Alexia and Tony went went for dinner and their meal cost $49.77. If they want to leave a 15% tip for their server, how much will the tip amount be? How much will their total bill be?

According to the histogram 87.5 - 90.5 range of length (in inches) contains the longest sampled eastern diamondback rattlesnake.

In statistics, a histogram is a graphic representation of data distribution. Each bar in the histogram represents a different type of data, and the histogram is displayed as a group of adjacent rectangles. Statistics is a discipline of mathematics that is used in many different fields.

Frequency, which may be expressed as a table and is known as a frequency distribution, is the repeating of numbers in statistical data. One type of graph that can be used to illustrate a frequency distribution visually is a histogram.

The range of a histogram is the x-axis breadth that the bars cover. Since histograms show bin values rather than actual data values, these numbers are approximations.

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Complete question:

Question According to the histogram, which range of length (in inches) contains the longest sampled Eastern diamondback rattlesnake? Provide your answer below: greater than but less than

The angular speed of the wheel is 0.314 rad/sec and the linear speed of the car is 8.164 feet/second .

Angular speed is defined as the rate of change of angular displacement, and it is expressed as follows: ω = θ/ t

one revolution = 360°

180° = π

360° = 2π

3 revolution = 3× 2π = 6π

1 minute = 60 ×1 = 60s

angular speed = 6× 3.14/60

= 0.314 rad/s

The linear velocity =

V = wr

r = d/2

r = 52/2 = 26 feet

V = wr

V = 0.314× 26

V = 8.164 feet/second

Question: A Ferris wheel at a carnival has a diameter of 52 feet. Suppose it turns at a rate of 3 revolutions per minute. i. What is the angular speed of the wheel.

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Answer:

The formula for the surface area of a sphere with radius r is 4πr^2. Plugging in the given radius of 8, we get:

Surface area = 4π * 8^2 = 4π * 64 = 256π

Using an approximate value of π = 3.14, the surface area of the sphere is approximately:

256 * 3.14 = 803.84

Rounding to the nearest hundredth, the surface area of the sphere is approximately 803.84 square units.

Answer:

803.84cm²

Area of a sphere = 4πr²

When we put the given values we get

Area of a sphere = 4x3.14x8²

Area of a sphere = 4x3.14X16

                             = 804.25cm²

Rounding to the nearest hundredth we get,

803.84cm²

H is a subgroup of G since it is closed under the group operation, contains the identity element and inverses of its elements.

A subset H of a group G is a subgroup of G if it satisfies the following three properties:

1. Closure: H is closed under the group operation, that is, if α, β∈H then αβ∈H.

2. Identity element: H contains the identity element e of G.

3. Inverses: For each element α∈H, its inverse (or reciprocal) α−1 is also an element of H.

In this case, the subset of G consisting of elements of finite order (H) satisfies all of these three properties. Since H is closed under the group operation, if α, β∈H then αβ∈H. The identity element of G, e, is also an element of H since the order of the identity element is always 1, which is finite. Finally, for each element α∈H, its inverse α−1 is also an element of H since the inverse of a finite order element is also of finite order. Therefore, by satisfying all of the three properties of a subgroup, H is indeed a subgroup of G.

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Answer:

f(x) =[tex]\frac{10}{11}[/tex]x [tex]-\frac{16}{11}[/tex]

Step-by-step explanation:

The format of the linear function f(x) is ax + b. Thus, we can list the following equations:

4 = 6a + b .... (1)

-6 = -5a + b .... (2)

We can use the first equation to subtract the second equation getting: 10 = 11a. This means a = [tex]\frac{10}{11}[/tex]. From that, if we plug in the value of a into the first equation, we get 4 = [tex]\frac{60}{11}[/tex] + b, so b = [tex]-\frac{16}{11}[/tex]. Thus, f(x) =[tex]\frac{10}{11}[/tex]x [tex]-\frac{16}{11}[/tex]

The original cost of the sweater is $60.

Percentage is simply defined as the parts of a number per fraction of 100.

Percentage is usually denoted by the symbol '%'.

Percentage of a number in a whole can be calculated by dividing the number by the whole and then multiply with 100.

Given that,

A sweater is on sale for a 20% discount. The amount of the discount is $12.

Percentage of discount = 20%

Amount of the discount = $12

Let x be the original cost of the sweater.

20% of x = 12

0.2x = 12

x = 60

Hence the original price of the sweater was $60.

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[tex]\begin{cases} x = -2 &\implies x +2=0\\ x = 5 &\implies x -5=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x +2 )( x -5 ) = \stackrel{0}{y}}\hspace{5em}\stackrel{\textit{since the leading coefficient is 2, let's a = 2}}{2(x+2)(x-5)=y} \\\\\\ 2\stackrel{\textit{F O I L}}{(x^2-3x-10)=y}\implies \boxed{2x^2-6x-20=y}[/tex]

Angle of triangle AFC is 37°

An angle is the formed when two lines meet at the same vertex. It is measured is degrees. There are three types of angles based on their measurements.

From the given figure consider ABCF as trapezium,

Given that angle of triangle BCF is 37°

Two pairs of adjacent angles of a trapezium formed between the parallel sides and one of the non-parallel side, add up to 180°

Therefore, ∠BCF + ∠CBF = 180°

                                  ⇒∠B = 180° - 37°⇒143°

Similarly ∠A = ∠B = 143°

⇒∠A+∠F=180°

⇒∠F=180°-143° ⇒ 37°

Hence, m∠AFC = 37°.

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a) The 22nd percentile for incubation times of chicken eggs is of: 20.5 days.

b) The middle 95% of incubation times is in this following interval: (19.1, 23.5) days.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 21.3, \sigma = 1.1[/tex]

The 22nd percentile is the value of X when Z has a p-value of 0.22, hence X when Z = -0.77, thus:

-0.77 = (X - 21.3)/1.1

X - 21.3 = -0.77 x 1.1

X = 20.5 days.

The middle 95% of incubation times is obtained from X when Z = -1.96(2.5th percentile) to X when Z = 1.96(97.5th percentile), hence:

-1.96 = (X - 21.3)/1.1

X - 21.3 = -1.96 x 1.1

X = 19.1 days.

1.96 = (X - 21.3)/1.1

X - 21.3 = 1.96 x 1.1

X = 23.5 days.

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One way to figure out the fairness of the coin is to conduct a large number of coin flips and record the number of heads and tails.

Probability is a measure of the likelihood of an event occurring. In the context of a coin flip, the probability of an event is the ratio of the number of favorable outcomes to the total number of possible outcomes.

For a fair coin, the two possible outcomes are heads (H) and tails (T). The probability of getting heads or tails in a single coin flip is equal to 1/2, or 50%. This means that if you flip a fair coin 100 times, you would expect to get approximately 50 heads and 50 tails.

It's important to note that probability is a theoretical concept, and the actual outcome of a coin flip can never be predicted with 100% certainty. However, the law of large numbers states that as the number of coin flips increases, the ratio of heads to tails will approach the theoretical probability.

The concept of probability can also be applied to more complex events involving multiple coin flips. For example, the probability of getting two heads in a row is (1/2) * (1/2) = 1/4, or 25%. The probability of any specific sequence of heads and tails can be calculated using the same method.

One way to figure out the fairness of the coin is to conduct a large number of coin flips and record the number of heads and tails. Then, calculate the proportion of heads and compare it to 0.5, which is the expected proportion for a fair coin. The larger the sample size, the more confident you can be in your conclusion about the fairness of the coin. If the proportion of heads is close to 0.5, it is likely that the coin is fair. If the proportion deviates significantly from 0.5, it is likely that the coin is not fair. It's also important to use a rigorous statistical method to test the hypothesis of fairness, such as a one-sample proportion test, to account for random fluctuations in the results.

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Answer:

Below

Step-by-step explanation:

This is an exercise in 'completing the square'

x^2 - 6x -3      

   take 1/2 of the x coefficient  (6) square it and add it and subtract it

x^2 - 6x + 9    - 9   - 3        Now you can reduce the underlined portion

(x-3)^2      - 12          a = 3   b= -12          Done

The new function of Jennifers's investment is f(t) = 50000 * (1.15)^t

From the question, we have the following parameters that can be used in our computation:

Initial investment, a = 50000

Rate of growth, r = 15%

Using the above as a guide, we have the following:

f(t) = a * (1 + r)^t

Substitute the known values in the above equation, so, we have the following representation

f(t) = 50000 * (1 + 15%)^t

So, we have

f(t) = 50000 * (1.15)^t

Hence, the function is f(t) = 50000 * (1.15)^t

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Complete question

ennifer starts a new investment account that grows exponentially. Her financial advisor tells her the initial investment of $50,000 grows at a rate of about 15% annually.

Write a new function, N(t), that represents the amount of money in Jennifer’s new account after t years. Be sure to use correct notation

Answer:

B

Step-by-step explanation:

if a polynomial f(x) is divisible by (x - a) , then f(a) = 0

for the polynomial to be divisible by (x - 3) then the polynomial will equal zero when x = 3 , that is

3³ - 9(3)² + 3n - 12 = 0

27 - 9(9) + 3n - 12 = 0

27 - 81 + 3n - 12 = 0

3n - 66 = 0 ( add 66 to both sides )

3n = 66 ( divide both sides by 3 )

n = 22

The point (-5,-3) reflected over the y-axis is (5, -3).

There are two ways of reflection.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

We have,

(-5, -3)

Along y-axis:

(x, y) → (-x, y)

So,

(-5, -3) → (-(-5), -3) = (5, -3)

Thus,

(5, -3) is the reflected point.

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The Height is 10 inch and radius is 10 inch.

Volume is the quantity of space a thing occupies, whereas capacity is a measure of the substance it can store, such as a solid, a liquid, or a gas. While capacity can be measured in virtually any other unit, such as litres, gallons, pounds, etc., volume is measured in cubic units.

Given:

Volume = 10,000π in³

Volume of b= π r² h

So, 10,000π= π r² h

10,000 =  r² h

r² h = 10 x 10 x 10

r² h = 10² x 10

Now, comparing the values

r= 10 inch and h= 10 inch

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The perimeter of this parallelogram is equal to 236/10 or 23 6/10 meters.

In Mathematics, a parallelogram simply refers to a geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that has two (2) equal and parallel opposite sides.

Mathematically, the perimeter of a parallelogram can be calculated by using this mathematical expression;

Perimeter = A + B + C + D

Where:

A, B, C, and D represents the length of sides of a parallelogram.

Substituting the given parameters into the perimeter of a parallelogram  formula, we have the following;

Perimeter = 3 3/10 + 8 5/10 + 3 3/10 + 8 5/10

Perimeter = 33/10 + 85/10 + 33/10 + 85/10

Perimeter = 66/10 + 170/10

Perimeter = 236/10 or 23 6/10 meters.

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If knowing the probability of an event occurring is known then it can be turned into one's favour as well as it can be obstructed if not in favour.

A way to determine the likelihood of something occurring is through probability. Many things are hard to predict with 100 percent certainty. We can only predict the likelihood of an event occurring or how likely it is using it. A probability can be between 0 and 1, with 0 signifying an impossibility and 1 signifying a certainty.

If the likelihood of an event occurring is known, one can attempt to influence the outcome in accordance with the likelihood.

The possibility of altering the likelihood that the event will go in one's favour is another useful tool.

Therefore, being aware of the probability can be beneficial.

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Answer: A = 6

Step-by-step explanation: Here to help! So, if "a" wants to know the numerator of the fraction, all you have to do is to multiply 0.6 by 10, and that would get you 6/10. 6/10 is equivalent to 60% or 0.6. :))))

Is your 2050 prediction realistic?

No, the 2050 prediction is not realistic because the literacy rate cannot exceed 100%

Given data is

x0=1976, y0=63.2

x1=2001, y1=86.7

x2=2012, y2=94.5

Then the Lagrange interpolation formula is

[tex]y - y_1 = \frac{y_2 - y_1}{x_2 -x_1} (x - x_1)[/tex]

Here we have to interpolate to predict the literacy rate in 1992.

i.e. x=1992.

It lies between 1976 and 2001.

Then

x1=1976, y1=63.2

x2=2001, y2=86.7

Then interpolation function become

[tex]63.2 + \frac{23.5}{25}(16)[/tex]

= 63.2 + 15.04 = 78.24

i.e. The predicted literacy rate in 1992 is 78.24%.

Now, to find the literacy rate in 2050, we have to use extrapolation.

Since, 2050 is not in between any of the given data, we will have to take last two datas.

i.e.

x1=2001, y1=86.7

x2=2012, y2=94.5

And x=2050.

Then our extrapolation formula become

[tex]86.7 + \frac{7.8}{11} (49)[/tex]

= 86.7 + 34.75

=121.45

i.e. The literacy rate in 2050 is 121.45%.

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To better understand the relationship between education level and organic produce sales, we need to have data on these variables.

The data would typically be in the form of a table or a graph, with education level on one axis and organic produce sales on the other. Once we have the data, we can look at the pattern of the points to determine the relationship between education level and organic produce sales. If there is a positive relationship between the two variables, then as the education level increases, we would expect to see an increase in organic produce sales. This positive relationship could be represented by a line that slopes upward from left to right on a graph.

The slope of the line represents the rate of change of organic produce sales with respect to education level. A steep slope would indicate that even small changes in education level lead to significant changes in organic produce sales, while a shallow slope would suggest that changes in education level have little effect on organic produce sales.

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(A) the x-intercepts of y = f(2x) are (-1)/2, 3/2, and 6/2.

(B) the x-intercepts of y = 2f(x) are 1, 3, and 6.

(C) the x-intercepts of y = f(x + 2) are (-1 - 2), (3 - 2), and (6 - 2), which are -3, 1, and 4.

(a) To find the x-intercepts of y = f(2x), we need to find the values of x for which f(2x) = 0. Since x-intercepts of y = f(x) are -1, 3, and 6, the corresponding x-intercepts of y = f(2x) are (-1)/2, 3/2, and 6/2.

(b) To find the x-intercepts of y = 2f(x), we need to find the values of x for which 2f(x) = 0. Since x-intercepts of y = f(x) are -1, 3, and 6, the x-intercepts of y = 2f(x) are the same: -1, 3, and 6.

(c) To find the x-intercepts of y = f(x + 2), we need to find the values of x for which f(x + 2) = 0. Since x-intercepts of y = f(x) are -1, 3, and 6, the corresponding x-intercepts of y = f(x + 2) are (-1 - 2), (3 - 2), and (6 - 2), which are -3, 1, and 4.

(d) The appearance of y = f(mx) will be a compression or expansion of the graph of y = f(x), depending on the value of m. If m < 1, the graph of y = f(mx) will be a compression of the graph of y = f(x) along the x-axis. If m > 1, the graph of y = f(mx) will be an expansion of the graph of y = f(x) along the x-axis. The x-intercepts of y = f(mx) can be found by finding the values of x for which f(mx) = 0.

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Answer:

Step-by-step explanation:

The wooden frame is a cuboid

and the volume of a cuboid = Length x Width x Depth

Therefore,

The volume of this wooden frame = (8 feet) x (5 feet) x (4 feet)

                                                         = 160 cubic feet

The purchasing rate for the sand is $20 per cubic meter (which is NOT the same as cubic feet)

Unit conversion has to be applied then:

1 foot = 0.3048 meters

1 cubic feet = (0.3048 meters) x (0.3048 meters) x (0.3048 meters)

                                           1 cubic feet = [tex]0.3048^{3}[/tex] cubic meters

Therefore:                     160 cubic feet = (160)([tex]0.3048^{3}[/tex]) cubic meters

                                                                 Cost of sand:
                                                          1 cubic meter = $20

     Therefore:             (160)([tex]0.3048^{3}[/tex]) cubic meters = $(20)(160)([tex]0.3048^{3}[/tex])

                                                                                = $90.61

                                                           = $91 (Rounded to the nearest dollar)

It will cost Andrea $91 to purchase sand for the sandbox

9.03 divided by 0.15 is equal to 60.2.

The opposite of multiplication in arithmetic is called division. It's used to determine how many times one quantity is contained inside another. Division is done by dividing the dividend by the divisor, which can be done visually by using the division sign () or a fraction bar (/). The quotient, which shows how many times the dividend can be divided by the divisor, is the operation's output. For instance, if you split up eight apples into four equally sized pieces, each piece would contain two apples. This division is denoted by the equation 8/4 = 2, where 8 is the dividend, 4 is the divisor, and 2 is the quotient.

The division of 9.03 by 0.15 can be calculated as follows:

9.03 ÷ 0.15 = 9.03 / 0.15

= 60.2

So, 9.03 divided by 0.15 is equal to 60.2.

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Answer:

34

Step-by-step explanation:

4r² + 3s² - rs ← substitute r = - 1, s = 3 into the expression

= 4(- 1)² + 3(3)² - (- 1)(3)

= 4(1) + 3(9) - (- 3)

= 4 + 27 + 3

= 34

Answer:

-18 - x = 107

Step-by-step explanation:

The time that is taken by the colony is 23 years.

The exponential growth function can be used to account for the exponential increase in the number of the organisms that are to be found in the colony.

Given that we have that;

P=Poe^rt

P = Number at time t

Po = Number initially present

r = rate of growth

t = time taken

Thus;

3480 = 1120e^0.0498t

3480/1120 = e^0.0498t

3.1 = e^0.0498t

ln(3.1) = 0.0498t

t = ln3.1/0.0498

t = 23 years

There are 23 years

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C. An IQ score of 80 is more unusual than an IQ score of 120

is the false answer

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

Firstly we need to find the probability of the test score to be less than 90(P<90) then we will continue finding the probability of the IQ score to be between 90 and 110(90<P<110) then we find the probability of the IQ score being more than 110 (P>110).

For P<90

Firstly we compute this using a scientific calculator where we choose the stat option and enter the mean of 100 and a standard deviation of 10, so we check if we make the normal random variable(X) to be 90 the outcome or answer for that is 0.16 so now we know the probability of the IQ score to be less than 90 is 16% chances.

For 90<P<110

then we check with the same method what will be the probability for an IQ score to be between 90 and 110 for a mean of 100 and a standard deviation of 10 we again check a normal  random variable(X) of 110 to see what will be the probability of P<110 which we find an answer of 0.84 which is 84% chances so now therefore the probability of an IQ score to be more than 110 is 0.

therefore this tells us an IQ score of 120 is more unusual than an IQ score of 120.

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Answer:

A vertical line that passes through the coordinate (25, 0).

Equation of the vertical line is x = 25

Step-by-step explanation:

2x = 50

x = 25

Answer:

B) False

Step-by-step explanation:

It can be simplified to 3/7 as they both have the common factor 3.