A group of 8 friends went to lunch and spent a total of $76, which included the food bill and a tip of $16. They decided to split the bill and tip evenly among themselves. Which equations and solutions describe the situation? Select two options. The equation StartFraction 1 over 8 EndFraction (x + 16) = StartFraction 76 over 8 EndFraction represents the situation, where x is the food bill. The equation StartFraction 1 over 8 EndFraction (x + 16) = 76 represents the situation, where x is the food bill. The solution x = 60 represents the total food bill. The solution x = 60 represents each friend’s share of the food bill and tip. The equation 8 (x + 16) = 76 represents the situation, where x is the food bill.

Answer:

£2947

Step-by-step explanation:

the formula for simple interest is interest = prt.

p is the principal value, or what omar had at the beginning.

r is the rate at that you gain interest.

t is the amount of time in years.

so, plugging in our values, we multiply 2800*3*0.0175 to get 147.

now, since that was the amount of interest omar gained, we still have to add the original amount that he had, and 2800+147 = 2947.

so, the answer is £2947.

Answer:

n=6 sides

Step-by-step explanation:

We know that the sum of Interior angles of Polygon = 180(n-2)

Sum of Exterior angles of Polygon = 360

so 180(n-2)=2x360

Therefore, by solving we get n=6 sides.

The number of sides of a regular polygon is 6 sides.

The formula for calculating the sum of interior angles is (n-2)×180° where is the number of sides. All the interior angles in a regular polygon are equal. The formula for calculating the size of an interior angle is: interior angle of a polygon = sum of interior angles ÷ number of sides.

Given that, the sum of the measures of its interior angles is twice the sum of the measures of its exterior angles.

We know that, the sum of the measures of its exterior angles is 360°.

Now, the sum of the measures of its interior angles

= 2×360°

= 720°

Now, (n-2)×180°=720°

n-2=4

n=6

Therefore, the number of sides of a regular polygon is 6 sides.

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The odds of answering at least 9 questions correctly out of 15 by choosing at random is approximately 0.120

To solve this problem, we can use the binomial distribution, which models the probability of getting a certain number of successes in a fixed number of independent trials, each with the same probability of success.

In this case, we have 15 independent trials (the 15 questions) and the probability of success in each trial is 1/4 (the probability of guessing the correct answer among 4 choices). We want to find the probability of getting at least 9 successes.

Using a binomial distribution calculator, we can calculate this probability as

P(X ≥ 9) = 1 - P(X < 9) = 1 - binomcdf(15, 1/4, 8) ≈ 0.120

where binomcdf is the cumulative distribution function of the binomial distribution, which gives the probability of getting up to a certain number of successes (in this case, up to 8). The complement of this probability (1 minus the probability of getting up to 8 successes) gives the probability of getting at least 9 successes.

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The length οf the bar that shοuld be inserted tο make the ring fit the finger is apprοximately 12.57 millimeters.

Length οf bar = π × (new diameter - οriginal diameter), where π is the cοnstant pi, and new diameter and οriginal diameter are in millimeters.

The οriginal diameter οf the ring is 20 millimeters, and the new diameter that the ring needs tο fit is 16 millimeters.

Therefοre, the length οf the bar that shοuld be inserted is:

length οf bar = π × (16 - 20)

= π × (-4)

≈ -12.57 millimeters

Since the length οf the bar cannοt be negative, we can assume that it shοuld be 12.57 millimetres lοng.

Therefοre, the length οf the bar that shοuld be inserted tο make the ring fit the finger is apprοximately 12.57 millimeters.

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The theoretical probability is 0.5 and the experimental probability is 0.583

Part A:

Since the coin is fair, the probability of it landing on heads is 0.5 or 50%.

The theoretical probability of a fair coin landing on heads is 0.5.

Part B:

Let's denote the outcome of flipping the coin as H (heads) or T (tails). We flip the coin 12 times and record the frequency of each outcome:

NB: This is an assumption and not a given data;

Outcome Frequency

    H              7

    T                      5

The experimental probability of landing on heads is calculated by dividing the number of times the coin landed on heads by the total number of coin flips:

Experimental probability of landing on heads = number of heads / total number of flips

Experimental probability of landing on heads = 7 / 12 = 0.583

Part C:

Comparing the experimental probability to the theoretical probability, we can see that they are different. The theoretical probability is 0.5, while the experimental probability is 0.583. This difference can be attributed to the randomness of the coin flips and the fact that we only flipped the coin 12 times, which is a relatively small sample size. As we increase the number of coin flips, the experimental probability should converge to the theoretical probability.

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The relation is not function . Because C)No; three range values exist for domain value 3.

What is function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

The given coordinates are {(3, –1), (3, 0), (–3, 4), (3, 8)}.

Here if 3 is output and -1 is input. We know that every function should have unique output.

In the given coordinates , we have 3 for three values.

Hence the correct option is C)No; three range values exist for domain value 3.

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Answer:

x=m+10

Step-by-step explanation:

Ur just making it into an equation

:)

Answer: To write 6^-5 in expanded form, we need to first recall the definition of negative exponents. If a number a is raised to a negative exponent, it means that we take the reciprocal of a raised to the absolute value of the exponent. In other words:

a^(-n) = 1 / a^n

Using this definition, we can write:

6^-5 = 1 / 6^5

Now, we can expand 6^5 using repeated multiplication or by using a calculator. 6^5 means 6 multiplied by itself five times:

6^5 = 6 × 6 × 6 × 6 × 6 = 7776

Therefore, we can write:

6^-5 = 1 / 6^5 = 1 / 7776

So, the expanded form of 6^-5 is 1/7776.

Step-by-step explanation:

The function to represent the bacteria population after t hours is f(t) = 7400 * [tex]e^(0.13/60 * t)[/tex].

A derivative is a measure of how much a function changes as its input value changes. It is defined as the limit of the rate of change of the function with respect to its input as the change in the input approaches zero.

The function to represent the bacteria population after t hours, where the function's constant can be used to calculate the rate of change per minute is:

f(t) = 7400 * [tex]e^(0.13/60 * t)[/tex]

where:

f(t) = population of bacteria after t hours

e = Euler's number (approximately 2.71828)

t = time in hours

0.13/60 = rate of change per minute (converted from 13% per hour)

To determine the percentage rate of change per minute, we can calculate the derivative of the function with respect to time (t):

df/dt = 7400 * 0.13/60 * [tex]e^(0.13/60 * t)[/tex]

At t = 0 (the start of the experiment), the rate of change per minute is:

df/dt = 7400 * 0.13/60 * [tex]e^(0.13/60 * 0)[/tex] = 12.1166

To express this rate of change as a percentage, we can divide it by the initial population and multiply by 100:

rate of change per minute = (df/dt) / P(0) * 100% = 12.1166 / 7400 * 100% = 0.1638% (rounded to the nearest hundredth of a percent)

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The slope or gradient of a line in mathematics is a numerical representation of the steepness and direction of the line and in the given situation the slope (m) is -1/4 respectively.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b.

M represents the line's slope.

And b is the b in the point that is the y-intercept (0, b).

For instance, the slope and y-intercept of the equation y = 3x - 7 are 3 and 0, respectively.

So, the slope formula is:

m = y₂-y₁/x₂-x₁

Now, insert values as follows:

m = y₂-y₁/x₂-x₁

m = 4-5/-3-(-7)
m = -1/-3+7

m = -1/4

Therefore, in the given situation the slope (m) is -1/4 respectively.

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The length of line segment AC is equal to 34 units.

In Mathematics and Geometry, the Tangent Secant Theorem states that if a secant segment and a tangent segment are drawn to an external point outside a circle, then, the product of the length of the external segment and the secant segment's length would be equal to the square of the tangent segment's length.

By applying the Tangent Secant Theorem to this circle, we have the following:

DC² = AB × BC

15² = (3x + 1) × 9

225 = 27x + 9

27x = 225 - 9

27x = 216

x = 216/27

x = 8

Now, we can determine the length of AC;

AC = AB + BC

AC = 3x + 1 + 9

AC = 3(8) + 1 + 9

AC = 34 units.

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Answer:

only [tex]\sqrt{101}[/tex] is irrational

Step-by-step explanation:

an irrational number cannot be expressed as a fraction

0.329 = 329/1000

127.5 = 1275/10

-89 = -89

[tex]\sqrt[3]{64}[/tex] = 4

Answer: The second piece-wise function, f(x), will produce the graph given.

The probability that your mail will be delivered before 2 pm for 2 consecutive days is 0.81.

Given,

The probability that your mail is delivered before 2 pm is 0.90.

To find:The probability that your mail will be delivered before 2 pm for 2 consecutive days

Probability that your mail will be delivered before 2 pm for 1 day = 0.90

Probability that your mail will be delivered before 2 pm for 2 consecutive days = P(1st day before 2pm) and

P(2nd day before 2pm)P(1st day before 2pm) and P(2nd day before 2pm) = 0.90 × 0.90= 0.81

Hence, The probability that your mail will be delivered before 2 pm for 2 consecutive days is 0.81.

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Answer:

Ignore this my answer is wrong

Therefore, the bumblebee bat is 0.5 centimeters shorter than the Etruscan pygmy shrew.

Inequalities are used in many areas of mathematics, including algebra, calculus, and geometry. They are also used in other fields such as economics, physics, and engineering to model real-world situations where values can vary within certain bounds. Solving inequalities involves finding the set of values that satisfy the inequality. This can be done using algebraic techniques such as adding or subtracting the same quantity from both sides of the inequality, multiplying or dividing both sides of the inequality by a positive number, or using the properties of absolute value. The solution to an inequality is often expressed as an interval or a set of numbers that satisfy the inequality.

Here,

According to the Guinness World Records, the bumblebee bat is the smallest mammal in the world, measuring only about 3 centimeters in length, while the Etruscan pygmy shrew measures about 3.5 centimeters in length.

To find out how much shorter the bat is than the shrew, we can subtract the length of the bat from the length of the shrew:

3.5 cm - 3 cm = 0.5 cm

The bumblebee bat and the Etruscan pygmy shrew are both very small mammals, but the bumblebee bat is actually shorter than the Etruscan pygmy shrew.

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The ship sailing in a straight line from the Isle of Strutay to Emerald Cay should travel on a bearing of approximately 72.6°.

We can use the Law of Cosines to find this angle. Let's call this angle θ.

cos θ = (a² + b² - c²) / (2ab)

where a is the distance between the Isle of Strutay and Crook Island (25 km), b is the distance between Crook Island and Emerald Cay (40 km), and c is the distance between the Isle of Strutay and Emerald Cay (65 km).

cos θ = (25² + 40² - 65²) / (2 x 25 x 40)

cos θ = 0.275

θ = cos⁻¹(0.275)

θ ≈ 72.6°

Therefore, the ship sailing in a straight line from the Isle of Strutay to Emerald Cay should travel on a bearing of approximately 72.6° (east of north).

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A line plot can be a useful tool for the students to analyze their results because it allows them to easily see the distribution of heights among the 20 students. By plotting each student's height as a dot above a number line, the students can quickly see how many students fall into each height range and identify any outliers or patterns in the data.

For example, if most of the dots fall within a small range of heights, the students can see that there is a cluster of heights in that range. Conversely, if there are only a few dots in a particular height range, the students can see that there is less variation in that range.

The line plot can also help the students to identify the mode, which is the most common height among the students, and the median, which is the middle height when the heights are ordered from smallest to largest. These measures of central tendency can help the students to understand the typical height of their classmates and how much variation there is in the data.

Overall, a line plot is a simple and effective way for the students to visualize and analyze their height data, and it can help them to draw meaningful conclusions about the distribution of heights among the 20 students.

Entertainment will comprise 90% of Ryan's total budget. The amount budgeted towards entertainment each month will be 90% of his take-home pay.

The number of periods or cycles per second is called frequency. The SI unit for frequency is the hertz (Hz). One hertz is the same as one cycle per second.

Let's assume Ryan's take-home pay is P dollars.

Given that Ryan saves 10% of his take-home pay for retirement, he will save 0.10P dollars.

The remainder of his take-home pay after saving for retirement will be 90% of his take-home pay, which is 0.90P dollars.

Now, if Ryan allocates the remainder of his take-home pay to entertainment, the percentage of his total budget that entertainment will comprise can be calculated as:

Percentage of entertainment budget = (Entertainment budget / Total budget) * 100

Since the entertainment budget is 0.90P dollars and the total budget is P dollars, the percentage of his total budget that entertainment will comprise is:

Percentage of entertainment budget = (0.90P / P) * 100

Percentage of entertainment budget = 90%

So, entertainment will comprise 90% of Ryan's total budget.

The amount of money budgeted towards entertainment each month will be 0.90P dollars, which is 90% of his take-home pay.

Therefore, Entertainment will comprise 90% of Ryan's total budget. The amount budgeted towards entertainment each month will be 90% of his take-home pay.

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Answer:

0.96%

Step-by-step explanation:

do not answer with 0.966% it WILL be wrong and is a VERY common calculation error due to a very small mistake

The mirror line will be on -2 on the x axis. Then from that, you reflect the shape

Using Trigonometric functions, the height of the tree is approximately 50.6 feet.

Let's call the height of the tree "h" and the distance between the forester's original position and the base of the tree "x". Then, when the forester moves 20 feet closer to the tree, the distance between the new position and the base of the tree is "x - 20".

We can use the tangent function to set up two equations relating the height of the tree to the angles of elevation:

tan(37°) = h/x ...(1)

tan(52°) = h/(x - 20) ...(2)

We can solve this system of equations to find the value of "h". First, we can rearrange equation (1) to get:

x = h/tan(37°)

Then, we can substitute this expression for "x" into equation (2) and solve for "h":

tan(52°) = h/(h/tan(37°) - 20)

Simplifying and solving for "h", we get:

h = (20 tan(52°) tan(37°)) / (tan(52°) - tan(37°))

Using a calculator, we can evaluate this expression and find that:

h ≈ 50.6 ft

Therefore, the height of the tree is approximately 50.6 feet.

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Answer:

can you like write it out normally please, i can answer it then

Step-by-step explanation:

Step-by-step explanation:

Equation of a circle

(x-h)^2  + (y-k)^2 = r^2

 so the given circle has center at  (h,k) = (5,-10)

    new circle center will be at x = 1 left of 5 = 4    y = 2 down from -10 = -12

            (4,-12)              

Equation then becomes     (x-4)^2 + ( y+ 12)^2 = 64                

Exponential smoothing, simple moving averages, autoregressive models, and regression-based models are all commonly used methods for analyzing and forecasting seasonal data.

Regression-based models are statistical models that use the relationship between a dependent variable and one or more independent variables to predict or explain the behavior of the dependent variable. These models estimate the strength and direction of the relationships between the variables by fitting a regression line or curve to the observed data. They can be used for both descriptive and predictive purposes and are widely used in various fields, including economics, finance, marketing, and social sciences. Examples of regression-based models include linear regression, logistic regression, and time-series regression.

Here,

Seasonal data refers to data that exhibits regular patterns that repeat over a fixed time period, such as weekly, monthly, or yearly. The methods that are best for dealing with seasonal data are those that take into account the regular patterns and fluctuations in the data over time. Methods that are best when you are dealing with seasonal data:

a. Exponential smoothing

c. Simple moving averages

d. Autoregressive models

e. Regression based models

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The exact value of the volume of the sphere is V = 20.833π cm³ and the exact value is V = 64.45 cm³

A sphere is defined as symmetrical and round in shape. It is also referred to as a three dimensional solid, that has all its surface points at equal distances from the center.

The formula for the volume of a sphere is:

V = ⁴/₃πr³

where:

V = volume

r = radius

The radius of a sphere is half its diameter.

We are given diameter = 5cm

Thus: r = 5/2 = 2.5 cm

V = ⁴/₃π * 2.5³

V = 20.833π cm³

V = 64.45 cm³

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The length of RS is approximately 73 meters (to the nearest meter).

What is Law of sines ?

The Law of Sines is a trigonometric formula that relates the side lengths of a triangle to the sine of its angles. It states that in any triangle ABC:

a / sin(A) = b / sin(B) = c / sin(C)

where a, b, and c are the side lengths of the triangle, and A, B, and C are the opposite angles.

This formula can be used to solve for the unknown sides or angles of a triangle when given enough information about the other sides and angles. The Law of Sines is especially useful when dealing with triangles that are not right triangles, or when only a few side lengths and angles are known.

According to the question:

We can solve this problem by using the Law of Sines and the fact that the sum of the angles in a triangle is 180 degrees.

First, we can find the measure of angle A in triangle ABC:

A = 180 - 48 - 48 = 84 degrees

Next, we can use the Law of Sines to find the length of side AC:

sin(84) / 50 = sin(48) / AC

AC = sin(84) * 50 / sin(48) ≈ 64.4

Now, we can use the fact that the sum of the angles in triangle AQS is 180 degrees to find the measure of angle QAS:

QAS = 180 - 20 - 90 = 70 degrees

Finally, we can use the Law of Sines again to find the length of RS:

sin(70) / RS = sin(48) / AC

RS = sin(70) * AC / sin(48) ≈ 72.6

Therefore, the length of RS is approximately 73 meters (to the nearest meter).

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Apples make up one-third of the dozen fruits in a fruit vendor cart. If bananas make up the remaining fruit and oranges make up 1/4 of the total fruit, there are 2.5 dozen bananas in the fruit vendor's cart.

First, let's calculate how many apples are in the cart:

1/3 of 6 dozen fruits = 2 dozen fruits are apples

Next, let's calculate what proportion of the fruits are oranges:

1/4 of all fruits = (1/4) x 6 dozen = 1.5 dozen fruits are oranges

To find the number of dozen bananas, we can subtract the number of dozen apples and oranges from the total number of dozen fruits in the cart:

Total number of dozen fruits = 6 dozen

Number of dozen apples = 2 dozen

Number of dozen oranges = 1.5 dozen

Number of dozen bananas = 6 dozen - 2 dozen - 1.5 dozen

Number of dozen bananas = 2.5 dozen

Therefore, there are 2.5 dozen bananas in the fruit seller's cart.

The complete question is:-

1/3 of the 6 dozen fruits in a fruit seller cart are apple. If 1/4 of all the fruits are oranges and the rest of the fruits are bananas, find how many dozen bananas are there in the fruits sellers cart

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Answer:

≈38.57 units.

Step-by-step explanation:

To find the perimeter of a rectangle, we need to add up the lengths of all its sides.

First, gather the coordinates:

R - (4, 5)

U - (8, -3)

F - (-6, 0)

O - (-2, -8)

Using the coordinates given, we can calculate the lengths of the sides of the rectangle using the distance formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)

So, for the rectangle with vertices R, U, F, and O, we have:

Side RU: d = √((8 - 4)^2 + (-3 - 5)^2) = √(16 + 64) = √80

Side UF: d = √((-6 - 8)^2 + (0 - (-3))^2) = √(196 + 9) = √205

Side FO: d = √((-6 - (-2))^2 + (0 - (-8))^2) = √(16 + 64) = √80

Side OR: d = √((-2 - 4)^2 + (-8 - 5)^2) = √(36 + 169) = √205

Since opposite sides of a rectangle are congruent, we have RU = FO and UF = OR. Therefore, the perimeter of the rectangle is:

Perimeter = RU + UF + FO + OR

Perimeter = √80 + √205 + √80 + √205

Perimeter ≈ 38.57

Therefore, the perimeter of the rectangle is approximately 38.57 units.