is therefore 29 years old.

Mathematicians use the unitary method, also referred to as the "single unit technique," to answer problems involving proportional relationships between two or more quantities. The unitary technique entails determining the value of a single unit or quantity and using that value to calculate the values of other quantities in relation to that unit or quantity. Problems requiring ratios, proportions, percentages, and other related ideas can be solved using this approach.

given

Shay's age will be denoted by the letter S, and her sister's age will be referred to as "Sister".

The first claim informs us of the following:

Sibling = 2S – 7

And based on the second assertion, we can infer that:

Sibling + S = 80

The result of putting the first equation into the second equation is:

S + (2S - 7) = 80

When we simplify this solution, we obtain:

3S - 7 = 80

7 added to both edges gives us:

3S = 87

When we multiply both parts by 3, we get:

S = 29

Since Shay's sibling is 7 years younger than twice her age, Shay is therefore 29 years old.

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The value of y when x = 25 is 30

What are direct variations ?

One quantity directly changes in response to a change in another quantity, which is referred to as direct variation. This suggests that if one quantity increases, the other will follow suit and rise in proportion. In a similar manner, if one quantity declines, the other amount also declines.

given y is directly proportional to x then the equation connecting them is

y = kx ← k is the constant of proportionality

To find k use the condition y = 36 when x = 30

So, 36=k(30)

=> k = 36/30 = 1.2

equation of proportionality:

y=1.2x

When x = 25 then

y=1.2(25) = 30

The value of y when x = 25 is 30

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Therefore, the length of the perpendicular is 1 cm. Therefore, the length of the perpendicular is approximately 1.335 cm (rounded to three decimal places).

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used to solve problems related to geometry, physics, engineering, and many other fields. Trigonometry is based on the study of the six trigonometric functions: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). These functions describe the ratios of the lengths of the sides of a right triangle, and can be used to calculate the unknown side lengths or angles of a triangle.

Here,

a. Given that the hypotenuse is 2 cm and the angle is 30 degrees, we can use trigonometry to find the length of the perpendicular. Let's call the length of the perpendicular x. Using the trigonometric ratio for sine (sin), we have:

sin(30°) = opposite/hypotenuse

sin(30°) = x/2

Multiplying both sides by 2:

2*sin(30°) = x

We know that sin(30°) is equal to 0.5, so we can substitute that in:

2*0.5 = x

x = 1

b. Given that the base is 3 cm and the angle is 24 degrees, we can use trigonometry to find the length of the perpendicular.

Let's call the length of the perpendicular x.

Using the trigonometric ratio for tangent (tan), we have:

tan(24°) = opposite/adjacent

tan(24°) = x/3

Multiplying both sides by 3:

3*tan(24°) = x

We may use a calculator to find the value of tan(24°), which is approximately 0.445:

3*0.445 = 1.335

c. cos 72°=x/9

0.3091*9=x

x=2.78 units

d.  cos 23°=5.9/x

x=5.9/0.9205

x=6.409 units

e. sin 36°=3.6/x

x=3.6/0.5877

x=6.1255 units

f. cos 48°=4.3/x

x=4.3/0.6691

x=6.4226 units

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There are 55 children in total, and each team will have 27 children.

Now, you mentioned that there are 55 children in total. To find out how many children are on each team, we need to divide the total number of children by the number of teams. In this case, there are two teams, so we divide 55 by 2.

When we divide 55 by 2, we get 27.5. However, we cannot have half a child on a team, so we need to round the number to the nearest whole number. In this case, the median can be used to determine the most appropriate rounding.

The median is the middle value of a set of numbers. In this case, if we arrange the numbers 1, 2, 3, ..., 55 in ascending order, the median will be the 28th number.

Now, we have two options for rounding. We can either round up to 28 or round down to 27. Since we cannot have a partial player, we must decide which option is most appropriate.

In this case, it's best to have an equal number of players on each team. Therefore, we'll round down to 27. This means that each team will have 27 children.

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Let p be the probability of an adult over 50 wearing glasses for driving. Since we don't know the value of p, we can't use the binomial distribution directly. However, we can use the normal approximation to the binomial distribution since n is large (assuming n * p >= 10 and n * (1-p) >= 10).

Let X be the number of adults over 50 wearing glasses for driving in a random sample of n adults. Then X ~ Binomial(n, p) can be approximated by a normal distribution with mean µ = n * p and standard deviation σ = sqrt(n * p * (1-p)).

We want to find the probability that at least six adults over 50 in a random sample of n wear glasses for driving. This is equivalent to finding P(X >= 6) = 1 - P(X < 6) using the normal approximation.

To apply the normal approximation, we need to standardize the random variable X:

Z = (X - µ) / σ

Using continuity correction:

P(X >= 6) = P(X > 5.5)

Z = (5.5 - n * p) / sqrt(n * p * (1-p))

We can use the standard normal distribution table or calculator to find the probability:

P(Z >= (5.5 - n * p) / sqrt(n * p * (1-p)))

Since we don't know the value of p, we can use a conservative estimate of p = 0.5 (assuming 50% of adults over 50 wear glasses for driving). Then:

P(Z >= (5.5 - n * 0.5) / sqrt(n * 0.5 * (1-0.5)))

For example, if we sample n = 100 adults over 50, the probability of at least six wearing glasses is:

P(Z >= (5.5 - 100 * 0.5) / sqrt(100 * 0.5 * (1-0.5)))

= P(Z >= 0.5)

Using a standard normal distribution table or calculator, P(Z >= 0.5) = 0.3085.

Therefore, the probability of at least six adults over 50 wearing glasses for driving in a random sample of 100 is approximately 0.3085 or 30.85%.

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Answer:96

Step-by-step explanation:

[tex]Area=\frac{d1 d2}{2}[/tex]

[tex]Area=\frac{(6+6)(8+8)}{2}[/tex]

[tex]Area=96[/tex]

From the given information provided, the area of the deck Edgar built in his backyard is 192 square feet.

The area of rectangular section is :

Area of rectangle = length x width

Substituting the given values, we get:

Area of rectangle = 16 ft x 8 ft

Area of rectangle = 128 square feet

The area of square section is :

Area of square = side x side

Substituting the given value, we get:

Area of square = 8 ft x 8 ft

Area of square = 64 square feet

Therefore, the total area of the deck is the sum of the area of the rectangular section and the area of the square section:

Total area of deck = Area of rectangle + Area of square

Total area of deck = 128 square feet + 64 square feet

Total area of deck = 192 square feet

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Answer:

Step-by-step explanation:

150.7083

Similarly, the conditional pdf of Y given X, fy|x(y|x), is found by dividing the joint pdf, fxy(x,y), by the marginal pdf of X, fx(x). Thus, fy|x(y|x) = fxy(x,y)/fx(x) = 3/11e-ly for 0 < x < y < ∞.

The marginal pdf of X, fx(x), is the probability density function of X. It is found by integrating the joint pdf, fxy(x,y), with respect to Y over all possible values of Y. Thus, fx(x) = ∫-∞∞fxy(x,y)dy = 11e-ly for 0 < x < ∞. The marginal pdf of Y, fy(y), is found in the same way, but by integrating with respect to X over all possible values of X. Thus, fy(y) =[tex]∫0yfxy(x,y)dx = 11e-lyy for 0 < y < ∞.[/tex]

The conditional pdf of X given Y, fx|y(x|y), is the probability density function of X given that Y has a certain value. It is found by dividing the joint pdf, fxy(x,y), by the marginal pdf of Y, fy(y).

Thus, fx|y(x|y) =[tex]fxy(x,y)/fy(y) = 3/11e-lyy for 0 < x < y < ∞.[/tex]

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Matthew can travel up to 150 miles for $50, assuming the cost of the limo ride remains constant at a $20 fixed cost plus $0.20 per mile. Let's say Matthew has $50 to spend on the limo ride.

We know that the cost per mile is $0.20, so we can set up an equation:

Cost = $20 + $0.20 x Distance

We can substitute $50 for Cost and solve for Distance:

$50 = $20 + $0.20 x Distance

$30 = $0.20 x Distance

Distance = $30 / $0.20

Distance = 150 miles

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Answer:

16

Step-by-step explanation:

a^2 + b^2 = c^2

a^2= 3^2 = 9

c^2=5^2 = 25

25-9= b^2

25-9=16

b^2 = 16

Hence, the population proportion's 95% confidence interval is (0.210, 0.290), rounded to the thousandths place.

A mathematical concept known as proportionality describes the relationship between two quantities that have different sizes but keep the same ratio or proportion. In other words, to preserve the same ratio, if one item changes, the other quantity must also change in proportion. For instance, if an automobile's speed and distance are proportionate, doubling the distance it travels will cause the car to go twice as quickly while retaining the same speed-to-distance ratio. Equations or ratios in mathematics are frequently used to express proportionality.

given

We can use the following formula to determine the lower and upper bounds of the 95% confidence interval for the population proportion:

Lower limit: sqrt((p * q) / n) * p - z

Upper limit: sqrt((p * q) / n) = p + z

With q = 1 - p, z is the z-score corresponding to the level of confidence, and p is the sample proportion.

Here, p = 130/520 = 0.25, q = 1 - p = 0.75, n = 520, and the z-score is 1.96 at a 95% confidence level (from the standard normal distribution).

Lower limit: 0.210 (0.25" * 0.75") - 1.96 * sqrt(0.25" * 0.75")

The maximum is equal to 0.25 + 1.96 * sqrt((0.25 * 0.75) / 520) = 0.290.

Hence, the population proportion's 95% confidence interval is (0.210, 0.290), rounded to the thousandths place.

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This equation represents the linear relationship between the dependent variable (y) and the independent variable (x) with a slope of 2 and a y-intercept of -3.

However, I can provide a general example using common terms in algebra:
Terms: Dependent variable (y), independent variable (x), slope (m), and y-intercept (b).
To represent a linear relationship between two variables, we can use the equation of a straight line, which is often written as:
[tex]y = mx + b[/tex]
Here's what each term in the equation represents:
1. y: This is the dependent variable, meaning its value depends on the value of the independent variable (x). In a graph, it is usually represented on the vertical axis.
2. x: This is the independent variable, which can take any value within a given range. It is usually represented on the horizontal axis in a graph.
3. m: This is the slope of the line, representing the rate at which the dependent variable (y) changes with respect to the independent variable (x). A positive slope indicates an increasing relationship, while a negative slope indicates a decreasing relationship.
4. b: This is the y-intercept, which is the point where the line crosses the y-axis. It represents the value of the dependent variable (y) when the independent variable (x) is equal to zero.
simply plug in the values for the slope (m) and y-intercept (b). For example, if the slope is 2 and the y-intercept is -3, the equation would be:
[tex]y = 2x - 3[/tex]

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Answer: 9 cm

Step-by-step explanation: 4+5=9

To paint an 8 foot by 10 foot wall with Sunset Orange, one needs 48 parts of Fire Red and 80 parts of Brilliant Yellow.Using the graph, we can calculate that for every 5 parts of Brilliant Yellow, 3 parts of Fire Red is needed.

Using the graph, we can calculate that for every 5 parts of Brilliant Yellow, 3 parts of Fire Red is needed. Since we need to paint an 8 foot by 10 foot wall, we need 80 square feet of paint. To calculate how much Fire Red is needed, we can use the equation: 3 parts of Fire Red = 5 parts of Brilliant Yellow. We can rearrange this equation to read: 5 parts of Brilliant Yellow = 3 parts of Fire Red. To get the amount of Fire Red required to paint the wall, we can multiply 80 (the square footage of the wall) by 3 and divide it by 5, giving us a total of 48 parts of Fire Red.

To paint an 8 foot by 10 foot wall with Sunset Orange, one needs 48 parts of Fire Red and 80 parts of Brilliant Yellow.

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The probability of winning is 1/42 expressed as a fraction.

Given that the odds on a bet are 41:1 against, we are to find the probability of winning.

We know that odds against = (Number of unfavorable outcomes) : (Number of favorable outcomes).

Thus, odds against = 41:1. This implies that the number of unfavorable outcomes is 41 and the number of favorable outcomes is 1.Probability of winning is given by the formula P(winning) = Number of favorable outcomes / Total number of possible outcomes. In this case, the total number of possible outcomes is the sum of the number of favorable and unfavorable outcomes.

Number of favorable outcomes = 1 and Number of unfavorable outcomes = 41

Therefore, the total number of possible outcomes = 1 + 41 = 42

Thus, P(winning) = Number of favorable outcomes / Total number of possible outcomes

P(winning) = 1 / 42

Therefore, the probability of winning is 1/42 expressed as a fraction.

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The admission fee at an amusement park is $4.25 for children and $7.00 for adults. on a certain day, 303 people entered the park, and the admission fees collected totaled 1824 dollars. There are 108 children and 195 adults were admitted

Let the number of children admitted = C and the number of adults admitted = A

Total number of people admitted = 303

We can form two equations from the given information.

The first equation is to represent the number of people admitted in terms of children and adults.

So, the equation will be

C + A = 303 ------(1)

The second equation represents the total amount collected from admission fees.

So, the equation will be

4.25C + 7A = 1824 ------(2)

Multiplying equation (1) by 4.25, we get

4.25C + 4.25A = 1289.25 ------(3)

Subtracting equation (3) from equation (2), we get:

7A - 4.25A = 1824 - 1289.25

Simplifying, we get:

2.75A = 534.75

Dividing by 2.75, we get:

A = 195

Putting A = 195 in equation (1), we get:

C + 195 = 303

Simplifying, we get:

C = 108

So, there were 108 children and 195 adults admitted on that day.

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Thus, the explicit formula for the simple interest sequence A(n) = P + (n-1)(i.P) is: A(n) = P * (1 + i * (n-1)).

Simple interest is a method of calculating interest on a loan or investment where interest is charged only on the initial principal amount. In simple interest, the interest rate is applied to the original principal amount, and the interest earned remains the same throughout the entire term of the loan or investment.

by the question.

The formula for a simple interest sequence A(n) = P + (n-1) (i.P) represents the value of an investment that earns simple interest over n periods, where:

A(n) is the value of the investment after n periods.

P is the principal or initial investment

i is the interest rate per period as a decimal fraction (e.g. 0.05 for 5%)

n is the number of periods

To derive the explicit formula for A(n), we can use the formula for simple interest:

I = P * i * n

where I am the total interest earned over n periods. We can then express A(n) as:

A(n) = P + I

Substituting the expression for I, we get:

A(n) = P + P * i * (n-1)

Simplifying, we can factor out P to get:

A(n) = P * (1 + i * (n-1))

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Therefore , the solution of the given problem of function comes out to be  growth factor resulting from the 4.6% yearly growth rate is represented by the constant factor e(0.046t).

On the midterm exam, there will be inquiries on design, arithmetic numbers, every class, and both actual and hypothetical places. a description of the connections between various components that come together to produce the same outcome. A service is built from a variety of unique parts that work together to deliver unique outcomes for each input. Each post also has a location, which might be the enclave, a municipality, or even something else altogether.

Here,

The value of the stock t years since 2000 can be represented by the function by assuming that the stock's value increases constantly at a rate of 4.6% per year:

=> V(t) = 1569 * e^(0.046t)

where t is the number of years since the year 2000 and e is the algebraic constant

=>e = 2.71828.

With this function, exponential growth is represented by multiplying the stock's starting value in the year 2000 (1569) by the constant factor e(0.046t) to get the value of the stock t years later.

The growth factor resulting from the 4.6% yearly growth rate is represented by the constant factor e(0.046t).

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As a result, the compound inequality has the following solution:               -1 ≤ x < 28/9

An inequality in mathematics is a claim that two values or expressions are not equivalent to one another. A spectrum of potential values for a variable can be described by an inequality, which can also be used to compare the values of two quantities. There are various kinds of inequality, such as: Inequalities involving linear expressions or formulae are referred to as linear inequalities. An illustration of a linear inequality is 2x + 3 7. Inequalities involving quadratic expressions or formulae are known as quadratic inequalities. x2 - 4x + 3 > 0 is an illustration of a quadratic equation.

given

The compound inequality is as follows:

-4 ≤ 3x - 1 < 8

This can be resolved by splitting it into two distinct inequalities:

-4 <= 3x - 1 and 3x - 1 < 8

By adding 1 to both sides and dividing by 3, we can solve the first equation for x:

-4 + 1 ≤ 3x - 1 + 1/3

-3/3 ≤ x

-1 ≤ x

Solving the second inequality for x, we add 1 to both sides and split by 3:

3x - 1 + 1/3 < 8 + 1/3

3x < 9 + 1/3

3x < 28/3

x < 28/9

As a result, the compound inequality has the following solution:               -1 ≤ x < 28/9

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The volume of the cone in terms of π is option (c) 100π in^3

The formula for the volume of a cone is given by:

V = (1/3)πr^2h

where r is the radius of the base of the cone, h is the height of the cone.

In this case, we are given that the radius of the cone is 5 in and the slant height is 13 in. We can use the Pythagorean theorem to find the height of the cone:

h^2 = y^2 - r^2

h^2 = 13^2 - 5^2

h^2 = 144

h = 12 in

Therefore, the volume of the cone is:

V = (1/3)πr^2h

V = (1/3)π(5^2)(12)

V = (1/3)π(25)(12)

V = (1/3)(300π)

V = 100π cubic inches

Therefore, the correct option is (c) 100π in^3

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Answer: 100π in3

Step-by-step explanation:

Answer:

a) 640 ml

b) 40 ml

Step-by-step explanation:

The ratio of lime to lemonade for the fizzy drink is 5 : 3 or as a fraction that would be

[tex]\dfrac{\text{Lime juice}}{\text{Lemonade}}= \dfrac{5}{3}[/tex]

[tex]\text{Therefore the ratio of lemonade to lime }\\\\ = \text{reciprocal of $ \dfrac{5}{3} $} }\\\\= \dfrac{3}{5}[/tex]

Part a)

For  all 400 ml of  lime juice we would need
[tex]\dfrac{3}{5} \times 400 \;ml = 3 \times 80 = 240 \;ml[/tex]  

Total amount of fizzy drink that can be maade
= amount of lime juice + amount of lemonade

= 400 + 240

= 640 ml

This is the answer to Part a)

Part b)

If Gianni has only 280 ml and is using all 400 ml of lime juice then the amount of lemonade used as calculated in part 1) is 240ml

That means the amount of lemonade left over = 280 - 240 = 40 ml

The value of x in the given triangle is 1.82 cm using the angle bisector theorem.

A triangle is a polygon with three edges and three vertices. It belongs to the basic geometric shapes. A triangle with the parts A, B, and C is referred to as triangle ABC. Any three points that are not collinear in Euclidean geometry result in a separate triangle and a distinct plane. A triangle is a type of polygon with three sides; the triangle's apex is the point where the two longest sides meet. Two sides are brought together at an angle.

What is angle bisector theorem?

The ratios of the two segments that a line that bisects the opposing angle splits a triangle's side into are the subject of the angle bisector theorem in mathematics. It contrasts their proportionate lengths with the other two triangle sides' proportional lengths.

In the given triangle,

5/6=x/4-x

20-5x=6x

20=11x

x=20/11= 1.82 cm

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Answer:

1.6.1) Inversely proportional

1.6.2) 0.6h

1.6.3) 120km

Step-by-step explanation:

1.6.1)

Inversely proportional relationships are in the form of [tex]y=k/x[/tex]

[tex]y=time=t[/tex]

[tex]x=speed=v[/tex]

If we the relationship is inversely proportional, [tex]k[/tex] must be constant for all values.

[tex]yx=k[/tex]

So we just have to check the value of [tex]yx[/tex] in all cases.

[tex]20*3=60\\50*1.2=60\\80*0.75=60[/tex]

Hence relation is inversely proportional.

1.6.2)

[tex]k=60, x=100, y=k/x\\[/tex]

∴[tex]y=60/100[/tex] ⇒[tex]y=0.6[/tex]

1.6.3)

Distance formula:

[tex]v=s/t\\v*t=s\\s=(20*3) + (50*1.2)\\s=60 + 60\\s=120[/tex]

The given statement "the sampling distribution becomes approximately normal, for all statistics, if there is a large enough sample size" is True as it is proved by the central limit theorem.

The central limit theorem (CLT) states that for large enough sample sizes, the distribution of the sample means approximates a normal distribution regardless of the shape of the initial population distribution.

It is a statistical theory that clarifies how the mean of a random sample of independent observations drawn from a non-normal population converges in distribution to a normal population.

According to this theory, the sample size should be at least 30 for the sample mean to have an approximately normal distribution. The following are the fundamental assumptions of the central limit theorem:

Therefore, we can say that the sampling distribution becomes approximately normal, for all statistics, if there is a large enough sample size. The statement is true.

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