Samuel buys 3 bottles of juice that each have an original price of $2.80. He uses a coupon for 35% off. How much does Samuel pay for 3 bottles of juice? Show your work.

Answer:

x = -4, y = 3.

Step-by-step explanation:

Substitute y = 3 into the first equation:

-5x - 6(3) = 2

-5x = 2 + 18

-5x = 20

x = -4

The 90% confidence interval of the new product has the potential to make the company an additional $3.8 million is (2.81, 4.79), option B.

Confidence intervals quantify how confident or uncertain a sampling technique is. They can take any number of probability thresholds, with a 95% or 99% confidence level being the most popular. The calculation of confidence intervals is done using statistical techniques like the t-test.

[tex]\bar x = $3.8[/tex]

sample standard deviation = s =1.7

sample size = n =10

Degrees of freedom = df = n - 1 = 10 - 1 = 9

At 90% confidence level

[tex]\alpha[/tex] = 1 - 90%

[tex]\alpha[/tex] =1 - 0.90 =0.1

[tex]\alpha/2[/tex] = 0.05

[tex]t\alpha/2[/tex] ,df = t0.05,9 =1.833

At 90% confidence level, the critical value is t = 1.833

The 90% confidence interval is:

[tex]\bar x \pm t*\frac{s}{\sqrt{n} }[/tex]

[tex]=3.8\pm 1.833*\frac{1.7}{\sqrt{10}}\\\\=3.8\pm 0.99[/tex]

=(2.81,4.79).

Therefore, 90% confidence interval estimate of the population mean is, (2.81,4.79).

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Complete question:

Market research indicates that a new product has the potential to make the company an additional $3.8 million, with a standard deviation of $1.7 million. If this estimate was based on a sample of 10 customers, what would be the 90% confidence interval? (2.76, 4.84) O (2.81, 4.79) (2.11, 5.56) (3.06, 4.54)

1/20 of the customers are dairy intolerant.

We know that 1/5 of the customers are vegetarian, and 3/4 eat meat. Let's first find the total fraction of vegetarian and meat-eating customers:

1/5 (vegetarian) + 3/4 (meat)

To add these fractions, we need a common denominator. The least common denominator (LCD) for 5 and 4 is 20. So, we'll convert both fractions to have the same denominator:

(1/5)*(4/4) = 4/20 (vegetarian)
(3/4)*(5/5) = 15/20 (meat)

Now, let's add the fractions:

4/20 (vegetarian) + 15/20 (meat) = 19/20 (vegetarian and meat)

Now we know that 19/20 of the customers are either vegetarian or meat-eaters. The remainder must be dairy intolerant. To find this fraction, subtract the combined fraction from 1:

1 - 19/20 = 1/20

So, 1/20 of the customers are dairy intolerant.

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The solution of the system of equations is given by the ordered pair (-4, 5).

In order to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

x - y = -9    ......equation 1.

3x + 4y = 8  ......equation 2.

Based on the graph shown in the image attached above, we can logically deduce that the solution to this system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant II, and it is given by the ordered pairs (-4, 5).

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The patient must be dispensed 45 tablets for a 30-day supply.

To determine how many 500 mg tablets must be dispensed for a 30-day supply given that a patient needs to take 0.5 g po  and 0.25 g po before sleeping, follow these steps:

1. Convert grams to milligrams:
0.5 g = 500 mg (morning dose)
0.25 g = 250 mg (evening dose)

2. Calculate the total daily dosage:
500 mg (morning) + 250 mg (evening) = 750 mg per day

3. Calculate the number of 500 mg tablets needed per day:
750 mg / 500 mg = 1.5 tablets per day

4. Calculate the number of tablets needed for a 30-day supply:
1.5 tablets per day * 30 days = 45 tablets

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the inflection points are x = 0 and x = 2, and the intervals of concavity are (-∞, 0) and (2, ∞) for concave down, and (0, 2) for concave up.

To find the inflection points and intervals of concavity of the function f(x) = x^4 - 4x^3, we need to find its second derivative.

f'(x) = 4x^3 - 12x^2
f''(x) = 12x^2 - 24x

The inflection points occur where f''(x) = 0 or is undefined. Therefore, we set 12x^2 - 24x = 0 and solve for x.

12x(x - 2) = 0
x = 0 or x = 2

These are the two possible inflection points.

To determine the intervals of concavity, we need to look at the sign of the second derivative in each interval. We can use test points to determine the sign.

Test point x = 1:
f''(1) = 12 - 24 = -12, so the function is concave down on the interval (-∞, 0) and concave up on the interval (0, ∞).

Test point x = 3:
f''(3) = 108 - 72 = 36, so the function is concave up on the interval (2, ∞) and concave down on the interval (-∞, 2).

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To estimate the proportion of admitted hospital patients who have type 2 diabetes at Orlando Health Hospitals within a certain margin of error and confidence level,

we can use the following formula to determine the necessary sample size:

[tex]n = [(Z^2 * p * q) / E^2] / [1 + ((Z^2 * p * q) / E^2N)][/tex]

where:

n = sample size

Z = z-score for the desired confidence level (in this case, 1.81 for a 93% confidence level)

p = estimated proportion of patients with type 2 diabetes (unknown)

q = 1 - p

E = margin of error (0.06)

N = population size (unknown)

Since we do not know the estimated proportion of patients with type 2 diabetes or the population size,

we can assume a conservative estimate of p = q = 0.5, which maximizes the sample size required.

Plugging in the values, we get:

[tex]n = [(1.81^2 * 0.5 * 0.5) / 0.06^2] / [1 + ((1.81^2 * 0.5 * 0.5) / 0.06^2N)][/tex]

Simplifying, we get:

[tex]n = 1242.95 / [1 + (2.4 / N)][/tex]

To satisfy the requirements of the problem, we need to round up to the nearest whole number, so we need a sample size of at least 1243 patients.

Note that if we had a better estimate for p or N, we could use those values in the formula to get a more precise sample size.

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Roy should cut the pizza at an angle of 4.7 radians if the total diameter of the pizza is 12 inches.

Diameter of the pizza = 12 inches

The area he can eat = 84. 8 inches

The area of the pizza for 12 inches diameter can be calculated by using the formula:

Area = π*[tex]r^2[/tex]

Area = π* ([tex]6^2[/tex])

Area = 36π

The angle of the slice of pizza he can eat about 84.8 square inches can be calculated as:

Area of sector = (θ/2) ×[tex]r^2[/tex]

84.8 = (θ/2) × [tex]6^2[/tex]

84.8 = 18*θ

θ = 84.8 / 18

θ = 4.71 radians

Therefore, we can conclude that Roy should cut the pizza at an angle of  4.7 radians.

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The value of b is 1,500, which means that the author had already written 1,500 words before starting the new plan.

In the equation y = 600x + b, x represents the number of days since the author started the new plan to write 600 words per day, and y represents the total number of words written.

After the fifth day, the author has written 4,500 words. Thus, we can substitute x = 5 and y = 4,500 into the equation and solve for b:

4,500 = 600(5) + b

4,500 = 3,000 + b

b = 4,500 - 3,000

b = 1,500

Therefore, the value of b is 1,500, which means that the author had already written 1,500 words before starting the new plan.

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When Kirill and Max work together, they can complete 11/60 of the puzzle in one hour.

To find out what part of the puzzle Kirill and Max can complete together in one hour, we need to calculate their combined work rate.

Step 1: Find the work rate of Kirill.
Kirill can complete the puzzle in 10 hours, so his work rate is 1/10 of the puzzle per hour.

Step 2: Find the work rate of Max.
Max can complete the puzzle in 12 hours, so his work rate is 1/12 of the puzzle per hour.

Step 3: Add Kirill's and Max's work rates together.
(1/10) + (1/12) = (12 + 10) / (10 * 12) = 22 / 120

Step 4: Simplify the fraction.
The simplified fraction is 11/60.

So, when Kirill and Max work together, they can complete 11/60 of the puzzle in one hour.

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When x = 5 and dx = 0.1, the differential dy is approximately 96.375.

When x = 5 and dx = 0.2, the differential dy is approximately 192.75.

We can use the chain rule to find the differential of y with respect to x. Let u = 5x + 3, then y = tan(u).

Using the chain rule, we have:

dy/dx = dy/du * du/dx

Taking the derivative of y with respect to u, we have:

dy/du = sec^2(u)

Substituting u = 5x + 3, we have:

dy/du = sec^2(5x + 3)

Taking the derivative of u with respect to x, we have:

du/dx = 5

Substituting x = 5 and dx = 0.1, we have:

dy = dy/du * du/dx * dx

= sec^2(5(5) + 3) * 5 * 0.1

= 192.75 * 0.5

= 96.375

Therefore, when x = 5 and dx = 0.1, the differential dy is approximately 96.375.

Substituting x = 5 and dx = 0.2, we have:

dy = dy/du * du/dx * dx

= sec^2(5(5) + 3) * 5 * 0.2

= 192.75 * 1

= 192.75

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The expression 4 that could be used to find spaces in the game piece was moved.

Since Integers are the collection of negative, and positive numbers including zero. Then the positive integers lie on the right side of the zero on the number line and the negative lie on the left side of zero on the number line.

We are given that Andi moved a game piece down 4 pieces

The expression in option 1: |-4| which is equal to 4

The expression in option 2: |4| which is equal to 4

The expression in option 3: -|4| which is equal to -4

The expression in option 4: 4 which is equal to -4

∴The correct expression is option 4

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While a sample of mall shoppers may be useful for certain types of research, it may not provide a trustworthy estimate of the current unemployment rate. Instead, a more appropriate method would be to conduct a survey that is designed to be representative of the population, using a random sampling technique, and ensuring that the sample size is large enough to provide reliable estimates.

While sampling at the mall may be a convenient way to gather data, it may not be an appropriate method for estimating the current unemployment rate for several reasons:

Sampling Bias: The people who visit malls may not be representative of the general population. For instance, people who are unemployed may not have the time or money to go to the mall during the day, which could skew the results.

Sampling Size: The sample size may not be large enough to provide an accurate estimate of the unemployment rate. Even if the interviewer approaches a large number of shoppers, it may not be sufficient to represent the entire population of the city or country.

Self-Selection Bias: People who choose to participate in the survey may not be representative of the population as a whole. For instance, people who are more interested in the topic may be more likely to participate, which could bias the results.

Data Collection Bias: Even if the sample is representative, the data collection method may introduce biases. For instance, the interviewer may have a certain tone of voice or demeanor that could influence how people respond to the questions.

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The volume of the triangular prism is 171 cubic inches.

To find the volume of a triangular prism, you need to multiply the area of the base by the height of the prism. In this case, the base of the prism has an area of 18 square inches and the height is 9.5 inches. So, the volume of the prism can be calculated as follows:

Volume = Base Area x Height
Volume = 18 sq. in. x 9.5 in.
Volume = 171 cubic inches

Therefore, the volume of the triangular prism is 171 cubic inches.

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So, to the nearest hundredth, the value of f(26.5) is approximately 59.81.

To find the value of f(26.5) for the given exponential function f(x), we will first determine the base and initial value of the function using the given points f(4.5) = 22 and f(14) = 40.
An exponential function has the form f(x) = ab^x, where a is the initial value and b is the base.
1. Write the two equations using the given points:
22 = ab^(4.5)
40 = ab^(14)
2. Divide the second equation by the first to eliminate the initial value, a:
(40/22) = (ab^(14))/(ab^(4.5))
3. Simplify and solve for the base, b:
1.81818 = b^(9.5)
b ≈ 1.05459
4. Now, plug b back into one of the original equations to solve for the initial value, a:
22 = a(1.05459)^4.5
a ≈ 16.08364
5. With a and b found, we can now find the value of f(26.5):
f(26.5) = 16.08364 * (1.05459)^26.5
f(26.5) ≈ 59.81
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The value of exponential function f(26. 5), to the nearest hundredth is 144.42.

To find the value of f(26.5) for the exponential function, we can use the given data points and apply the exponential function formula.

Let's assume the exponential function is of the form: f(x) = a * b^x, where a and b are constants.

Using the given data points:

f(4.5) = 22

f(14) = 40

Substituting these values into the exponential function equation:

22 = a * b^4.5 ---(1)

40 = a * b^14 ---(2)

Dividing equation (2) by equation (1), we can eliminate the constant 'a':

40/22 = (a * b^14) / (a * b^4.5)

1.8182 = b^(14 - 4.5)

1.8182 = b^9.5

To find the value of b, we take the 9.5th root of 1.8182:

b ≈ 1.109

Now we can substitute the value of b into equation (1) to solve for 'a':

22 = a * (1.109)^4.5

a ≈ 4.95

Therefore, the exponential function can be approximated as: f(x) ≈ 4.95 * (1.109)^x

Now we can find the value of f(26.5):

f(26.5) ≈ 4.95 * (1.109)^26.5 ≈ 144.42

Hence, the value of f(26.5), to the nearest hundredth, is approximately 144.42.

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The volume of the frustum is approximately 634.3 cubic centimeters.

Let the radius of the smaller cone be 'r' and the radius of the bigger cone be 'R'.

Since the height of the smaller cone is 8 cm and its volume is 160 cm³, we have:

1/3 * π * r² * 8 = 160

r² = 60/π

r ≈ 4.03 cm

Now, using similar triangles, we can find the radius 'R' of the bigger cone:

(R - r)/16 = R/24

24R - 24r = 16R

R = 2r/3

R ≈ 2.69 cm

Therefore, the volume of the frustum is:

1/3 * π * (2.69² + 2.69*4.03 + 4.03²) * 16 - 1/3 * π * 4.03² * 8

≈ 634.3 cm³

So, the volume of the frustum is approximately 634.3 cubic centimeters.

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Answer:

The distance along Park Street from King Street to Queen Street is 0.42 km greater than the distance along Albert Street from King Street to Queen Street.

Step-by-step explanation:

Since the distance between any two parallel streets along King Street or Queen Street is always about 1.42 km, the distance along Park Street from King Street to Queen Street is:

1.42 km + 1 km + 1.42 km = 3.84 km

Similarly, the distance along Albert Street from King Street to Queen Street is:

1 km + 1.42 km + 1 km = 3.42 km

Therefore, the difference in distance is:

3.84 km - 3.42 km = 0.42 km

So, the distance along Park Street from King Street to Queen Street is 0.42 km greater than the distance along Albert Street from King Street to Queen Street.

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option D is correct ,the triangle are not similar because only angle c and z are congruent .

what is  congruent ?

In mathematics, congruent means having the same size and shape. Two objects are said to be congruent if they have the same dimensions and angles, and can be transformed into each other by a combination of translations, rotations, and reflections.

In the given question,

congruent means having the same size and shape. Two objects are said to be congruent if they have the same dimensions and angles, and can be transformed into each other by a combination of translations, rotations, and reflections.

so we can conclude that option D is correct answer as other 2 angle are not equal

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Answer:

about 12.67 cm²

Step-by-step explanation:

The area of a sector of a circle is given by:

A = (θ/360) x πr²

where A is the area of the sector, θ is the central angle of the sector (in degrees), and r is the radius of the circle.

In this case, we are given the central angle of the sector, which is 86.4 degrees, and the radius of the circle, which is 4.1 cm. Therefore, we can calculate the area of the sector formed by angle CBA as follows:

A = (86.4/360) x π(4.1)²

A ≈ 12.67 cm²

So, the area "about 12.67 cm²" is a possible area of the sector formed by angle CBA.

To determine if any of the other given areas are possible, we can calculate the central angle of each sector using the same formula as above, and then check if it matches the given angle of 86.4 degrees.

For the area "about 23.35 cm²":

23.35 = (θ/360) x π(4.1)²

θ ≈ 149.6 degrees

The central angle of this sector is approximately 149.6 degrees, which is not equal to the given angle of 86.4 degrees. Therefore, the area "about 23.35 cm²" is not a possible area of the sector formed by angle CBA.

For the area "about 3.09 cm²":

3.09 = (θ/360) x π(4.1)²

θ ≈ 19.16 degrees

The central angle of this sector is approximately 19.16 degrees, which is not equal to the given angle of 86.4 degrees. Therefore, the area "about 3.09 cm²" is not a possible area of the sector formed by angle CBA.

For the area "about 40.14 cm²":

40.14 = (θ/360) x π(4.1)²

θ ≈ 256.4 degrees

The central angle of this sector is approximately 256.4 degrees, which is not equal to the given angle of 86.4 degrees. Therefore, the area "about 40.14 cm²" is not a possible area of the sector formed by angle CBA.

Therefore, the only possible area of the sector formed by angle CBA is "about 12.67 cm²".

To test whether shoes cost less on average at Payless than at Famous Footwear, we can conduct a two-sample t-test for the difference in means.

The null hypothesis is that there is no difference in the mean prices between the two stores, and the alternative hypothesis is that the mean price at Payless is less than the mean price at Famous Footwear.

We can calculate the t-statistic using the formula:

t = [tex](x1 - x2 - 0) / sqrt(s1^2/n1 + s2^2/n2)[/tex]

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Substituting the values given in the table, we get:

t =[tex](21.39 - 45.66 - 0) / sqrt((7.47^2/30) + (16.54^2/30))[/tex] = -10.78

The degrees of freedom for this test is (30-1) + (30-1) = 58.

Using a t-table or calculator, we find the p-value to be very small, much less than 0.05.

Therefore, we reject the null hypothesis and conclude that there is convincing evidence at the 0.05 significance level that shoes cost less on average at Payless than at Famous Footwear.

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The total volume of juice in the 5 glasses is 925 milliliters. To find the total volume of juice in the 5 glasses, we simply need to multiply the volume of juice in one glass by the number of glasses.

In this case, each glass contains 185 milliliters of juice and Ian has stacked 5 glasses, so we can use the formula:
Total volume of juice = Volume of juice per glass x Number of glasses
Plugging in the numbers, we get:
Total volume of juice = 185 ml/glass x 5 glasses
Total volume of juice = 925 ml

Therefore, the total volume of juice in the 5 glasses is 925 milliliters. This is a simple example of using multiplication to find the total quantity of something when we know the amount in one unit and the number of units. In this case, we were able to find the total volume of juice by multiplying the volume in one glass by the number of glasses.

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To find the average amount that Sarah saved per month over the last six months, we need to add up the total amount saved and divide by the number of months.

Total amount saved = $135.00 + $144.00 + $104.00 + $80.00 + $90.00 + $160.00 = $713.00

Number of months = 6

Average amount saved per month = Total amount saved / Number of months = $713.00 / 6 = $118.83

Therefore, the correct answer is d. $118.83.

It is important to note that when working with numbers and calculations, accuracy is crucial. In this case, rounding off the answer to the nearest cent would result in a different answer.

Additionally, checking the calculations multiple times to ensure accuracy is always recommended.

Overall, tracking and analyzing expenses and savings is important for financial planning and achieving financial goals. By keeping track of how much she saved each month,

Sarah can make informed decisions about her spending and saving habits and adjust accordingly to reach her vacation savings goal.

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Answer:  csc M =  [tex]\frac{\sqrt{86} }{8}[/tex]

Step-by-step explanation:

The csc is related to sin

csc x =  1/sin x

find sin M first  then flip it to find csc M

sin M= opposite/hypotenuse

sin M= [tex]\frac{8}{\sqrt{86} }[/tex]                >flip that

csc M =  1/sin M

csc M =  [tex]\frac{\sqrt{86} }{8}[/tex]              >root cannot be simplified it breaks down into 2 and 43

                                     which are 2 prime numbers

amount of paint needed to cover all the wood in the frame, we need to first determine the total length of the wood in meters. Let's assume that each plank of wood is 1 meter long, so the total length of wood in the frame is 3 meters.

Next, we need to calculate the amount of paint required per meter of wood. The problem states that 80ml of emulsion paint is needed per meter of wood. So, we can multiply 80ml by 3 meters to get the total amount of paint needed for the entire frame.

80ml/meter x 3 meters = 240ml
Therefore, we need 240ml of emulsion paint to cover all the wood in the frame.
It is important to note that this calculation assumes that only one coat of paint will be applied to the wood. If multiple coats are desired, the amount of paint required will need to be adjusted accordingly.

In conclusion, to paint the wooden frame made of three planks of wood attached with glue and nails, we would need 240ml of emulsion paint.

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To find the extremes of 4x−4y subject to the condition x2 + 2y2 = 1, we can use the method of Lagrange multipliers.

First, we set up the Lagrange equation:

∇f(x,y) = λ∇g(x,y)

where f(x,y) = 4x-4y and g(x,y) = x2 + 2y2 - 1.

Taking partial derivatives, we have:

∂f/∂x = 4
∂f/∂y = -4
∂g/∂x = 2x
∂g/∂y = 4y

Setting these equal to their respective Lagrange multipliers, we have:

4 = 2λx
-4 = 4λy
x2 + 2y2 = 1

Solving for x and y in terms of λ, we get:

x = 2λ/4 = λ/2
y = -λ/4

Substituting these back into the constraint equation, we have:

(λ/2)2 + 2(-λ/4)2 = 1
λ2/4 + λ2/8 = 1
3λ2/8 = 1
λ2 = 8/3

Taking the positive and negative square roots of λ2, we have:

λ = ±2√2/3

Substituting these values back into x and y, we get:

For λ = 2√2/3:
x = (2√2/3)/2 = √2/3
y = -(2√2/3)/4 = -√2/6

For λ = -2√2/3:
x = (-2√2/3)/2 = -√2/3
y = -(-2√2/3)/4 = √2/6

Now we can find the extreme values of f(x,y) by plugging in these values of x and y:

f(√2/3, -√2/6) = 4(√2/3) - 4(-√2/6) = 4√2
f(-√2/3, √2/6) = 4(-√2/3) - 4(√2/6) = -4√2

Therefore, the maximum value of 4x-4y subject to the condition x2 + 2y2 = 1 is 4√2 and the minimum value is -4√2.

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The measures of central tendencies changed as mode remained the same, the median increased and the mean increased.

To determine how the data set would've changed if she entered the competition, we simply need to work on the mean, median and mode of the data.

Given data;

35, 22, 31, 23, 35, 22, 30, 35, 40

Rearranging this data;

22, 22, 23, 30, 31, 35, 35, 35, 40

The mean of this data will be

mean = 30.3

The mode = 35

The median = 31

When her weight is added, the measures of central tendencies change to;

mean = 31.5

median = 33

mode = 35

The median decreases, the mode remains the same and the mean increases

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Kelly made at least $28 in 75% of the weeks

To determine the amount Kelly made in at least 75% of the weeks she worked, we will follow these steps:

1. Arrange the weekly earnings in ascending order:

16, 18, 21, 21, 28, 28, 32, 35.

2. Calculate 75% of the total number of weeks:

0.75 x 8 = 6 weeks.

3. Identify the earning corresponding to the 6th week: 28 dollars.

So, Kelly made at least $28 in 75% of the weeks she worked.

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The statement that best describes how pollination begins is that it starts when pollen from the male reproductive organ of a flower is transferred to the female reproductive organ of the same or a different flower. Pollination is an essential step in the reproduction of plants, and it allows for the exchange of genetic material between different plants.

Pollination can occur through various methods, including wind, water, and animals such as bees, butterflies, and birds. Once the pollen is transferred, it begins to grow and develop, ultimately leading to the formation of a seed and the growth of a new plant.

Pollination is vital to the continuation of plant life, and without it, many plant species would not be able to survive. It is essential for plant breeders to understand the pollination process, as they can use it to cross different plant varieties and produce new and improved plants.

In conclusion, pollination begins when pollen from the male reproductive organ of a flower is transferred to the female reproductive organ of the same or a different flower, allowing for the exchange of genetic material and the growth and development of new plants.

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The population grows by a factor of 2 every year.

The number of fish in a lake is growing exponentially, with given data for different numbers of years since the population was first measured as follows:

Years | Population (in thousands)
0     | 10
1     |
2     | 40
3     |
4     |
5     |
6     |

By what factor does the population grow every two years?
From year 0 to year 2, the population grows from 10,000 to 40,000. To find the growth factor, divide the population in year 2 by the population in year 0:
40,000 ÷ 10,000 = 4.

Thus, the population grows by a factor of 4 every two years.

Using this information, we can calculate the population for years 4 and 6:
Year 4: 40,000 × 4 = 160,000 (160 in thousands)
Year 6: 160,000 × 4 = 640,000 (640 in thousands)

By what factor does the population grow every year?
To find the yearly growth factor, take the square root of the growth factor every two years:
√4 = 2.

Thus, the population grows by a factor of 2 every year.

Using this information, we can complete the table:
Years | Population (in thousands)
0     | 10
1     | 20
2     | 40
3     | 80
4     | 160
5     | 320
6     | 640

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The solutions to the equation are x= -9 and x = 6

From the information given, we have that;

|x2 + 9x| = 6x + 54

To solve the quadratic equation, collect the like terms, we have;

x² + 9x - 6x = 54

subtract the terms

x² + 3x = 54

Put in standard form

x² + 3x - 54 = 0

Find the pair factors of -54 that add up to give 3 and substitute the values

x² + 9x - 6x - 54 = 0

group in pairs

(x² + 9x) - (6x - 54) = 0

factorize the expressions

x(x + 9) - 6(x + 9) = 0

Then, we have;

x- 6 = 0

x = 6

x + 9 = 0

x = -9

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