A line drawn from one side of a circular plate to the other, through the center of the plate, measures 25 centimeters.







What is the approximate area of the plate to the nearest square centimeter?




39 centimeters²

79 centimeters²

156 centimeters²

491 centimeters²

The distance between the lines is 5 units

The equations of the lines are given as

y = 1/2x + 2

x - 2y = 6

We start by expressing the equation x - 2y = 6 in slope-intercept form

So, we have

x - 2y = 6

Subtract x from both sides

-2y = -x + 6

Divide by -2

y = 1/2x - 3

The equations are then represented as

y = 1/2x - 3 and y = 1/2x+2

Where the slopes are

m = 1/2

And the intercepts are

c₁ = -3

c₂ = 2

Because the slopes are the same, the lines are parallel lines

The distance between the lines is then calculated by subtracting the y-intercepts

So, we have

Distance = |-3 - 2 |

Evaluate

Distance = 5

Hence, the lines are 5 units apart

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Answer:

D. t(x) = 4x - 1

Step-by-step explanation:

The sequence shows the first four terms. As such, the x coordinates of the graph will be 1, 2, 3, and 4. The y coordinates will be 3, 7, 11, and 15 respectively.

Graphing that, the 4 points all lie on the line 4x - 1, so D is the answer.

The graph I made for this is below.

Answer:

Systematic Sampling

Step-by-step explanation:

According to the Question,

So, systematic sampling is right Answer.

Answer:

Systematic Sampling

Step-by-step explanation:

What type of sampling did the daycare operator use Systematic Sampling.

Step-by-step explanation:

the correct answer is option a 6a-7

the equation s=700+0.07c models between his weekly sales in dollars and the amount of his sales in dollars. pastels salary in dollars for a week when his sales were 0$ is $700.

Pastels weekly salary includes base pay plus commission of his sales.

the equation s=700+0.07c models between his weekly sales in dollars and the amount of his sales in dollars.

find pastels salary in dollars for a week when his sales were 0$

the model is given as

s=700+0.07c

let us solve for c, the sales made

s =700 +0.07c given sales is 0$

then s=700

Hence , the equation s=700+0.07c models between his weekly sales in dollars and the amount of his sales in dollars. pastels salary in dollars for a week when his sales were 0$ is $700.

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Answer:

x+12 / 12-x im pretty sure but i dont know

Step-by-step explanation:

hope this helps? <3

Answer:

(x < 12) / x + 12

Step-by-step explanation:

6.9 inches of snow would be necessary for march for Chicago to exceed its monthly average snowfall of 7.28 in. for these five months.

The given data is as follows:

Snowfall months and their fallen depth is:

November = 2

December = 8.4

January = 11.2

February = 7.9

First, we need to first find out the total snowfall for the five months of November, December, January, February, and March.

Total snowfall = 2 + 8.4 + 11.2 + 7.9 + March

The average snowfall =  7.28 iches.

7.28 inches/month x 5 months = 36.4 inches

2 + 8.4 + 11.2 + 7.9 + March  = 36.4

29.5 + March = 36.4

March =  36.4 - 29.5

March = 6.9 inches.

Therefore, we can conclude that more than 6.9 inches of snow would be necessary for march for Chicago to exceed its monthly average snowfall of 7.28 in. for these five months.

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Answer: B. A right circular Cylinder

Step-by-step explanation:

Answer:

x = 180-(30+50)

=100°

Y = 30+50

=80°

...............................................

=======================================================

Explanation:

The angles shown are alternate exterior angles. They are exterior of the parallel lines (ie outside the parallel lines) and they alternate on either side of the diagonal transversal cut.

If those alternate exterior angles are congruent, then lines L and M are parallel.

2x-3 = x+4

2x-x = 4+3

x = 7

Answer:

x = 7

Step-by-step explanation:

2x - 3 and x + 4 are alternate exterior angles with same measure

2x - 3 = x + 4

2x - x = 4 + 3

x = 7

Answer: ($3.90)(12) - (2)($3.90) = 39.00

39.00/12 = 3.25 per pretzel

Answer:

125

Step-by-step explanation:

2:5

50: ?

50 divided by 2 = 25

25 times 5 is = ?

50:125

di sure kung tama ^^

a) To find the percentage of pregnancies that should last between 26 and 275 days, we can calculate the area under the normal curve between these two values.

Using the standard normal distribution, we need to standardize the values by subtracting the mean and dividing by the standard deviation.

For 26 days:

Z = (26 - 262) / 18 = -12.222

For 275 days:

Z = (275 - 262) / 18 = 0.722

Now, we can find the corresponding probabilities using a standard normal table or a calculator.

The probability of a pregnancy lasting less than 26 days is P(Z < -12.222) which is essentially 0.

The probability of a pregnancy lasting less than 275 days is P(Z < 0.722) = 0.766.

To find the percentage between 26 and 275 days, we subtract the probability of less than 26 days from the probability of less than 275 days:

Percentage = 0.766 - 0 = 0.766 = 76.6%

Therefore, approximately 76.6% of pregnancies should last between 26 and 275 days.

b) To find the number of days for the longest 30% of all pregnancies, we need to find the corresponding Z-score for the upper 30% of the standard normal distribution.

Z(0.30) = 0.524 (approximately)

Now, we can reverse the standardization process to find the corresponding number of days:

X = Z * σ + μ

X = 0.524 * 18 + 262

X ≈ 271.43

Therefore, the longest 30% of all pregnancies should last at least approximately 271.43 days.

c) According to the Central Limit Theorem, the distribution of the sample mean will be approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

Mean (μ) of the sample mean (y) = Mean of the population = 262 days

Standard deviation (σ) of the sample mean (y) = Standard deviation of the population / √n

σ(y) = 18 / √80 ≈ 2.015

Therefore, the mean of the distribution of the sample mean is 262 days and the standard deviation is approximately 2.015 days.

d) To find the probability that the mean duration of the patients' pregnancies will be less than 200 days, we can standardize the value using the sample mean and standard deviation:

Z = (200 - 262) / (18 / √80) ≈ -7.150

Using a standard normal table or a calculator, we find that P(Z < -7.150) is essentially 0.

Therefore, the probability of the mean duration of the patients' pregnancies being less than 200 days is very close to 0.

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5)

we need first to calculate the radius of the circumference, this is the distance between the center to any point of the circumference, then the radius will be:

then the circumference equation is:

Step-by-step explanation:

3. Slope is postive

x1=6

x2=3

y1=10

y2=6

m=6-10/3-6

m=4/3

y=mx+b find b

10=4/3*3+b

10=4+b

b=6

y=4/3x+b

4.slope is zero

y=b

Y=3

4 is the length of missing length of polygon.

Polygon, in geometry, any closed curve consisting of a set of line segments (sides) connected such that no two segments cross. The simplest polygons are triangles (three sides), quadrilaterals (four sides), and pentagons (five sides)

Similar polygons are two polygons with the same shape, but not the same size. Similar polygons have corresponding angles that are congruent, and corresponding sides that are proportional.

16/2=8

15.4/2=7.7

16/2=8

8/2=4

Hence, 4 is the length of missing length.

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Answer:

56 units long

Step-by-step explanation:

the whole line is 73 units long, and CB is 17 units long. You would subtract 17 from 73 and then you have the missing value which is 56. (or in other words 17 plus what equals 73).

Answer:

SAS is the answer

Step-by-step explanation:

Answer:

HL.

Step-by-step explanation:

Right triangles with the hypotenuse and one leg congruent

Answer: b < - 10

Step-by-step explanation:

move the constant to the right.

- b > 8 + 2

calculate.

- b > 10

change the signs.

b < - 10

The can apply the zero-product property and multiply the factors corresponding to each zero to create a polynomial from the provided zeros.

Let's say, for illustration, that the bzeros are 2, -1, and 3.

We can express the polynomial in factored form as P(x) = (x - 2)(x + 1)(x - 3) to create it. This expression can be expanded to give P(x) = (x2 - x - 2)(x - 3).

The result of additional multiplication is P(x) = x3 - 4x2 + 5x + 6.

Thus, the polynomial P(x) = x3 - 4x2 + 5x + 6 has zeros at positions 2, -1, and 3. The largest power of x, which in this case is 3, gives us the degree of the polynomial, which is 3.

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The value of the growth factor of the function is found as 15.

A exponential function is one where the exponent contains the input, x.

Typically, an exponential function's equation looks like this:

y = abˣ

where,

In this issue

There are;

f(x) = 1/5.(15ˣ)

where,

1/5  -------> is the starting point.

15 --------> the growth factor.

Thus, the value of the growth factor of the function is found as 15.

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Answer:

D) 15 is the answer

Step-by-step explanation:

The time categories are divided into "<1 hour," "1-2 hours," "2-3 hours," and ">3 hours."  

What does the frequency distribution in the table reveal about the homework habits of the two samples of high school students?

The frequency distribution in the table provides insights into the distribution of homework habits among the two samples of high school students. By examining the frequency counts in each time category, we can determine the proportion of students spending different amounts of time on homework each night. This information helps identify patterns and differences in homework habits between the two samples, allowing for a comparison of their study behaviors.

Here is an example of a 4-column table with 2 rows representing the results of a random survey asking two samples of 100 high school students about the amount of time they spend on homework each night:

Sample 1:

  Sample 1                                                     Number of Students

    Time                                                                   Frequency

   <1 hour                                                                     20

  1-2 hours                                                                    40

 2-3 hours                                                                     30

    >3 hours                                                                   10

Sample 2:

 Sample 2                                                        Number of Students

Time                                                                      Frequency

<1 hour                                                                        30

1-2 hours                                                                    35

2-3 hours                                                                   20

>3 hours                                                                      15

In this table, each sample represents a different group of 100 high school students, and the frequency of students spending a particular amount of time on homework each night is recorded. The time categories are divided into "<1 hour," "1-2 hours," "2-3 hours," and ">3 hours." The table provides an overview of the distribution of homework time among the two samples of high school students.

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Answer:

C) 240ma

Step-by-step explanation:

Answer:50

Step-by-step explanation:

Answer:

The scale factor is 1/5.

Step-by-step explanation:

You can find the side length of triangles by looking at the points or it might be easier to see if you look at the graphs that I have attached.  I can see that the legs of the small triangle are 3 and the legs of the large triangle are 15.  What do I need to multiple 3 by to get 15?  5.  That is the scale factor from the little triangle to the big triangle.  If I go the other way, the scale factor is the reciprocal of 5 or 1.5

To find the maximums and minimums of the function f(x,y)=x^2+y^2+xy in the region {(x,y): x^2+y^2<=1}, we need to use the method of Lagrange multipliers.

First, we need to find the gradient of the function and set it equal to the gradient of the constraint (which is the equation of the circle x^2+y^2=1).

∇f(x,y) = <2x+y, 2y+x>
∇g(x,y) = <2x, 2y>

So, we have the equations:
2x+y = 2λx
2y+x = 2λy
x^2+y^2 = 1

Simplifying the first two equations, we get:
y = (2λ-2)x
x = (2λ-2)y

Substituting these into the equation of the circle, we get:
x^2+y^2 = 1
(2λ-2)^2 x^2 + (2λ-2)^2 y^2 = 1
(2λ-2)^2 (x^2+y^2) = 1
(2λ-2)^2 = 1/(x^2+y^2)

Solving for λ, we get:
λ = 1/2 or λ = 3/2

If λ = 1/2, then we get x = -y and x^2+y^2=1, which gives us the critical points (-1/√2, 1/√2) and (1/√2, -1/√2). We can plug these into the function to find that f(-1/√2, 1/√2) = f(1/√2, -1/√2) = -1/4.

If λ = 3/2, then we get x = 2y and x^2+y^2=1, which gives us the critical point (2/√5, 1/√5). We can plug this into the function to find that f(2/√5, 1/√5) = 3/5.

Therefore, the local maximum is (2/√5, 1/√5) with a value of 3/5, the local minimum is (-1/√2, 1/√2) and (1/√2, -1/√2) with a value of -1/4, and the absolute maximum is also (2/√5, 1/√5) with a value of 3/5, and the absolute minimum is on the border, which occurs at (0,1) and (0,-1) with a value of 0.

There are no critical points in the interior of the disk (not the border) that are not extremes or saddle points.
(i) Local extrema:
To find the local extrema, we first find the partial derivatives of f(x, y) with respect to x and y:

f_x = 2x + y
f_y = 2y + x

Set both partial derivatives equal to zero to find critical points:

2x + y = 0
2y + x = 0

Solving this system of equations, we find that the only critical point is (0, 0).

(ii) Absolute extrema:
To determine whether the critical point is an absolute maximum, minimum, or saddle point, we must examine the second partial derivatives:

f_xx = 2
f_yy = 2
f_xy = f_yx = 1

Compute the discriminant: D = f_xx * f_yy - (f_xy)^2 = 2 * 2 - 1^2 = 3

Since D > 0 and f_xx > 0, the point (0, 0) is an absolute minimum of the function.

(iii) Critical points and their classification:
The only critical point in the interior of the disk is (0, 0). As determined earlier, this point is an absolute minimum. No saddle points or other extrema are present within the interior of the disk.

To find any extrema on the boundary of the disk (x^2 + y^2 = 1), we use the method of Lagrange multipliers. However, as the boundary is not part of the domain specified in the question, we will not delve into that here.

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On that day, approximately 77.5% of the carpenters were at work.

To calculate the percentage of carpenters at work on a given day, we can use the following formula:

Percentage = (Number at Work / Total Number) * 100

Given:

Total number of carpenters = 40

Number of carpenters at work = 31

Using the formula:

Percentage = (31 / 40) * 100

Calculating the percentage:

Percentage = 0.775 * 100

Percentage = 77.5%

Therefore, on that day, approximately 77.5% of the carpenters were at work.

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Answer:

i would say the first one

Step-by-step explanation:

Answer:

No the rate of dollars per lawn is not constant

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Step-by-step explanation: