Find the measure of the exterior 21.
A. 36°
B. 56°
C. 136
D. 144°

Therefore, the displacement of the wheel during this interval is approximately 141.372 cm.

To find the displacement of the wheel during this interval, we need to determine the distance traveled by a point on the rim of the wheel.

Given:

Radius of the wheel: 45.0 cm

The wheel rolls without slipping

The wheel rolls through one-half of a revolution

Since the wheel rolls without slipping, the distance traveled by a point on the rim of the wheel is equal to the circumference of the wheel for each complete revolution. Therefore, the distance traveled for one-half of a revolution is equal to half the circumference of the wheel.

The circumference of a circle can be calculated using the formula: C = 2πr, where r is the radius of the circle.

Using the given radius of the wheel, we can calculate the circumference:

C = 2π(45.0 cm) ≈ 2π(45.0) cm ≈ 282.743 cm (rounded to three decimal places)

Since the wheel rolls through one-half of a revolution, the displacement is equal to half the circumference of the wheel:

Displacement = 0.5 × 282.743 cm ≈ 141.372 cm (rounded to three decimal places)

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The wheel's displacement is equal to the 282.6 cm that it has covered in its voyage.

We must ascertain the wheel's distance traveled and the displacement's direction.

Since the wheel has completed one-half of a revolution, the distance it has gone is equal to half its circumference. The formula: can be used to determine a circle's circumference:

Circumference = 2 * π * radius

In this case, the radius of the wheel is 45.0 cm. Let's calculate the circumference:

Circumference = 2 * π * 45.0 cm

Circumference ≈ 2 * 3.14 * 45.0 cm

Circumference ≈ 282.6 cm

So, the distance traveled by the wheel is approximately 282.6 cm.

The wheel's displacement is the angular separation between its starting point, where it first makes contact with the ground, and its finishing point, where it stops after rolling through one-half of a rotation. The point of contact with the floor does not move since the wheel is moving without slipping.

Therefore, the wheel's displacement is equal to the 282.6 cm that it has covered in its voyage.

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The length of the microorganism that measure 5μm is equivalent to 0.005 mm

It is the transformation of a value expressed in one unit of measurement into an equivalent value expressed in another unit of measurement of the same nature.

To solve this problem the we have to convert the units with the given information.

1mm is equal to 1000 μm

5μm * (1 mm/1000μm) = (5*1) / 1000 = 5/1000 = 0.005 mm = 5x10^-3 mm

The length of the microorganism that measure 5μm is equivalent to 0.005 mm

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If the city worker released the statement that 60% of dairy city's 3,000 homes are in violation of city codes , then the City Worker's statement is an example of : (d) Statistical Inference .

The Statistical Inference involves making generalizations about a population based on a sample.

In this case, the city worker has taken a sample of 200 homes out of the total 3,000 homes in Dairy City, and based on that sample, the City Worker is making an inference about the proportion of homes in violation of city codes for the entire population of Dairy City.

The statement is not a census as a census would involve collecting data from every single unit in the population, in this case every single home in Dairy City.

The given question is incomplete , the complete question is

A city worker inspected 200 homes in dairy city. during that inspection, 120 homes were found to violate one or more city codes. the city worker released a statement that 60% of dairy city's 3,000 homes are in violation of city codes.

The City Worker's statement is an example of :

(a) Census

(b) An experiment

(c) Descriptive Statistics

(d) Statistical Inference

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Answer:

It is the equation for the table y=ab^x (b>1,and b≠1）

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

the answer

Step-by-step explanation:

168/3 = 56

so 112 sodas

56 hotdogs

Answer:

you have a 50/50 chance to get equal number of heads & tails

Answer:

75.35km/h

Step-by-step explanation:

Answer:

75.4

Step-by-step explanation:

Answer:

Approximately 95

Step-by-step explanation:

19 x 5 = 95

According to the text, one result of the large surveys conducted among American college graduates regarding their college experience was that a majority of them felt that their college education helped them develop critical thinking and problem-solving skills.

In fact, around 80% of the respondents agreed that their college experience had helped them develop such skills, which they found useful in their personal as well as professional lives.

This is an important finding, as critical thinking and problem-solving abilities are highly valued in today's job market and are often considered essential for career success.

Moreover, the results suggest that American colleges are doing a good job in imparting these skills to their students. However, these survey also revealed that there were differences in the level of satisfaction with college education across different demographic groups, such as gender and ethnicity.

These findings highlight the need for colleges to ensure that their educational programs are inclusive and accessible to all students, regardless of their background.

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(a) There is no statistically significant relationship between race and receiving services from the program.

(b) Black homeless people were more likely to receive services (60%) than white homeless people (43.75%).

a. To test whether there is a statistically significant relationship between race and whether the person received services from the program, we can use a chi-squared test of independence.

The null hypothesis is that there is no relationship between race and receiving services, and the alternative hypothesis is that there is a relationship.

Using a chi-squared calculator, we obtain a chi-squared statistic of 0.267 and a p-value of 0.605. Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis and conclude that there is no statistically significant relationship between race and receiving services from the program.

b. To compute column and row percentages, we can first calculate the total number of black and white homeless people who received services and who did not receive services:

We can also calculate the percentage of all homeless people who received services or did not receive services, by adding up the numbers in each column:

In the sample, black homeless people were more likely to receive services (60%) than white homeless people (43.75%).

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Answer:Angle x is congruent with the interior angle opposite side 8 (alternate interior angles)

Use tangent:

tan x = 8/15

x = arctan (8/15)

x = 28.1° (rounded)

Step-by-step explanation:

The polynomial x² + 5x + 4 can be factored as (x + 1)(x + 4).

To factor the polynomial x² + 5x + 4, we need to determine two binomials whose product equals the original polynomial. We look for two factors that, when multiplied together, result in the given quadratic expression.

In this case, we consider the coefficient of x², which is 1. We know that the factors will have the form (x + a)(x + b), where 'a' and 'b' are the constants we need to determine. We then look for values of 'a' and 'b' such that their sum equals the coefficient of x, which is 5 in this case, and their product equals the constant term, which is 4.

After some trial and error or by applying factoring techniques, we find that 'a' = 1 and 'b' = 4 satisfy these conditions. Therefore, we can express the polynomial x² + 5x + 4 as the product of the binomials (x + 1)(x + 4).

To verify the factorization, we can multiply (x + 1)(x + 4) using the distributive property:

(x + 1)(x + 4) = x(x) + x(4) + 1(x) + 1(4) = x² + 4x + x + 4 = x² + 5x + 4.

Thus, we have successfully factored the polynomial x² + 5x + 4 as (x + 1)(x + 4).

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According to the question, the mean, variation, standard deviation, quartiles, median, and percentile for the given data set are:

Mean = 43.33

Variation = 9646.22

Standard Deviation = 98.21

First Quartile (Q1) = 12

Median = 48

Third Quartile (Q3) = 70

65th Percentile = 50

​

To find the mean, variation, standard deviation, quartiles, median, and percentile for the given data set, we can follow these steps:

Step 1: Sort the data in ascending order: 8, 12, 30, 35, 48, 50, 62, 70, 78.

Step 2: Calculate the mean:

\(Mean = \frac{8 + 12 + 30 + 35 + 48 + 50 + 62 + 70 + 78}{9} = 43.33\) (rounded to two decimal places).

Step 3: Calculate the variation:

\(\text{Variation} = \frac{{\sum((x_i - \text{mean})^2)}}{n}\\\\= \frac{{((8 - 43.33)^2 + (12 - 43.33)^2 + \ldots + (78 - 43.33)^2)}}{9}\\\\= 9646.22 \quad\)

Step 4: Calculate the standard deviation:

Standard Deviation = \(\sqrt{(Variation)} = \sqrt{(9646.22)} = 98.21\) (rounded to two decimal places).

Step 5: Calculate the quartiles:

First Quartile (Q1) = 12 (since it is the median of the lower half of the data).

Third Quartile (Q3) = 70 (since it is the median of the upper half of the data).

Step 6: Calculate the median:

The median is the middle value of the sorted data set, which is 48.

Step 7: Calculate the percentile:

To find the 65th percentile, we need to determine the value that separates the lowest 65% of the data from the highest 35%. Since the data set has 9 elements, 65% of 9 is 5.85. Rounding up, we get 6. The 6th element in the sorted data set is 50, which represents the 65th percentile.

Hence, the mean, variation, standard deviation, quartiles, median, and percentile for the given data set can be represented in LaTeX as follows:

\(\text{Mean} &= 43.33 \\\text{Variation} &= 9646.22 \\\text{Standard Deviation} &= 98.21 \\\text{First Quartile (Q1)} &= 12 \\\text{Median} &= 48 \\\text{Third Quartile (Q3)} &= 70 \\\text{65th Percentile} &= 50 \\\)

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we know that

An equilateral truangle has three equal length sides

so

If triangle ABC is an equilateral triangle

then

AB=BC=AC

so

step 1

Find out the distance AB

The formula to calculate the distance between two points is equal to

we have

A (-4,6)

B (6,6)

substitue in the formula

step 2

Find the distance BC

we have

B (6,6)

C( 1,-3)

substitute the values in the formula

we have that

AB is not equal to BC

therefore

Is not an equilateral triangle

Is not necessary calculate the distance AC

The limit of (f(x) + 1) / sin(x) as x approaches 0 is 0, the approximation for f(1/2) using Euler's method with two steps is 19/32 and the particular solution to the differential equation with the initial condition f(0) = -1 is: y(x) = -1 / (x²  + 2x + 1) - 1.

(a) To find the limit of (f(x) + 1) / sin(x) as x approaches 0, we can first rewrite the given differential equation as:

dy / dx = y²  (2x + 2)

Separating variables, we get:

dy / y²  = (2x + 2) dx

Integrating both sides, we have:

∫(1 / y² ) dy = ∫(2x + 2) dx

Integrating the left side gives:

-1 / y = x²  + 2x + C1

where C1 is the constant of integration.

Since we have the initial condition f(0) = -1, we substitute x = 0 and y = -1 into the above equation:

-1 / (-1) = 0²  + 2(0) + C1

1 = C1

So the particular solution is:

-1 / y = x²  + 2x + 1

Multiplying through by y gives:

-1 = y(x²  + 2x + 1)

Simplifying further:

y(x²  + 2x + 1) + 1 = 0

Now, to find the limit (f(x) + 1) / sin(x) as x approaches 0, we substitute x = 0 into the particular solution equation:

f(0)(0²  + 2(0) + 1) + 1 = 0

-1(0) + 1 = 0

1 = 0

Therefore, the limit of (f(x) + 1) / sin(x) as x approaches 0 is 0.

(b) Using Euler's method, we approximate the value of f(1/2) starting at x = 0 with two steps of equal size. Let's choose the step size h = 1/4.

First step:

x0 = 0, y0 = f(0) = -1

Using the differential equation, we have:

dy / dx = y²  (2x + 2)

dy = y²  (2x + 2) dx

Approximating the derivative using the Euler's method:

Δy ≈ y²  (2x + 2) Δx

Δy ≈ (-1)²  (2(0) + 2) (1/4)

Δy ≈ 1/2

Next, we update the values:

x1 = x0 + Δx = 0 + 1/4 = 1/4

y1 = y0 + Δy = -1 + 1/2 = 1/2

Second step:

x0 = 1/4, y0 = 1/2

Using the differential equation again:

dy / dx = y^2 (2x + 2)

dy = y²  (2x + 2) dx

Approximating the derivative using the Euler's method:

Δy ≈ y²  (2x + 2) Δx

Δy ≈ (1/2)²  (2(1/4) + 2) (1/4)

Δy ≈ 3/32

Updating the values:

x2 = x1 + Δx = 1/4 + 1/4 = 1/2

y2 = y1 + Δy = 1/2 + 3/32 = 19/32

Therefore, the approximation for f(1/2) using Euler's method with two steps is 19/32.

c)To find the particular solution to the differential equation dy/dx = y^2 (2x + 2) with the initial condition f(0) = -1, we can solve the separable differential equation.

Separating variables, we have:

dy / y² = (2x + 2) dx

Integrating both sides:

∫(1 / y² ) dy = ∫(2x + 2) dx

Integrating the left side:

-1 / y = x²  + 2x + C

where C is the constant of integration.

To find the particular solution, we substitute the initial condition f(0) = -1:

-1 / (-1) = 0²  + 2(0) + C

1 = C

So the particular solution is:

-1 / y = x²  + 2x + 1

Multiplying through by y gives:

-1 = y(x²  + 2x + 1)

Simplifying further:

y(x²  + 2x + 1) + 1 = 0

Therefore, the particular solution to the differential equation with the initial condition f(0) = -1 is: y(x) = -1 / (x²  + 2x + 1) - 1

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A scalene triangle is a triangle that has 3 sides that are all different lengths.

Let these letters represent the problem:

a = 8.7

b = side 2

c = side 3

P = 54.6

To find the perimeter, we just need to add all the sides [ P = a + b + c ]

So, put what we have in the formula above.

54.6 = 8.7 + b + c

Best of Luck!

Answer:

17.4 + b= 54.6

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

7 + 6 = 13

Answer:

Step-by-step explanation:

So assuming that all the toilet paper rolls cost the same amount we need to find the unit rate. To find the unit rate it's a lot easier than teachers explain it. You just divide the first number by the second number and bam. 36/15 is 2.4. Trish payed 2 dollars and 40 cents for one toilet paper roll.

Amount $593.84 will be in the account after five years.

According to the question we have been given that the

 amount invested initially = $500

annual interest rate = 0.035

 Time = 5 years.

The formula for the future value is given as

         \(FV = a(1 + r)^{t}\)        (1)

where , FV = future value

              a = amount invested initially

               r = annual interest rate

              t = time

putting the required values in equation (1) we get

       \(FV = 500 (1 + 0.035)^{5} \\FV = 500 ( 1.035)^{5}\)

       FV = 500*1.188

       FV = $ 593.84

Thus, $593.84 will be the amount in the account after five years.

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Evaluating the given expressions and inequalities, we have;

\(11) \: \frac{x}{4} \cdot \left(2 + y - x \right) = 4\)

12) (8•a - 5•b) - 2•(a + b) = 4

\( 13) \: \frac{p \cdot (p + {a}^{2} )}{6} = 55 \)

\( 14) \: 3\cdot m - \frac{2\cdot m}{2} +\frac{n}{3} = 12 \)

\( 16) \: x \geq 11\frac{2}{3} \)

17) k > 9

18) v > 9

20) m ≤ 16

The given expressions are;

\(11) \: \frac{x}{4} \cdot \left(2 + y - x \right)\)

Where x = 4, and y = 6, we have;

\(\frac{x}{4} \cdot \left(2 + y - x \right) = \frac{4}{4} \cdot \left(2 + 6 - 4 \right) = 4\)

Therefore;

\(\frac{x}{4} \cdot \left(2 + y - x \right) = 4\)

12) (8•a - 5•b) - 2•(a + b)

Where a = 3 and b = 2, we have;

(8•a - 5•b) - 2•(a + b) = (8×3 - 5×2) - 2•(3 + 2) = 4

Therefore;

\(13) \: \mathbf{\frac{p \cdot (p + {a}^{2} )}{6}} \)

Where a = 7, and p = 6, we have;

\( \frac{p \cdot (p + {a}^{2} )}{6} = \mathbf{ \frac{6 \times (6 + {7}^{2} )}{6}} = 55 \)

Therefore;

\( \frac{p \cdot (p + {a}^{2} )}{6} = 55 \)

\(14) \: \mathbf{3\cdot m - \frac{2\cdot m}{2} +\frac{n}{3} } \)

Where m = 5, and n = 6, we have;

\( 3\cdot m - \frac{2\cdot m}{2} +\frac{n}{3} = \mathbf{3\times 5 - \frac{2\times 5}{2} +\frac{6}{3} }= 12 \)

Therefore;

\( 3\cdot m - \frac{2\cdot m}{2} +\frac{n}{3} = 12 \)

\(16) \: \mathbf{1 \frac{1}{6} }\leq \frac{x}{10} \)

Which gives;

\( \frac{7}{6} \times 10 \leq x \)

\( \mathbf{ \frac{35}{3} }\leq x \)

\( x \geq 11\frac{2}{3} \)

17) 20 < k + 11

Therefore;

k > 20 - 11 = 9

18) 6•v > 54

v > 54 ÷ 6 = 9

Therefore;

\(20) \: 8 \geq \mathbf{ \frac{m}{2}} \)

Therefore;

2 × 8 = 16 ≥ m

Which gives;

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Answer: International Date Line

Maria spends $22 on lottery tickets every week and $133 every month on food yearly

This means that in a year

there are 52 weeks and she spends 22 x 52 = $1,144 on Lottery tickets

and there are 12 months in a year, so she spends 133 x 12 = $1,596 on food

The money spent to buy lottery tickets in relation to the money spent on food yearly in percentage is

Answer:

100

Step-by-step explanation:

Just add

Answer: A, C, D

Step-by-step explanation:

1) AD=BD must be true because the angle bisector drawn from the vertex angle of an isosceles triangle is the perpendicular bisector of the base.

2) AC=CD does not need to be true because angles ADC and CAD do not need to be congruent.

3) This must be true by the definition of an angle bisector.

4) This must be true because angles CDA and CDB are both right angles.

5) This does not need to be true because triangle ADC does not need to be isosceles.

Answer:

706.86 cm

Step-by-step explanation:

=4pi(r^2)

=12.56(r^2)

=12.56(7.5^2)

=12.56(56.25)

=706.86

To convert hour into minute: (No. of hour × 60) minutes

So, 2/5 hours = (2/5 × 60) minutes = (120/5) minutes = 24 minutes

2\5 is 0.4 so 0.4 multiplied by 60 u get 24 so the answer is 24 minutes

To set up the artificial variable LP (Phase I LP) for the given problem, we introduce an artificial variable, LP, to the objective function with a coefficient of 1. The artificial variable is used to identify infeasible solutions.

To set up the artificial variable LP (Phase I LP), we modify the objective function as follows:

Maximize Z = 4x1 + 7x2 + x3 + LP

The artificial variable LP is introduced to the objective function with a coefficient of 1. This allows us to track its value during the iterations.

The initial constraints remain the same:

2x1 + 3x2 + x3 = 20

3x1 + 4x2 + x3 + x4 = 40

8x1 + 5x2 + 2x3 - x5 = 70

The initial basic variables (BV) are the slack variables corresponding to the equality and inequality constraints, namely, x3 and x4. The artificial variable LP is initially a non-basic variable.

The initial artificial variables' basic variable (BVB) values are set to the right-hand side values of the constraints:

x3 = 20

x4 = 40

The initial artificial variable LP's value is set to 0.

Next, the artificial variable LP is selected as the entering variable, as it has a positive coefficient in the objective function. To determine the leaving variable, we perform the ratio test using the ratios of the right-hand side values and the entering column values (coefficients of LP) for the respective constraints.

The leaving variable is determined based on the minimum ratio, ensuring that the corresponding row represents a valid pivot element. If no valid pivot element is found, the problem is infeasible.

This completes the setup of the artificial variable LP (Phase I LP) without performing a complete pivot. Further steps would involve applying the simplex method and iteratively pivoting to find the optimal solution or identify infeasibility.

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