Janie has a paper cicle witha radius of 3 inches she cuts a smaller circle with a diameter of 2 inches out of the larger circle and discads it what is the appoximate are of the larger circle that s left

The solution to the inequality is y ≤ -8. This means that any value of y that is less than or equal to -8 will satisfy the original inequality.

To solve the inequality y + 7 ≤ -1, we need to isolate the variable y on one side of the inequality sign.

Starting with the given inequality:

y + 7 ≤ -1

We can begin by subtracting 7 from both sides of the inequality:

y + 7 - 7 ≤ -1 - 7

y ≤ -8

The solution to the inequality is y ≤ -8. This means that any value of y that is less than or equal to -8 will satisfy the original inequality.

In the context of a number line, all values to the left of -8, including -8 itself, will make the inequality true. For example, -10, -9, -8, -8.5, and any other value less than -8 will satisfy the inequality. However, any value greater than -8 will not satisfy the inequality.

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The following question may be like this:

What is a solution of the inequality shown below? y+7≤-1

An exponent is a number written above and to the right side of a value or number in math. The value or number is called the base, and the expression is read out as;

"Base raised to the power of exponent."

An example is given below;

In this example, 10 is the base and 3 is the EXPONENT.

The expression is now read out as,

"10 raised to the power of 3"

Note that even unknown values (such x as we commonly use in math) can also be an exponent or base. For example, we can have;

So basically, an exponent indicates the number of times a number is used to multiply itself.

Answer:

x = 15.9

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2  where a and b are the legs and c is the hypotenuse

6^2 + x^2 = 17^2

36+ x^2 = 289

x^2 = 289-36

x^2 =253

Take the square root of each side

sqrt(x^2) = sqrt( 253)

x = 15.90597

Rounding to the nearest tenth

x = 15.9

The value after double integration is 45.73

We can evaluate rectangle integrals in any order we like in Cartesian coordinates. We treat the other integral as a constant regardless of which integral we assess first; this is something to keep in mind while choosing the order of integration.

We want that x to be constant; we can easily integrate with respect to y. So we will evaluate y first. We get:

\(\int\limits^ \int\limits^ \frac{6x}{1+xy} dA=6\int\limits^6_0 \int\limits^1_0 {\frac{x}{1+xy} } \, dydx\)

\(or, 6\int\limits^6_0 {[In(1+xy)}_{0} ^{1} ]} \, dx\)

\(or, 6\int\limits^6_0 {In(1+x)} } \, -In 1dx\)

\(or, 6\int\limits^6_0 {In(1+x)} } \, dx\)

\(or,[(1+x)In(1+x)-(1-x)]^{6} _{0}\)

\(or,[7In7-In1-7+1]\\or,6(7In7-6)\\or,45.73\)

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The appropriate sample size formula on the TI-84 calculator, you can determine the sample size needed to achieve your desired margin of error for estimating population parameters.

To find the sample size with a desired margin of error on a TI-84 calculator, you can use the following steps:

1. Determine the desired margin of error: Decide on the maximum allowable difference between the sample estimate and the true population parameter. For example, if you want a margin of error of ±2%, your desired margin of error would be 0.02.

2. Determine the confidence level: Choose the desired level of confidence for your interval estimate. Common choices include 90%, 95%, or 99%.

Convert the confidence level to a corresponding z-score. For instance, a 95% confidence level corresponds to a z-score of approximately 1.96.

3. Calculate the estimated standard deviation: If you have an estimate of the population standard deviation, use that value. Otherwise, you can use a conservative estimate or a pilot study's standard deviation as a substitute.

4. Use the formula: The sample size formula for estimating a population mean is n = (z^2 * s^2) / E^2, where n represents the sample size, z is the z-score, s is the estimated standard deviation, and E is the desired margin of error.

5. Plug in the values: Input the values of the z-score, estimated standard deviation, and desired margin of error into the formula. Use parentheses and proper order of operations to ensure accurate calculations.

6. Calculate the sample size: Perform the calculations using the calculator, making sure to include the appropriate multiplication and division symbols. The result will be the recommended sample size to achieve the desired margin of error.

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If the bag contains a total of n blocks and m of them are blue, we would expect to have selected a blue block approximately (m/n) * 12 times out of the 12 draws, assuming the selection process is random and the probabilities remain constant.

Let's assume that the bag contains a total of n blocks, and m of them are blue blocks. The probability of selecting a blue block on each draw, P(blue), would be m/n.

Since we are replacing the block after each selection, the total number of blocks in the bag remains the same throughout the process. Therefore, the probability of selecting a blue block on each draw remains constant at m/n.

To find the expected number of times we would select a blue block, we can multiply the probability of selecting a blue block on each draw (m/n) by the total number of draws (12):

Expected number of blue blocks = (m/n) * 12

The reasoning behind this is that in each individual draw, the probability of selecting a blue block is m/n. By performing 12 independent draws, we can expect to encounter this probability m/n a total of 12 times on average.

Therefore, if the bag contains n blocks with m blue blocks, we would expect to have selected a blue block approximately (m/n) * 12 times out of the 12 draws.

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Answer:

  34 square units

Step-by-step explanation:

You want the area of the triangle with vertices X(6, 8), Y(3, 3), and Z(13, -3).

There are several ways the area of a triangle can be calculated from the coordinates of the vertices. One relatively easy method is to find half the absolute value of the sum of the determinants of adjacent pairs of points.

This calculation is shown in the second attachment.

The area of ∆XYZ is 34 square units.

A slope calculation will tell you side XY is perpendicular to side YZ. This means you can find the area from the lengths of these two sides. The distance formula can tell you the lengths.

  XY = √((3 -6)² +(3 -8)²) = √(9 +25) = √34

  YZ = √((13 -3)² +(-3 -3)²) = √(100 +36) = 2√34

 Area = 1/2bh = (1/2)(√34)(2√34) = 34 . . . . square units

Pick's theorem tells you the area of a polygon with vertices on grid points can be found by counting the grid points on the boundary and interior to the boundary.

  A = i + (b/2) -1

This triangle has the three given vertices on grid points, along with point (8, 0), which is the midpoint of YZ. There are 33 interior points, so the area is ...

  A  = 33 +(4/2) -1 = 34 . . . . square units

The length of XZ is ...

  XZ = √((13 -6)² +(-3 -8)²) = √(49 +121) = √170

Heron's formula tells you the area is given by ...

  A = √(s(s -a)(s -b)(s -c)) . . . . . . where s = (a+b+c)/2, the semiperimeter

The third attachment shows this calculation gives an area of 34 square units.

__

Additional comments

The slope calculation tells you the slope of XY is ...

  m = (y2 -y1)/(x2 -x1) = -5/-3 = 5/3

and the slope of YZ is ...

  m = -6/10 = -3/5 . . . . . . . . the opposite reciprocal of the slope of XY

Hence these sides are perpendicular, as we noted above.

We like Pick's theorem for finding the areas of small figures with irrational side lengths (such as this one). It just involves counting, which is often easier than using a bunch of different formulas for slope or length.

The determinant formula is easy to compute, but tedious to enter on a calculator. It is much easier to program a spreadsheet for this. As with Pick's theorem, the method applies to a polygon with any number of vertices.

  \(\left|\begin{array}{cc}a&b\\c&d\end{array}\right|=ad-bc\)

In these 2×2 matrices, the coordinates can be listed in rows or in columns. It makes no difference to the calculation. The key is to work in one direction around the figure. (Here, we went CCW.)

The triangle is drawn in the first attachment. The geometry program that drew it also calculated its area to be 34 square units.

You may have noticed that the "determinant" method and Pick's theorem guarantee that the area of any polygon with integer coordinates will be an integer multiple of 1/2 square unit. That is, it will never be irrational. (You might not see that using Heron's formula.)

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Answer:

x=4

Step-by-step explanation:

Answer:

X=4

Step-by-step explanation:

All work shown below. Y cannot be solved for because it is not a variable in the equation.

Answer:

2/6

Step-by-step explanation:

In this triangle, the product of tan A and tan C is `(BC)^2/(AB)^2`.

The given triangle ABC has angle A measuring 45 degrees, angle B measuring 90 degrees, and angle C measuring 45 degrees , Answer: `(BC)^2/(AB)^2`.

We have to find the product of tan A and tan C.

In triangle ABC, tan A and tan C are equal as the opposite and adjacent sides of angles A and C are the same.

So, we have, tan A = tan C

Therefore, the product of tan A and tan C will be equal to (tan A)^2 or (tan C)^2.

Using the formula of tan: tan A = opposite/adjacent=BC/A Band, tan C = opposite/adjacent=AB/BC.

Thus, tan A = BC/AB tan C = AB/BC Taking the ratio of these two equations, we have: tan A/tan C = BC/AB ÷ AB/BC Tan A * tan C = BC^2/AB^2So, the product of tan A and tan C is equal to `(BC)^2/(AB)^2`.

Answer: `(BC)^2/(AB)^2`.

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Answer:

A: \(\frac{3}{2}\)

Step-by-step explanation:

\(\mathrm{The\:roots\:are\:the\:intercepts\:with\:the\:x-axis}\:\left(y=0\right)\)

\(2x-3=0\)

\(\mathrm{Add\:}3\mathrm{\:to\:both\:sides}\)

\(2x-3+3=0+3\)

\(\mathrm{Simplify}\)

\(2x=3\)

\(\mathrm{Divide\:both\:sides\:by\:}2\)

\(\frac{2x}{2}=\frac{3}{2}\)

\(Simplify\)

\(x=\frac{3}{2}\)

Given the information, the triangle congruence prove is explained below.

If the corresponding sides or measure of angles of two or more triangles have common properties, then the triangles are said to be congruent. Such that on comparing their sides and internal angles, some have equal values.

With the given information in the question, the prove is explained below:

               STATEMENTS                         REASONS

1. AB ≅ CD                                             Given

2. <ABD ≅<CDB                                    Given

3. AD ≅ BC                                            Equal sides of a parallelogram

4. <ADB ≅ <CBD                                   Alternate angle theorem

5. <A ≅ <C                                             Opposite property of a parallelogram

Therefore, it can be deduced that;

ΔABD ≅ ΔCDB

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The quality of milk reaching the ultimate consumer is largely determined at the plant, where processing and handling occurs. a

Once milk is collected from the farm, it is transported to processing plants where it undergoes a series of treatments to ensure that it is safe for consumption.

This includes pasteurization, homogenization, and standardization.
The pasteurization process involves heating the milk to a specific temperature for a certain amount of time to kill harmful bacteria.

Homogenization helps to evenly distribute the milk's fat content, while standardization ensures that the milk meets certain regulatory requirements for fat content and nutritional value.
The plant, milk undergoes rigorous quality control testing to ensure that it meets certain standards.

This includes testing for bacterial count, somatic cell count, and antibiotic residue.

Any milk that fails to meet these standards is discarded.
The USDA and FDA also play a role in ensuring that milk reaching consumers is of high quality.

The USDA sets standards for milk production, while the FDA regulates the use of antibiotics and other drugs in milk production.

The primary responsibility for ensuring milk quality rests with the processing plant.
The USDA and FDA do play a role in ensuring the quality of milk reaching consumers, the majority of the responsibility lies with the processing plant.

It is at the plant where the milk undergoes treatments to ensure that it is safe for consumption and undergoes rigorous quality control testing to meet certain standards.

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The first three terms of the sequence are -4 , -1, 4. The 10th term of the sequence is given as 95

The general form of the nth term of a sequence can be represented as an expression involving n, such as n^2 - 5.

The first three terms of the sequence are:

n = 1, term = 1^2 - 5 = -4

n = 2, term = 2^2 - 5 = -1

n = 3, term = 3^2 - 5 = 4

The tenth term of the sequence is:

n = 10, term = 10^2 - 5 = 95

So, the first three terms are -4, -1, 4, and the tenth term is 95.

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The set of all first components of the ordered pairs of a function are called the Independent Variable.

In a function, the first component of the ordered pairs is known as the independent variable, which is the input value of the function. The second component of the ordered pairs is known as the dependent variable, which is the output value of the function. The set of all first components is also called the domain of the function, while the set of all second components is called the range of the function.

Therefore, the correct term to complete the statement is the Independent Variable.

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Based on the total number of species of birds, and the number that stayed at the zoo, the equation that shows the species of birds that were transported is b + 24 = 68.

The total number of birds in Roaring Zoo adds up to 68 different species which means that the number of birds that stayed and the number that were trasnported will add up to 68.

Assuming the number of birds transported was b, the equation to find this number of birds is:

Number of transported birds + Number of birds that stayed at zoo = Total number of birds

b + 24 = 68

Options for this question are:

b + 24 = 68

b − 24 = 68

b + 68 = 24

b − 68 = 24

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Answer:

The measures of this complementary angles is:

45°

Step-by-step explanation:

Complementary angles sum 90°

∡A + ∡B= 90°

∡A = ∡B

Then:

∡A + ∡A = 90°

2∡A = 90°

∡A = 90/2

∡A = 45°

∡B = 45°

To find the probability of passing the true/false examination when the number of questions is n, we need to use binomial distribution. We need to plug in the values and calculate the probability of passing for a specific number of questions n

Let X be the number of correct answers the student gets. Since the probability of getting a correct answer is 0.50, we have X ~ Bin(n, 0.50).

To pass the exam, the student must answer at least 70% of the questions correctly. This means that X must be greater than or equal to 0.70n. We can write this as:

P(X >= 0.70n) = 1 - P(X < 0.70n)

Using the binomial distribution formula, we can find the probability of getting less than 0.70n correct answers:

P(X < 0.70n) = ∑(i=0 to 0.70n-1) (n choose i) * 0.50^i * 0.50^(n-i)

We can use a calculator or software to evaluate this sum. For example, if n = 50, we get:

P(X < 0.70n) = P(X < 35) = 0.0738

Therefore, the probability of passing the exam when the number of questions is 50 is:

P(X >= 0.70n) = 1 - P(X < 0.70n) = 1 - 0.0738 = 0.9262

So, the student has a 92.62% chance of passing the exam if there are 50 true/false questions and he answers them by tossing a coin.

To find the probability of passing the true/false examination with a 70% correct answer requirement, we will use the binomial probability formula. The binomial probability formula is:

P(X = k) = C(n, k) * p^k * (1-p)^(n-k)

Where:
- P(X = k) is the probability of getting k correct answers out of n questions
- C(n, k) is the number of combinations of n items taken k at a time
- p is the probability of getting a correct answer (0.50 in this case)
- n is the number of questions
- k is the number of correct answers

Since we need to find the probability of passing when the number of questions is not specified, let's assume there are n questions. To pass the exam, the student must answer at least 70% of the questions correctly. Therefore, k must be greater than or equal to 0.7n.

The probability of passing the exam can be calculated by summing up the probabilities of getting at least 70% correct answers:

P(passing) = sum(P(X = k)) for k = ceil(0.7n) to n

Where ceil() is the ceiling function that rounds up to the nearest integer.

Now we need to plug in the values and calculate the probability of passing for a specific number of questions n. Please provide the number of questions on the examination to get the exact probability of passing.

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The p-value for testing the difference in productivity levels between the east coast and midwest warehouse employees is less than 0.01, suggesting strong evidence of a significant difference in productivity.

To test the difference in productivity levels, the CEO can use a two-sample t-test since she has two independent samples (east coast and midwest) and wants to compare their means.

The null hypothesis (H₀) assumes that there is no difference in productivity, while the alternative hypothesis (H₁) assumes that there is a difference.

The formula for calculating the t-test statistic is:

t = (x₁ - x₂) / √[(s₁² / n₁) + (s₂² / n₂)]

Where x₁ and x₂ are the sample means (1299 and 1456), s₁ and s₂ are the population standard deviations (350 and 297), and n₁ and n₂ are the sample sizes (35 for both groups).

By plugging in the values into the formula, we can calculate the t-test statistic, which in this case is approximately -3.828. With 68 degrees of freedom (35 + 35 - 2), the critical t-value for a 0.01 significance level (two-tailed test) is approximately ±2.623.

Comparing the calculated t-value with the critical t-value, we find that -3.828 < -2.623, indicating that the calculated t-value falls in the rejection region.

Therefore, we reject the null hypothesis.

The p-value is the probability of observing a t-value as extreme as the calculated value under the null hypothesis.

In this case, the p-value is less than 0.01, indicating strong evidence against the null hypothesis.

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The 90% confidence interval for the mean airborne time for flights from San Francisco to Washington Dulles is between 259.801 and 280.199 minutes.

In statistical terms, a 90% confidence interval means that if we were to repeatedly sample flights from San Francisco to Washington Dulles and calculate their mean airborne time, approximately 90% of the resulting confidence intervals would contain the true mean airborne time. The calculated interval of 259.801 to 280.199 minutes suggests that we are 90% confident that the true mean airborne time falls within this range. This means that based on the given sample data, there is a high likelihood that the average flight duration from San Francisco to Washington Dulles is somewhere between 259.801 and 280.199 minutes.

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Answer:12.8 hours

Step-by-step explanation:divide 5 by 4 you get 1.25 witch is one hour 15 min then you times 5 by 3 then add

Sherry make 16 pies in 12.9 hours.

What is Division method?

Division method is used to distributing a group of things into equal parts.

Given that;

Sherry can make 5 pies in 4 hours.

Now,

Since, Sherry can make 5 pies in 4 hours.

So, Sherry can make 1 pies in = 4/5 hours.

Thus, Sherry can make 16 pies in = 16 x 4/5 hours.

                                                    = 64/5 hours

                                                    = 12.9 hours

So, Sherry make 16 pies in 12.9 hours.

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Step 1:

The formula for the area of a hexagon can also be given in terms of the apothem as,

Area of hexagon

where 'a' is the length of the apothem and 'P' is the perimeter of the hexagon.

Step 2:

Length of the sides = 15 cm

Step 3:

Find the Apothem ' a '

Find each angle

Next

Answer:

We do not have any problem to solve?

Step-by-step explanation:

The equation in the vertex form will be y = (x + b/2a)² - b²/4a² + c/a and the equation in the standard form will be ax² + bx + c = 0.

The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.

Convert the standard equation into a vertex form, then we have

x² + (b/a)x + (c/a) = 0

x² + (b/a)x + b²/4a² - b²/4a² + c/a = 0

(x + b/2a)² - b²/4a² + c/a = 0

Put h = - b/2a and k = - b²/4a² + c/a, where (h, k) be the vertex of the parabola. Then the equation will be

(x - h)² + k = 0

The function written in vertex form will be y = (x - h)² + k and in the standard form will be ax² + bx + c = 0.

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The accumulation points of the given function are -1 and 1, with upper and lower accumulation points being 1 and -1 respectively.

To find the accumulation points of a function, we need to determine the values towards which the function approaches as the input approaches certain values. In this case, we have the function 11.9. Since it is a constant function, it takes the value 11.9 for all inputs.

Thus, there are no accumulation points other than the constant value itself, which is -1. However, when considering upper and lower accumulation points, we need to include the endpoints of the interval.

As the function is constant, the upper accumulation point is the maximum value of the function, which is 11.9, and the lower accumulation point is the minimum value, which is also 11.9. Hence, the accumulation points are -1 and 1, with upper and lower accumulation points being 1 and -1 respectively.

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