The letters r and θ represent polar coordinates. Write the equation using rectangular coordinates (x, y).
r sin θ = 10
y = 10
x = 10
y = 10x
x = 10y

Answer: Let's call the total amount of grass that Austin collected "G" in kilograms. We know that he collected 30 9/10 kilograms, which can be written as a mixed number or an improper fraction:

30 9/10 = 309/10

So, we have:

G = 309/10

We also know that 2/3 of the grass he collected was blue grass. So, let's call the amount of blue grass "B" in kilograms. We can set up an equation based on the information given:

B = (2/3)G

Substituting G = 309/10, we get:

B = (2/3)(309/10)

B = 206/5

B = 41 1/5

Therefore, the total amount of blue grass Austin collected was 41 1/5 kilograms.

Step-by-step explanation:

The height of the cylinder, given the volume and the diameter of the base, would be 2, 592.46 feet

The given diameter of the base is 10 inches, so we need to find the radius first. The radius is half the diameter:

Radius (r) = Diameter / 2 = 10 inches / 2 = 5 inches

We also need to convert the radius from inches to feet since the volume is given in cubic feet:

5 inches = 5/12 feet = 0.4167 feet

Volume of a cylinder:

Volume (V) = πr²h

450π = π x (0.4167)^2 x h

450 = (0.4167)^2 x h

h = 450 / (0.4167)^2 = 2, 592.46 feet

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Answer:

Step-by-step explanation:

Hopefully this is right.

Area = (pi)r²

Which is pi times the the radius squared

The radius is 2, so 2² is 4, So we multiply 3.14, which is pi, by 4.

Multiply 3.14 by 4, and the answer is 12.56, the question says round to the nearest tenth, so the final answer will be 12.6

My math teacher back in 7th grade gave us this sentence to help us memorize the equations.

Cherry Pie Delicious (C=(pi)d), Apple Pie Are Too (A=(pi)r²)

Do the same with the other two questions, and the answer for question two will be 3.14, rounded to the nearest tenth will be 3.1

Question three do the same as well, and the answer will be 660.185, rounded will be 660.2

Hope this helps!

Answer:

To write a possible quadratic inequality, we first need to determine which quadratic function has roots at x = -0.5 and x = 1.5.

We know that the solution to the quadratic inequality is x < -0.5 or x > 1.5, which means that the parabola associated with our quadratic function should not intersect the x-axis between x = -0.5 and x = 1.5.

One quadratic function with roots at x = -0.5 and x = 1.5 is:

(x + 0.5)(x - 1.5) ≤ 0

To see why this is the case, we can use a graphing calculator to graph the quadratic function y = (x + 0.5)(x - 1.5) and observe that the function is negative (i.e., has a y-value less than zero) when x is less than -0.5 or greater than 1.5.

Alternatively, we can use the fact that the product of two factors is less than or equal to zero if and only if one factor is positive and the other is negative.

Since (x + 0.5) is positive for x > -0.5 and negative for x < -0.5, and (x - 1.5) is positive for x > 1.5 and negative for x < 1.5, the inequality (x + 0.5)(x - 1.5) ≤ 0 is true for x < -0.5 or x > 1.5, but false for -0.5 < x < 1.5.

Therefore, a possible quadratic inequality that satisfies the given set of values for x is:

(x + 0.5)(x - 1.5) ≤ 0

It is possible that there is right-sided dominance in kissing behavior, based on the reported study. The fact that in a random sample of 127 kissing couples, both people in 79 of the couples tended to lean more to the right than to the left suggests a pattern of right-sided dominance.

However, it is important to note that this study alone is not conclusive evidence of right-sided dominance in kissing behavior.

Further research would be needed to confirm whether there is a consistent pattern of right-sided dominance in kissing behavior across different populations and cultures. It is also possible that other factors, such as social or psychological factors, could influence the direction in which people lean during a kiss. Therefore, it is important to approach this topic with caution and not draw any firm conclusions based on a single study.

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Answer:6

Step-by-step explanation:

Answer:9

Step-by-step explanation:

Answer:

75lbs

Step-by-step explanation:

if the mean of the packages was 15 then all the items averaged to 5 pounds each meaning they had a total of 15*5 or 75lbs

The surface areas of the prisms are listed below:

Case 1: 94 in²

Case 2: 72 cm²

Case 3: 40.5 m²

Case 4: 39.1 mm²

Case 5: 130 ft²

Case 6: 136 m²

In this problem we find six cases of prisms, whose surface areas have to be found. Surface area is the sum of the areas of all faces in the prism. Face have either a rectangular or a triangular form, whose area formulas are:

Rectangle

A = b · h

Triangle

A = 0.5 · b ·h

Where:

Now we proceed to determine the surface areas:

Case 1

A = 2 · (4 in) · (5 in) + 2 · (3 in) · (4 in) + 2 · (5 in) · (3 in)

A = 40 in² + 24 in² + 30 in²

A = 94 in²

Case 2

A = 2 · 0.5 · (3 cm) · (4 cm) + (5 cm) · (4 cm) + (5 cm) · (3 cm) + (5 cm)²

A = 12 cm² + 20 cm² + 15 cm² + 25 cm²

A = 72 cm²

Case 3

A = 2 · (3 m) · (7 m) + 2 · (6 m) · (7 m) + 2 · (6 m) · (3 m)

A = 10.5 m² + 21 m² + 9 m²

A = 40.5 m²

Case 4

A = 2 · 0.5 · (4 mm)² + 2 · (4 mm) · (3 mm) + (5.7 mm) · (3 mm)

A = 16 mm² + 6 mm² + 17.1 mm²

A = 39.1 mm²

Case 5

A = 2 · (10 ft) · (5 ft) + 2 · (5 ft) · (1 ft) + 2 · (10 ft) · (1 ft)

A = 100 ft² + 10 ft² + 20 ft²

A = 130 ft²

Case 6

A = 2 · 0.5 · (6 m) · (4 m) + 2 · (7 m) · (5 m) + (7 m) · (6 m)

A = 24 m² + 70 m² + 42 m²

A = 136 m²

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Answer:

68 3/4 yds

Step-by-step explanation:

trust me :)

Answer:

see below

Step-by-step explanation:

area of triangle formula  = 1/2 base * height

so 1/2*6*22 =66

not sure why there's no choice of 66

Sampling methods that may be biased for finding the percentage of defective boards in a sawmill production are: selecting 30 consecutive boards, emailing customers and relying on their responses, and selecting every 40th board produced. So, the correct answer is A, B and D.

The biased sampling methods are Examining 30 consecutive boards one hour after production begins may be biased because it only captures a snapshot of the production at that specific time, and the boards selected may not be representative of the entire batch produced during the day.

Emailing customers to ask about defective boards may be biased because the response rate may vary among customers, and customers who experienced a higher or lower number of defective boards may be more likely to respond.

Selecting 20 boards at random each day for 5 days and examining them is less likely to be biased, as long as the selection process is truly random and representative of the entire production.

Selecting every 40th board produced over the course of one week is also less likely to be biased if the production process is consistent and there are no patterns or variations in the production that would affect the quality of every 40th board. So, the correct answer for biased is A, B and D.

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False. While all relationships should be valued and respected, it's unrealistic to say that they all have equal weight. Some relationships may be closer and more intimate than others, or may require more time and energy to maintain.

Additionally, some relationships may have greater consequences or impact on our lives than others. It's important to prioritize and nurture our relationships based on their individual significance and value to us.
In the context of relationships, the term "weight" refers to the importance or influence of a particular relationship. Not all relationships have equal weight because the significance of each relationship varies based on factors such as trust, communication, shared experiences, and emotional connections.

Some relationships are naturally stronger and more influential than others due to these factors, making them more valuable and impactful in a person's life. In contrast, weaker relationships may not have the same level of trust, connection, or influence, making them less important overall. It is essential to recognize and nurture the stronger relationships in one's life to maintain a healthy support system and overall well-being.

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The area of the rectangle is 48 in².

The area of the triangle is 24 in².

The area of the triangle is half the area of the rectangle.

To calculate the area of a rectangle, we multiply the length of the rectangle by its width. And to calculate the area of a triangle we multiply the base of the triangle to the height of the triangle and divide by 2.

To calculate the area of the rectangle, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute into equation 1

Also, the area of the triangle is given by the formula below

Where:

Substitute into equation 2

Hence, the area of the triangle is half the area of the rectangle.

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Answer:

1Step-by-step explanation:

The cumulative probability of obtaining a sample result will be approximately 0.0001

We have to apply Formula of Binomial Distribution:

P(X ≤ 168) = ΣP(X = i) for i = 0, 1, 2, .., 168, here in a sample of size n, P(X = i) is the probability of getting exactly i success

We assume that company's claim is true, 0.8 is the probability of success for each trial

P(X = i) = (200 choose i)×[tex]0.8^{i}[/tex] ×[tex]0.2^{200- i}[/tex]

By using this, we can easily find that cumulative probability is 0.0001

So, the probability is very low, this means that company's claim of an 80% success rate can be incorrect

So, further analysis may be needed to draw some conclusions and results

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The distance that the fish was able to travel in all was 23. 9 meters .

The distance from Harry to the fish' s hole can be found by the Pythagorean theorem:

a ² + b ² = c ²

7 ² + 7 ² = c ²

49 + 49 = c²

98 = c²

c = 9. 9

The total distance that the fish traveled can then be found by summing the distance it already traveled with the distance to Harry's:

= 14 + 9. 9

= 23. 9 meters

The fish traveled approximately 23.9 meters in all, rounded to the nearest tenth.

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Answer: x=4

Step-by-step explanation:

Isolate x using opposite operations.

2x + 3 = 11

2x = 8

x = 4

Answer:

4

Step-by-step explanation:

subract 3 from 11

2x=8

divide by 2

x=4

The value of x in the circle is 19.5 .

What is secant line of circle?

A secant is a straight line that intersects a circle at least twice in different places. We can draw an endless number of secants on a circle since a circle has an infinite number of points around its perimeter.

Here the given circle using formula for secant line ,

(A+B).B = (C+D).D

Here A = x , B = 8 , C= 12 and D=10. Then,

=> (x+8).8= (12+10).10

=> 8x+64 = 22*10

=> 8x+64 = 220

=> 8x = 220-64 = 156

=> x = 156/8 = 19.5

Hence the value of x in circle is 19.5.

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The equation of a parabola with a vertex at (-1, -1) is y = (x +1)²- 1.

The length of the third side ​of a triangle cannot be 15 cm

The correct answer is an option (b)

We know that the triangle inequality theorem states that the sum of any two sides of a triangle is greater than or equal to the third side.

For example if a, b, c represents the side of a triangle then by above theorem a + b ≥ c

Here, the two sides of a triangle measure 4 cm and 8 cm.

Let a = 4 cm and b = 8 cm and c represents the third side of a triangle.

Using triangle inequality theorem,

a + b ≥ c

4 + 8 ≥ c

12 ≥ c

This means that the third side of the triangle must be less than or equal to 12 cm.

Thus, the correct answer is an option (b)

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The complete question is:

A triangle has two sides measuring 4 cm and 8 cm. Which lengths cannot be the length of the third side ​

a) 7 cm

b) 15 cm

c) 10 cm

d) 5 cm

We would need 168 square inches of Teflon to completely cover the triangular prism machinery.

To calculate the surface area of a triangular prism, we need to find the area of each face and then add them up. Let's assume that the triangular bases of the prism have base b and height h, and that the length of the prism is l.

The surface area of the triangular bases is (1/2)bh for each base, so the total area is (1/2)bh + (1/2)bh = bh.

The lateral surface area of the prism is the area of the three rectangular faces. Each rectangular face has length l and height h, so the total lateral surface area is 3lh.

Therefore, the total surface area of the triangular prism is

bh + 3lh

To determine how much Teflon is needed to cover the machinery, we need to know the dimensions of the triangular prism. Once we have those dimensions, we can calculate the surface area using the formula above and then use that value to determine the amount of Teflon required.

Let's say the base of the triangular prism is 4 inches and the height is 6 inches, and the length of the prism is 8 inches. Then the surface area of the triangular prism is

bh + 3lh

= (4 in. x 6 in.) + 3(8 in. x 6 in.)

= 24 in² + 144 in²

= 168 in²

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The rate at which Sheila charges customers for each serving =  $2.5 per serving.

Here the table that shows the cost of a cake from Sheila based on the number of servings is:

SERVINGS          TOTAL COST

    100                       $280

    150                       $405

    200                       $530

    250                       $655

We need to find the rate at which Sheila charge customers for each serving.

Consider points (x₁, y₁) = (100, 280) and  (x₂, y₂) = (200, 530)

where x is the number of servings and y coordinate represents the cost of servings.

The rate at which Sheila charges customers for each serving would be,

r = (y₂ - y₁) / (x₂ - x₁)

r = (530 - 280) / (200 - 100)

r = 250 / 100

r = 2.5

Therefore, the required rate is $2.5 per serving.

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Answer:

$14.612

Step-by-step explanation:

40% = 0.4

Find a 40% tip on a 36.53 meal.

We Take

36.53 x 0.4 = $14.612

So, the tip is $14.612

Step 1: The test statistic is 56.56.

Step 2: Using a chi-square distribution table with 30 degrees of freedom (n - 1), we find that the p-value is less than 0.0001.

Step 3: The rejection region for a left-tailed test with 30 degrees of freedom at the 10% level of significance is any test statistic less than 18.307.

Step 4: The test statistic of 56.56 is greater than the critical value of 18.307.

Step 5:  The 90% confidence interval for the variance of force on the helmets is [1615.46, 4123.82]

In statistics, variance is a measure of the spread or dispersion of a set of data points. It is calculated as the average of the squared differences from the mean.

Step 1: To test whether the standard deviation is significantly less than 40, we can use a chi-square test with the null hypothesis H0: [tex]σ^{2}[/tex] ≥ 1600 lbs² and the alternative hypothesis H1: σ² < 1600 lb[tex]s^{2}[/tex]. The test statistic is:

chi-square = (n - 1) *[tex]s^{2}[/tex] / [tex]σ^{2}[/tex]

where n is the sample size, [tex]s^{2}[/tex] is the sample variance, and [tex]σ^{2}[/tex] is the population variance under the null hypothesis.

Substituting the given values, we have:

chi-square = (31 - 1) * 2350 / 1600 = 56.56

Rounding to two decimal places, the test statistic is 56.56.

Step 2: To determine the p-value for a left-tailed test, we need to find the area under the chi-square distribution to the left of the test statistic. Using a chi-square distribution table with 30 degrees of freedom (n - 1), we find that the p-value is less than 0.0001.

Step 3: The rejection region for a left-tailed test with 30 degrees of freedom at the 10% level of significance is any test statistic less than 18.307.

Step 4: Since the test statistic of 56.56 is greater than the critical value of 18.307, we reject the null hypothesis and conclude that there is sufficient evidence to indicate that the standard deviation is significantly less than 40 at the 5% level of significance.

Step 5: To calculate a 90% confidence interval for the variance of force on the helmets, we can use the formula:

[(n - 1) * [tex]s^{2}[/tex]/ chi-square upper, (n - 1) * [tex]s^{2}[/tex] / chi-square lower]

where chi-square upper and chi-square lower are the upper and lower critical values, respectively, from the chi-square distribution table for 30 degrees of freedom at the 5% level of significance. Substituting the given values, we have:

chi-square upper = 45.722

chi-square lower = 18.307

[(31 - 1) * 2350 / 45.722, (31 - 1) * 2350 / 18.307] = [1615.46, 4123.82]

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Answer:

3

Step-by-step explanation:

Because same numbers = same y intercept but I'm not sure

Answer:

  1) The image has the same slope, different y-intercept

Step-by-step explanation:

You want the relationship between the line 3x -5y = 4 and its image dilated by a factor of 5/3 centered at the origin.

Dilation about the origin multiplies every coordinate by the dilation factor. Dilation does not change slopes or angles, but it changes lengths by the dilation factor.

When the equation of a line is written in standard form, the dilation of it effectively multiplies the constant by the dilation factor.

The given line has intercepts ...

  ax +by = c

  x-intercept = c/a = 4/3

  y-intercept = c/b = -4/5

If these values are multiplied by the dilation factor 5/3, they become ...

  x-intercept' = (5/3)(4/3) = 20/9 = 2 2/9

  y-intercept' = (5/3)(-4/5) = -4/3 . . . . . note the y-intercept has changed

The slope of the given line can be determined from its intercepts:

  m = (-y intercept)/(x intercept) = -(-4/5)/(4/3) = 3/5

Since both of these intercepts are multiplied by the same dilation factor, their ratio remains unchanged. The slope of the dilated line is the same.

Effectively, the dilated line's equation is ...

  3x -5y = 4(5/3)

  3x -5y = 20/3

__

Additional comment

The original (dashed) line and its dilated image are shown in the attachment.

Answer:

I believe it's 148.

Step-by-step explanation:

You must do L x W x H to find the volume of a rectangular prism or cube.

Answer:

2/5

Step-by-step explanation:

slope= y2-y1 / x2-x1

in this case:

y2=7                            y1=5                      x2= 8                      x1=3

plug that into the formula above to get the answer

slope= 2/5 or 0.4

Answer:

22.2

Step-by-step explanation:

Answer:

3.6 can go into 80 22 times.

Step-by-step explanation: