The 28 students in Mrs. Colby's class will share 98 slices of
pizza equally
How many slices will each student get?

Answer:

3%=0.03 3%1÷2 =0.015. ..........,...

\(3 \frac{1}{4} - 4 \frac{1}{2} \\ \\ \longrightarrow \: \frac{13}{4} - \frac{9}{2} \\ \\ taking \: LCM \\ \\ \longrightarrow \: \frac{13 - 18}{4} \\ \\ \longrightarrow \: \boxed{ \frac{ - 5}{4} }\)

hope helpful! :-;

The quotient is -58x2 + 131x - 234 with a remainder of -5898.To solve this problem, we need to use long division. The dividend is 223 + 3x2 + 5x - 4 and the divisor is 22 + 2 + 1, which simplifies to 25.

We start by dividing 2 into 22, which gives us 11. We then write 11 above the 2 and multiply it by 25, which gives us 275. We subtract 275 from 223, which gives us -52. We bring down the 3, which gives us -523. We then repeat the process by dividing 2 into 52, which gives us 26. We write 26 above the 5 and multiply it by 25, which gives us 650. We subtract 650 from -523, which gives us -1173. We bring down the 1, which gives us -11731. We divide 2 into 117, which gives us 58.

We write 58 above the x and multiply it by 25, which gives us 1450. We subtract 1450 from -1173, which gives us -2623. We bring down the -4, which gives us -26234. We divide 2 into 262, which gives us 131. We write 131 above the 5 and multiply it by 25, which gives us 3275. We subtract 3275 from -2623, which gives us -5898. Therefore, the quotient is -58x2 + 131x - 234 with a remainder of -5898.

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Answer:

-3x² - 3x - 2

Step-by-step explanation:

simplify the first part

-2x * x - 2x * 3

-2xx - 6x

simplify the second part

(x-1)(x-2)

x * x + x * -2 + -1 * x + -1 * -2

xx + -2x - x + 2

xx - 3x + 2

subtract the simplified expressions

-2xx - 6x - (xx - 3x + 2)

-2xx - 6x - xx + 3x - 2

-3xx - 3x - 2

Answer:

5.33

Hope this helps

Answer:

5.5 meters

Step-by-step explanation:

Hope this helps ^^

Have a great day and enjoy your assignment!

:p

~sunny~

The equations that represent proportional relationships are:

A. 2x/12 = 3x/18

C. 4/6 = 10/15

E. 5/5 = 11/11

To determine if an equation represents a proportional relationship, ensure each side of the equation gives the same value when simplified. If they do not have the same value, then the equation does not represent a proportional relationship.

A. 2x/12 = x/6

3x/18 = x/6

Therefore, 2x/12 = 3x/18 represents a proportional relationship.

B. 3/6 = 1/2

6/3 = 2

Therefore, 3/6 = 6/3 does not represent a proportional relationship.

C. 4/6 = 2/3

10/15 = 2/3

Therefore, 4/6 = 10/15 represents a proportional relationship.

D. 4x/18 = 2x/9

x/18 = x/18

Therefore, 4x/18 = x/18 does not represent a proportional relationship.

E. 5/5 = 1

11/11 = 1

Therefore, 5/5 = 11/11 represents a proportional relationship.

F. 8/15 = 8/15

4/30 = 2/15

Therefore, 8/15/2/15 does not represent a proportional relationship.

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Answer: 0.10...

Step-by-step explanation:

The exact prοbability οf there being exactly 70 accidents at the intersectiοn in οne year is apprοximately 0.00382.

Prοbability can be defined as ratiο οf number οf favοurable οutcοmes and tοtal number οutcοmes.

(a) Tο find the exact prοbability that there wοuld be exactly 70 accidents at the intersectiοn in οne year, we can use the Pοissοn distributiοn fοrmula:

P(X = k) =( \(e^{(-λ)\) * \(λ^k\)) / k!

where X is the number of accidents, λ is the average rate of accidents per week (1.4), and k is the number of accidents we're interested in (70).

To find the probability of 70 accidents in one year, we need to adjust the value of λ to reflect the rate over a full year instead of just one week. Since there are 52 weeks in a year, the rate of accidents over a year would be 52 * λ = 72.8.

So, we have:

P(X = 70) = (\(e^{(-72.8)\)* \(72.8^(70)\)) / 70!

Using a calculatοr οr sοftware, we can evaluate this expressiοn and find that:

P(X = 70) ≈ 0.00382

Therefοre, the exact prοbability οf there being exactly 70 accidents at the intersectiοn in οne year is apprοximately 0.00382.

(b) Tο use the nοrmal distributiοn as an apprοximatiοn, we need tο assume that the Pοissοn distributiοn can be apprοximated by a nοrmal distributiοn with the same mean and variance. Fοr a Pοissοn distributiοn, the mean and variance are bοth equal tο λ, sο we have:

mean = λ = 1.4

variance = λ = 1.4

Tο use the nοrmal apprοximatiοn, we need tο standardize the Pοissοn randοm variable X by subtracting the mean and dividing by the square rοοt οf the variance:

\(Z = (X - mean) / \sqrt{(variance)\)

Fοr X = 70, we have:

Z = (70 - 1.4) / \(\sqrt{(1.4)\) ≈ 57.09

We can then use a standard nοrmal table οr calculatοr tο find the prοbability that a standard nοrmal randοm variable is greater than οr equal tο 57.09. This prοbability is extremely small and practically 0, indicating that the nοrmal apprοximatiοn is nοt very accurate fοr this particular case.

Therefοre, the exact prοbability οf there being exactly 70 accidents at the intersectiοn in οne year is apprοximately 0.00382.

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The approximation using the normal distribution gives a probability of approximately 0.3300 that there would be exactly 70 accidents at this intersection in one year.

what is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

(a) Using the Poisson distribution, the probability of exactly 70 accidents at this intersection in one year (i.e., 52 weeks) is:

P(X = 70) = (e^(-λ) * λ^x) / x!

where λ = average rate of accidents per week = 1.4

and x = number of accidents in 52 weeks = 70

Therefore, P(X = 70) = (e^(-1.4) * 1.4^70) / 70! ≈ 3.33 x 10^-23

(b) We can use the normal approximation to the Poisson distribution to approximate the probability that there would be exactly 70 accidents at this intersection in one year. The mean of the Poisson distribution is λ = 1.4 accidents per week, and the variance is also λ, so the standard deviation is √λ.

To use the normal distribution approximation, we need to standardize the Poisson distribution by subtracting the mean and dividing by the standard deviation:

z = (x - μ) / σ

where x = 70, μ = 1.452 = 72.8, σ = √(1.452) ≈ 6.37

Now we can use the standard normal distribution table to find the probability that z is less than or equal to a certain value, which corresponds to the probability that there would be exactly 70 accidents at this intersection in one year:

P(X = 70) ≈ P((X-μ)/σ ≤ (70-72.8)/6.37)

≈ P(Z ≤ -0.44)

≈ 0.3300

Therefore, the approximation using the normal distribution gives a probability of approximately 0.3300 that there would be exactly 70 accidents at this intersection in one year.

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Answer:

Yes it is a function

Step-by-step explanation:

The measure of the angle between the end of the shadow and the vertical side of the building is approximately 71 degrees.

Given the building is 290 feet tall and casts a 100 foot shadow.

Let x be the angle formed between the end of the shadow and the vertical side of the building.

Therefore, we can construct the following diagram;

From the diagram;

The tangent function relates the angle and the opposite side of a right triangle.

Therefore;

Tangent = opposite/adjacent

Tangent x = opposite/adjacent

Tangent x = 290/100

We can now take the inverse tangent of both sides;

x = tan^-1 (290/100)

x = 71.57 degrees, correct to two decimal places.

Therefore, the measure of the angle between the end of the shadow and the vertical side of the building is approximately 71 degrees.

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The cost of four and three-fourths pounds of beef is $18.95.

Given,

Amount of beef purchased = 4 and 3/4th  pounds.

Cost of beef per pound = $3.99

We need to find how much four and three-fourths pounds of beef cost.

Find the cost of 1 pound of beef.

1 pound = $3.99

We can write four and three-fourths as:

= 4 3/4

= 19/4

Find the cost of 19/4 pounds of beef.

1 pound = $3.99

Multiplying by 19/4 on both sides.

19/4  x 1 pound = 19/4 x $3.99

19/4 pounds =$18.95

Thus the cost of four and three-fourths pounds of beef is $18.95.

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Answer:

what is the question?

Answer to what?

The percentage of the reservations were for Friday or Saturday is 67%

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

The graph

On the graph, we have the following data values for reservation

The total number of reservations in the bar chart is then calculated as

Total number of reservations = 5 + 3 + 4 + 7 + 26 + 30 + 9

Evaluate the sum

So, we have the following representation

Total number of reservations = 84

The total number of reservations for Friday or Saturday is then calculated as

Total number for Friday or Saturday = 26 + 30

Evaluate the sum

So, we have the following representation

Total number for Friday or Saturday = 56

The percentage of the reservations were for Friday or Saturday is then calculated as

Percentage = Total number for Friday or Saturday/Total number of reservations

This gives

Percentage = 56/84

Evaluate

Percentage = 67%

Hence, the percentage is 67%

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An equation highlighting the discount: y = (65 - 7)x

A simpler equation: y = 58x

Answer:

25.12

Step-by-step explanation:

Radius=4

4x2=8

Diameter=8

8x3.14= 25.12

Answer:

a

Step-by-step explanation:

if you do it right it is a

the answer would be (9•3 divided by 4)+y which is A

Transitional forms in the fossil record, including Archaeopteryx, provide evidence for the pattern of evolution known as "gradualism."

This pattern suggests that species change over time through a slow and continuous process of accumulation of small, incremental changes. Transitional fossils like Archaeopteryx exhibit characteristics that are intermediate between two different groups of organisms, indicating a gradual transition from one form to another.

The presence of transitional fossils supports the idea that species do not undergo abrupt transformations but instead evolve gradually over long periods of time.

These fossils provide a tangible link between different groups of organisms, such as dinosaurs and birds in the case of Archaeopteryx, and offer evidence for the gradual transformation of one group into another. This supports the broader concept of evolution as a slow and continuous process of change in populations over generations.

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According to the information provided, the correct answers are as follows:

1. The shape of the distribution of sample means will be normal because the population mean is not known and the sample size is considered large enough.

2. The standard deviation of the distribution of the sample mean is always smaller than the standard deviation of the population.

1. According to the Central Limit Theorem, when the sample size is large enough, regardless of the shape of the population distribution, the distribution of sample means tends to follow a normal distribution.

2. The standard deviation of the distribution of the sample mean, also known as the standard error of the mean, is equal to the population standard deviation divided by the square root of the sample size. Since the sample mean is an average of observations, the variability of the sample mean is reduced compared to the variability of individual observations in the population.

The Central Limit Theorem states that when the sample size is sufficiently large, the distribution of sample means will be approximately normal, regardless of the shape of the population distribution. The standard deviation of the sample mean will be smaller than the standard deviation of the population.

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Answer:

Rachel will have 9.25$ more than Bob after 13 weeks

(a) the present value of $28,500 due 9 periods from now, discounted at 9%, is approximately $14,656.01

(b) the present value of $28,500 to be received at the end of each of 6 periods, discounted at 9%, is approximately $132,937.51

(a) To calculate the present value of $28,500 due 9 periods from now, discounted at 9%, we can use the present value formula:

Present Value = Future Value / (1 + Interest Rate)^Number of Periods

Plugging in the values, we have:

Present Value = $28,500 / (1 + 0.09)^9

Calculating this expression gives us:

Present Value = $28,500 / 1.9487179487

Present Value ≈ $14,656.01

Therefore, the present value of $28,500 due 9 periods from now, discounted at 9%, is approximately $14,656.01.

(b) To calculate the present value of $28,500 to be received at the end of each of 6 periods, discounted at 9%, we can use the present value of an annuity formula:

Present Value = Cash Flow * (1 - (1 + Interest Rate)^(-Number of Periods)) / Interest Rate

Plugging in the values, we have:

Present Value = $28,500 * (1 - (1 + 0.09)^(-6)) / 0.09

Calculating this expression gives us:

Present Value ≈ $132,937.51

Therefore, the present value of $28,500 to be received at the end of each of 6 periods, discounted at 9%, is approximately $132,937.51.

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The area of the heptagon is 175.12 mm²

A central angle is the angle created by the two radii. A small sector is one that has a center angle of less than 180 degrees. A significant sector is one that has a center angle greater than 180 degrees.

Area of heptagon = number of sides of heptagon × area of one triangle

Since the regular heptagon is inscribed in the circle of radius r = 8 mm, the angle subtended by any two radii at the center of the circle is Ф = 360/n where n = number of sides of heptagon = 7.

So Ф = 360/7

= 51.43°

Now, two radii and a chord between the two radii form a triangle.

Area of triangle between two radii

The area of the triangle A = (1/2)r²sinФ

So, there are 7 of such triangles in the heptagon.

Area of heptagon

So, the area of the heptagon, B = number of sides of heptagon × area of one triangle

= nA

= (nr²sinФ)/2

So, substituting the values of the variables into the equation, we have

B =  (nr²sinФ)/2

B=  (7 × (8 mm)²sin51.43°)/2

B=  (7 × 64 mm² × 0.7818)/2

B = 443.3 mm²/2

B = 175.12 mm²

So, the area of the heptagon is 175.12 mm²

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The area of the heptagon is 175.12 mm²

What is central angle?

A central angle is the angle created by the two radii. A small sector is one that has a center angle of less than 180 degrees. A significant sector is one that has a center angle greater than 180 degrees.

What is the formula to find area of heptagon?
Area of heptagon = number of sides of heptagon × area of one triangle

Since the regular heptagon is inscribed in the circle of radius r = 8 mm, the angle subtended by any two radii at the center of the circle is Ф = 360/n where n = number of sides of heptagon = 7.
So Ф = 360/7
= 51.43°
Now, two radii and a chord between the two radii form a triangle.
Area of triangle between two radii
The area of the triangle A = (1/2)r²sinФ
So, there are 7 of such triangles in the heptagon.
Area of heptagon
So, the area of the heptagon, B = number of sides of heptagon × area of one triangle
= nA
= (nr²sinФ)/2
So, substituting the values of the variables into the equation, we have
B =  (nr²sinФ)/2
B=  (7 × (8 mm)²sin51.43°)/2
B=  (7 × 64 mm² × 0.7818)/2
B = 443.3 mm²/2
B = 175.12 mm²
So, the area of the heptagon is 175.12 mm²

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Answer:

1.......c

2.....a

3.....b

4......e

5.....d

Because of the size of the black section,

The equation of the line passing through  (-4,-6), (5,-6) will be y = -6

In the given question, it is stated that the line passes through points  (-4,-6), and (5,-6). We need to find out an equation of the line that satisfies the given condition.

Firstly, we will need to find out the slope of the line. We can find the slope by using the point-slope form which is represented by:

=> \(m = \frac{y_{2}-y_{1} }{x_{2} - x_{1} }\)

Putting values (x₁, y₁) =  (-4,-6) and (x₂, y₂) = (5,-6) we get:

=> \(m = \frac{-6+ 6 }{5+ 4 }\)

=> m = 0

We get slope m = 0. Now, putting the value of slope into the point-slope form and taking (x₁, y₁) =  (-4,-6), we get values:

=> y - y₁ = m(x - x₁)

=> y + 6 = 0(x + 4)

=> y = -6

Hence, we get the equation of line y = -6

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The slope-intercept form of the equation of the line through the given point and parallel to the given line is y=x−14.

In the given question we have to write the slope-intercept form of the equation of the line through the given point and parallel to the given line.

The given points are (–2, –16).

The given equation of line is y = x – 5.

Standard equation of line is y=mx+c.

After comparing to the standard equation.

Slope m(1) = 1

The line passes through (−2,−16), so the point will satisfy the equation y=mx+c. So

−16=−2*1+c

Simlifying

−16=−2+c

Add 2 on both side, we get

c = −16+2

c = −14

As we know that if line is parallel then

m(1)=m(2)

So the value of solpe m = 1

Now the equation of line

y=1*x+(−14)

y=x−14

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The right answer is:

How do you write the slope-intercept form of the equation of the line through the given point and parallel to the given line?

Point (−2,−16), y = x – 5

Answer:

D

Step-by-step explanation:

f(x) < 25

x² - 11 < 25

x² < 36

-6 < x < 6

Answer:

1 = 2x      2= -3    4 =3

Step-by-step explanation:

Answer:

1. 5x-3=-15

2. -15/5=-3

3. -15/-3=5

Step-by-step explanation:

Hope this helps :)

The minimum cost will be at (2.5 , 3) and the minimum cost be $25.

Given, a landscaping contractor plans to use the least expensive combination of two brands of fertilizer.

A package of Brand X costs $16 and contains 12 oz of phosphates and 10 oz of nitrates.

A package of Brand Y costs $7 and contains 10 oz of phosphates and 5 oz of nitrates.

The lawn requires at least 60 oz of phosphates and 40 oz of nitrates.

Let the number of Brand X packages be, x

the number of Brand Y packages be, y

According to the question,

12x + 10y ≥ 60 = 6x + 5y ≥ 30

10x + 5y ≥ 40 = 2x + y ≥ 8

x ≥ 0

y ≥ 0

Z = 16x + 7y

On solving the equations, we get

6x + 5y = 30

6x + 3y = 24

On subtracting, we get

2y = 6

y = 3

and x = 2.5

So, minimum cost will be at (2.5 , 3) and the minimum cost be

Z = 16(2.5) + 7(3)

Z = 4 + 21

Z = 25

Hence, the minimum cost will be at (2.5 , 3) and the minimum cost be $25.

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Using inequalities we know that x=68 and x=66 respectively.

A mathematical phrase in which the sides are not equal is referred to as being unequal.

In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.

So, solve the inequalities as follows:

x+3>70

x>70-3

x>67

Then, it will be x = 68.

Then,

x+3<70

x<70-3

x<67

Then, it will be s = 66.

Therefore, using inequalities we know that x=68 and x=66 respectively.

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