Match each expression with its equivalent.

Answer:

a) model a: 50/hr

model b: 40/hr

b) model a

Step-by-step explanation:

b) since the money raised started at 0, the rate of change can be found by calculating 400/8

If Pamela has registered for the first time, it will remain on the Do Not Call list permanently. If she has re-registered, it will remain on the list for an additional five years from the date of re-registration.

The length of time that Pamela's phone number will remain on the National Do Not Call Registry depends on whether she registered her number on the Do Not Call Registry for the first time or if she has re-registered her number after it has already been on the list for a while.

If Pamela registered her phone number for the first time, it will be added to the Do Not Call Registry within 31 days of her registration date. Her phone number will remain on the list permanently, unless she requests to remove it or the number is disconnected.

If Pamela has re-registered her phone number after it has already been on the list for a while, her number's registration will be extended for another five years from the date she re-registered it.

Therefore, if Pamela registered her phone number for the first time, it will remain on the list permanently. If she has re-registered her number, it will remain on the list for an additional five years from the date of re-registration.

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The function is a linear function because as x increases, the y-value changes at a constant rate . The rate of change of this equation is 2.

The difference between linear and exponential functions is that  Linear functions change at a constant rate per unit interval while an exponential function changes by a common ratio over equal intervals.

We are given the function table as:

(0, -3)

(1, -1)

(2, 1)

(3, 3)

Thus, we can see that as x increases, the y-value changes at a constant rate of  + 2.

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Given a sample of 36 male mosquitos of a species with a mean lifespan of 8.88 days and a standard deviation of 6.66 days, the probability of the sample mean lifespan exceeding 10 days is approximately 0.14. So, the correct choice is option B is P ( x ˉ > 10 ) ≈ 0. 14 P( x ˉ >10)≈0. 14P, left parenthesis, x, with, \bar, on top, is greater than, 10, right parenthesis, approximately equals, 0, point, 14.

The sampling distribution of the mean lifespan is approximately normal due to the Central Limit Theorem.

The standard error of the mean is 6.66 / sqrt(36) = 1.11. The z-score for a sample mean of 10 is (10 - 8.88) / 1.11 = 1.08. Using a standard normal distribution table or calculator, the probability of a z-score greater than 1.08 is approximately 0.14.

Therefore, the answer is Choice B is P(X > 10) ≈ 0.14.

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Answer: Let's use the following variables to represent the unknown quantities in the problem:

x: the number of cupcakes purchased

y: the number of muffins purchased

From the problem statement, we can write two equations:

The total amount spent on cupcakes and muffins is $21.50:

2x + 1.25y = 21.50

The number of muffins purchased is one fewer than the number of cupcakes:

y = x - 1

These two equations form a system of equations that can be solved simultaneously to find the values of x and y.

Substituting equation 2 into equation 1, we get:

2x + 1.25(x - 1) = 21.50

Simplifying and solving for x:

2x + 1.25x - 1.25 = 21.50

3.25x = 22.75

x = 7

Now that we know x, we can use equation 2 to find y:

y = x - 1 = 7 - 1 = 6

Therefore, the customer purchased 7 cupcakes and 6 muffins, spending a total of $21.50.

Step-by-step explanation:

The dimensions of Noah's Ark in feet are 450 feet by 75 feet if the dimensions of Noah's Ark is 3.0 × 102 cubits by 5.0 × 101 cubits.

Noah's Ark is said to have dimensions of 3.0 × 10^2 cubits by 5.0 × 10^1 cubits. To convert these measurements to feet, we can use the conversion factor of 1 cubit = 1.5 feet.

First, we need to convert the length of the ark from cubits to feet. To do this, we multiply the length of the ark in cubits (3.0 × 10^2) by the conversion factor of 1.5 feet/cubit. This gives us a length of

3.0 × 10^2 cubits x 1.5 feet/cubit = 450 feet

Similarly, we can convert the width of the ark from cubits to feet by multiplying the width in cubits (5.0 × 10^1) by the conversion factor of 1.5 feet/cubit. This gives us a width of:

5.0 × 10^1 cubits x 1.5 feet/cubit = 75 feet

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The probability that Julian will roll a 3 on the next roll is approximately 16.67%. The probability of rolling a 3 on a normal 6-sided die is independent of the previous rolls. This means that regardless of the outcomes of Julian's previous rolls, the probability remains the same.

Explanation

On a 6-sided die, there is 1 favorable outcome for rolling a 3 (the number 3 itself) out of 6 possible outcomes (1, 2, 3, 4, 5, and 6).

To find the probability, you can use the formula:

Probability = (Number of favorable outcomes) / (Total number of outcomes)

In this case:

Probability of rolling a 3 = 1 (favorable outcome) / 6 (total outcomes)

Probability of rolling a 3 = 1/6 ≈ 0.1667 or 16.67%

So, the probability that Julian will roll a 3 on the next roll is approximately 16.67%.

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The required area of the given triangle is 63 ft² respectively.

A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon.

There are three sides and three angles in every triangle, some of which may be the same.

A unique triangle and plane (i.e., a two-dimensional Euclidean space) are determined by any three non-collinear points in Euclidean geometry.

In other words, every triangle is contained in a plane, and there is only one plane that contains that triangle.

Area of a triangle:

1/2 * b * h

Now, insert values as follows:

1/2 * b * h

1/2 * 14 * 9

7 * 9

63 ft²

Therefore, the required area of the given triangle is 63 ft² respectively.

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The minimum of the given expression can be found to be 3 x ∛(√2).

Use these inequalities to find the minimum of the given expression:

(a / (b + c)) + (b / (c + a)) + √(2c / (a + b)) ≥ (a / (√(bc))) + (b / (√(ac))) + √(2c / (√(ab)))

Now, simplify the expression:

(a / (√(bc))) + (b / (√(ac))) + √(2c / (√(ab))) = (√(a²/bc)) + (√(b²/ac)) + (√(2c²/ab))

Apply AM-GM inequality to the terms (√(a²/bc)), (√(b²/ac)), and (√(2c²/ab)):

AM = [(√(a²/bc)) + (√(b²/ac)) + (√(2c²/ab))] / 3 ≥ GM = ∛[(√(a²/bc)) * (√(b²/ac)) * (√(2c²/ab))]

The geometric mean (GM) is:

GM = ∛[(√(a²/bc)) x (√(b²/ac)) x (√(2c²/ab))]

GM = ∛(√(2a²b²c² / a²b²c²))

GM = ∛(√2)

Thus, the minimum of the given expression is:

= 3 x ∛(√2)

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The empirical rule does not apply to this dataset because the empirical rule is used to describe data that is normally distributed.

The empirical rule is a statistical rule that states that for a normal distribution.

Approximately 68% of the data will fall within one standard deviation of the mean, 95% of the data will fall within two standard deviations of the mean, and 99.7% of the data will fall within three standard deviations of the mean.

The empirical rule does not apply to this dataset because the empirical rule is used to describe data that is normally distributed.

This dataset does not appear to be normally distributed, as evidenced by the large outlier (1 Insidi High Gross Revenue).

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Answer:

96

Step-by-step explanation:

The number of balls that must be selected to ensure that 4 balls of the same color are chosen is 10 balls.

To ensure that 4 balls of the same color are chosen, we must consider the worst-case scenario where we select 3 balls of each color before selecting the fourth ball. Therefore, the minimum number of balls that must be selected is:

= 3 (red balls) + 3 (blue balls) + 3 (yellow balls) + 1 (any color)

= 10 balls.

Therefore, we must select at least 10 balls to ensure that 4 balls of the same color are chosen.

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Thus, the value of x for the given angle of cyclic quadrilateral is found as the x = 50.

When you hear the word "cyclic," think of the two round wheels on you bicycle. A quadrilateral is a figure with four sides. The result is a cyclic quadrilateral, which is defined as any four-sided shape (quadrilateral) its four vertices (corners) are located on a circle.

A cyclic quadrilateral's opposite angles add up to 180 degrees, making them supplementary to one another.

Given data:

Using the property of cyclic quadrilateral: sum of opposite angle are 180 degrees.

∠T + ∠R = 180

x + 60 + x + 20 = 180

2x + 80 = 180

2x = 180 - 80

2x = 100

x = 50

Thus, the value of x for the given angle of cyclic quadrilateral is found as the x = 50.

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Shawna wants to make sure her three dogs are fed and cared for when she leaves town for the day. She intends to give each of her dogs 12 ounces of food to achieve this. She must therefore leave a total of 36 ounces of food (3 dogs x 12 ounces of food per dog). 36 ounces are equivalent to 2.25 pounds of food because 16 ounces make up one pound.

There are 0.75 pounds of food in each can of dog food. We must divide 2.25 by 0.75 to find the quantity of dog food Shawna should leave for her companion. 3 dog food cans are the end outcome.Shawna ought to give her buddy three cans of dog food so that she can feed her dogs.

Shawna may make sure her dogs have enough food and are well cared for while she is away by leaving adequate food for them. Shawna may put any fears or concerns about her pets' welfare to rest by leaving ample food and clear directions.

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Step-by-step explanation:

-27 [tex]\sqrt{72}[/tex]  = -27 [tex]\sqrt{36*2}[/tex]  = -27 (6) [tex]\sqrt{2}[/tex]   =      - 162 [tex]\sqrt{2}[/tex]    =   - 229.1  

the probability of a customer choosing a Ribeye, well done or medium with corn is [tex]1[/tex] out of [tex]12[/tex], which is answer B [tex]- 1/12[/tex] Thus, option B is correct.

There are two possible steaks that a customer can choose from, and for each steak, there are three possible ways to cook it: rare, medium, or well-done. Additionally, there are two possible sides to choose from: corn or some other option.

Thus, there are a total of   [tex]2 \times 3 \times 2 = 12[/tex] possible meal combinations that a customer can choose from.

Out of these 12 possibilities, there is only one way to get a Ribeye cooked well-done or medium with corn, since there is only one Ribeye option on the menu.

Therefore, the probability of a customer choosing a Ribeye, well done or medium with corn is 1 out of 12, which is answer B- 1/12

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Answer:

Aiden should use the Standard unit of Mass

Kilogram.

Step-by-step explanation:

He can use other unit also like gram, pound, ounce, tone etc

Therefore, 11 3/4 - 8 1/2 = 13/4, or 3 1/4 as a mixed number.

A mixed number is a type of number that represents a whole number and a fraction together. It is written in the form of a whole number followed by a fraction, such as 3 1/2. The whole number represents the number of whole units, while the fraction represents the part of a unit.

For example, the mixed number 3 1/2 can be interpreted as three whole units and one half of a unit. Another example of a mixed number is 2 3/4, which represents two whole units and three-quarters of a unit. Mixed numbers are commonly used in everyday life, such as in cooking and measuring, and in mathematical calculations involving fractions.

To subtract mixed numbers like these, we need to convert them to improper fractions first:

[tex]11 3/4 = (4 * 11 + 3)/4 = 47/4[/tex]

[tex]8 1/2 = (2 * 8 + 1)/2 = 17/2[/tex]

Now, we can subtract the fractions:

[tex]47/4 - 17/2[/tex]

To subtract these fractions, we need to find a common denominator. The least common multiple of 4 and 2 is 4 × 2 = 8. We can convert both fractions to have a denominator of 8:

[tex]47/4 = (47/4) * (2/2) = 94/8[/tex]

[tex]17/2 = (17/2) * (4/4) = 68/8[/tex]

Now, we can subtract the numerators:

[tex]94/8 - 68/8 = 26/8[/tex]

Finally, we can simplify the result by dividing both numerator and denominator by their greatest common factor, which is 2:

[tex]26/8 = (2 * 13)/(2 * 4) = 13/4[/tex]

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Answer:

We can find the sum of the interior angles of any polygon using the formula

[tex]S_{n}=180(n-2)[/tex], where n is the number of sides.

Because each of these polygons have four sides, we can use one formula where our n is 4 to find the sum of the interior angles:

[tex]S_{4}=180(4-2)\\ S_{4}=180*2\\ S_{4}=360[/tex]

Thus, for all four problems, we can set the four angles equal in the four polygons equal to 360 and solve for the variables

(15) *Note the right angle symbol in this problem which always equals 90°

[tex]84+90+(2x+118)+(2x+68)=360\\174+2x+118+2x+68=360\\360+4x=360\\4x=0\\x=0[/tex]

Now, to find the measure of <Y, we simply plug in 0 for x in its equation

m<Y = 2(0) + 118 = 118°

(16):

[tex]82+105+(8x+11)+10x=360\\187+8x+11+10x=360\\198+18x=360\\18x=162\\x=9[/tex]

To find the measure of <F, we plug in 9 for x in its equation

m<F = 10(9) = 90°

(17):

[tex]95+95+(10x-5)+(8x+13)=360\\190+10x-5+8x+13=360\\198+18x=360\\18x=162\\x=9[/tex]

To find the measure of <M, we plug in 9 for x in its equation

m<M = 10(9) - 5 = 85°

(18):

[tex](14x-7)+(11x-2)+93+76=360\\14x-7+11x-2+169=360\\25x+160=360\\25x=200\\x=8[/tex]

To find the measure of <M, we plug in 8 for x in its equation

m<M = 11(8) - 2 = 86°

The number of bags that have zips on them is 28.

To solve this problem, we can use the principle of inclusion-exclusion.

First, we know that the total number of bags is 110.

Next, we know that 24 of the bags have neither zips nor buttons. Therefore, the number of bags that have either zips or buttons is 110 - 24 = 86.

We also know that 32 of the bags have buttons but no zips, and 28 of the bags have zips but no buttons.

To find the number of bags that have both zips and buttons, we can subtract the number of bags that have only buttons from the total number of bags with zips, or vice versa:

Number of bags with both zips and buttons = (Number of bags with zips) + (Number of bags with buttons) - (Number of bags with either zips or buttons)

Number of bags with both zips and buttons = 28 + 32 - 86 = -26

This result is clearly nonsensical, so we can conclude that there are no bags with both zips and buttons.

Therefore, the number of bags that have zips on them is simply the number of bags with zips but no buttons, which is 28.

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( 5 - 2t ) < - 4 is an inequalty that represents t, the number of hours past midnight, when the temperature was coler than -4 degrees celsius.

What is  linear equation?

An algebraic equation with simply a constant and a first- order( direct) element, similar as y = mx b, where m is the pitch and b is the y- intercept, is known as a linear equation.

                         The below is sometimes appertained to as a" direct equation of two variables," where y and x are the variables. Equations whose variables have a power of one are called direct equations. One illustration with only one variable is where layoff b = 0, where a and b are real values and x is the variable.

The midnight temperature is 5 °C and the temperature is decreasing at the rate of 2°C per hour.

If t is the hours past midnight then after t hours the temperature will be ( 5 - 2t ).

Now, if this temperature is colder than - 4° C, then the inequality can be written as   ( 5 - 2t ) < - 4.

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The inequality that represents t, the number of hours past midnight, when the temperature was cooler than -4 degrees celsius( 5 - 2t ) < - 4

What is  inequality?

The term "inequality" is used in mathematics to describe a relationship between two expressions or values that is not equal to one another. Inequality results from a lack of balance. When two quantities are equal, we use the symbol '=', and when they are not equal, we use the symbol. If two values are not equal, the first value can be greater than (>) or less than (), or greater than equal to () or less than equal to ().

The midnight temperature is 5 °C and the temperature is decreasing at the rate of 2°C per hour.

If t is the hours past midnight then after t hours the temperature will be

=>  ( 5 - 2t ).

Now, if this temperature is colder than - 4° C, then the inequality can be written as   ( 5 - 2t ) < - 4.

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a) The probability that exactly two customers arrive between 2:00 p.m. and 4:00 p.m. is 0.0915 (or approximately 9.15%).

b) The probability of at least one customer arriving between 1:00 p.m. and 2:00 p.m. or between 3:00 p.m. and 4:00 p.m. is approximately 0.99999917.

For a Poisson process, the number of arrivals in a fixed time interval follows a Poisson distribution.

Let's denote the number of arrivals in a two-hour period as X.

Since the average number of arrivals per hour is 7, the average number of arrivals in a two-hour period is 14.

Therefore, we have λ = 14.

a) Probability of exactly 2 customers arriving between 2:00 p.m. and 4:00 p.m.:

Using the Poisson distribution formula, the probability of X arrivals in a two-hour period is:

[tex]P(X = x) = (e^{-\lambda} * \lambda^x) / x![/tex]

So, for X = 2, we have:

[tex]P(X = 2) = (e^{-14} * 14^2) / 2! = 0.0915[/tex] (rounded to four decimal places)

Therefore, the probability that exactly two customers arrive between 2:00 p.m. and 4:00 p.m. is 0.0915 (or approximately 9.15%).

b) Probability of at least one customer arriving between 1:00 p.m. and 2:00 p.m. or between 3:00 p.m. and 4:00 p.m.:

We can approach this problem by using the complementary probability. The complementary probability of at least one customer arriving in a two-hour period is the probability of no customers arriving in that period. Since the arrival rate is the same for each hour, we can divide the two-hour period into two one-hour periods and use the Poisson distribution formula for each period separately.

The probability of no customers arriving in a one-hour period with λ = 7 is:

[tex]P(X = 0) = (e^{-7}* 7^0) / 0! = 0.000911[/tex]

The probability of no customers arriving in a two-hour period is the product of the probabilities for each one-hour period:

P(no customers in two-hour period) = P(X = 0) * P(X = 0) = 0.000911 * 0.000911 = 8.30e-7

The complementary probability of at least one customer arriving in a two-hour period is:

P(at least one customer in two-hour period) = 1 - P(no customers in two-hour period) = 1 - 8.30e-7 = 0.99999917 (rounded to eight decimal places).

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The distance between your location and the epicenter is just slightly larger than the maximum distance that the earthquake can be felt (76 miles), so you would be able to feel the earthquake.

A triangle is a polygon with three sides and three angles. The sum of the angles in a triangle is always 180 degrees. There are different types of triangles such as equilateral, isosceles, scalene, right-angled, obtuse-angled, and acute-angled triangles. Triangles are used in geometry and other fields of mathematics to solve problems related to areas, angles, and side lengths.

Here,

Yes, you feel the earthquake.

To see why, imagine drawing a circle around the epicenter with a radius of 76 miles. This circle represents the maximum distance that the earthquake can be felt. Then, draw a line from the epicenter to your location. This line represents the distance between you and the epicenter.

To determine whether you feel the earthquake, we need to calculate the distance between your location and the epicenter using the Pythagorean theorem:

distance = √(65² + 40²)

distance ≈ 76.06 miles

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Standard unit chose to measure the mass of a bowling ball is equal to kilogram .

The unit typically used to measure the mass of a bowling ball is the pound (lb) or the kilogram (kg).

It depends on the country as different countries have different standard unit for measuring mass.

In the United States, the weight of a bowling ball is often measured in pounds.

While in many other countries, the weight is measured in kilograms.

When measuring the mass of a bowling ball,

It is important to use a calibrated scale that is designed to handle the weight of the ball.

Some scales are specifically designed for weighing bowling balls.

And they may have a higher weight capacity than a typical bathroom scale.

It is also important to ensure that the scale is on a flat, stable surface to ensure an accurate measurement.

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The total surface area of each figure are:

1)  2,557.3 yd²

2) 601.02 m₂

3) 3782.5 mm²

4)750 in²

1) The total surface area of a cylinder is:

2πrh + 2πr².

where:

r is radius

h is height

Thus:

TSA = 2π(11 * 26) + 2π(11)²

TSA = 2π(286) + 2π(121)

TSA = 2π(407)

TSA = 2,557.3 yd²

2) The total surface area is:

2(¹/₂ * 9 * 11.12) + (16 * 15) + (16 * 12) + (9 * 16)

= 25.02 + 240 + 192 + 144

= 601.02 m₂

3) The total surface area of a cylinder is:

2πrh + 2πr².

where:

r is radius

h is height

Thus:

TSA = 2π(14 * 29) + 2π(14)²

TSA = 2π(406) + 2π(196)

TSA = 2π(602)

TSA = 3782.5 mm²

4) The total surface area of the pyramid is:

TSA = (15 * 8) + (21 * 17) + (21 * 15) + (8 * 21)

TSA = 120 + 147 + 315 + 168

TSA = 750 in²

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Out of these powers, the highest is 5.

Therefore, the degree of the polynomial is 5.

The degree of a polynomial is the highest power of the variable in the polynomial. In the given polynomial, the highest power of x is 5,

so the degree of the polynomial is 5.

The degree of a polynomial is the highest power of the variable (x) in the expression.

In the polynomial you provided:
[tex]8x^5 + 4x^3 - 5x^2 - 9[/tex]
Let's identify the terms and their respective powers of x:
[tex]8x^5[/tex]has a power of 5.
[tex]4x^3[/tex]has a power of 3.
[tex]-5x^2[/tex] has a power of 2.

-9 is a constant term, so there is no power of x.

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The answer to this question is  x = 6

Answer: 5 m

Step-by-step explanation:

A radius is half of the diameter which is the black line. Hope this helps!

Answer:

The radius of the larger grass area is 5m

Step-by-step explanation:

d=2r

r=d/2

r=10/2

r=5m