Beth pulls a slinky a distance of 24 inches from its equilibrium position and then releases it. The time for one oscillation is 2 seconds. Step 2 of 2 : Find the function in terms of t for the displacement of the slinky. Assume that the slinky is at its maximum displacement at t=0 . Also assume that the function includes no horizontal or vertical shifts.

The area of sector GHJ is:

3.125π cm² (in terms of pi)

9.8 cm² (As a decimal rounded to the nearest tenth)

The formula for area of a sector when the angle is in radians is:

A = (1/2) * r²θ

Where θ is the angle subtended at the center and r is the radius of the circle.

In this case, r = 5 cm and θ = π/4

Substituting:

A = (1/2) * 5² * π/4

A = 3.125π cm² (in terms of pi)

As a decimal rounded to the nearest tenth:

A = 3.125 * 22/7

A = 9.8 cm²

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The total surface area of this countertop is 522 square feet.Once all of these factors are taken into account, Mrs. Miller can then calculate the total cost of the countertop.

Surface area is the total area of the visible surface of an object, such as a cube or a sphere. It is measured in square units such as square inches, square feet, or square meters. It is important in mathematics, science, and engineering because it is used to calculate the amount of material needed to cover an object, the volume of a container, and other measurements. Surface area is also helpful in solving problems involving friction, heat transfer, and air flow.

Mrs. Miller is ordering an L-shaped countertop with the dimensions shown for her kitchen. The total surface area of this countertop is 522 square feet. This is calculated by multiplying the length of the countertop (34 feet) by the width of the countertop (15 feet), which yields 510 square feet. Then, the total surface area of the countertop is increased by adding the surface area of the 3-ft by 3-ft corner (9 square feet). Therefore, the total surface area of the countertop is 522 square feet.

Part B

To determine the cost of the countertop, Mrs. Miller would need to consider several factors, such as the material used, the labor required to install the countertop, and any additional fees associated with the purchase. Generally speaking, countertops made of granite, quartz, and marble tend to be more expensive than countertops made of laminate and solid surface. The installation labor cost will vary depending on the complexity of the installation, as well as the type of material used and the size of the countertop. Additionally, there may be additional fees associated with the purchase, such as the cost of delivery and taxes. Once Mrs. Miller has determined all of these factors, she can then calculate the total cost of the countertop.

Conclusion

In conclusion, Mrs. Miller is ordering an L-shaped countertop with the dimensions shown for her kitchen. The total surface area of this countertop is 522 square feet. To determine the cost of the countertop, Mrs. Miller would need to consider several factors, such as the material used, the labor required to install the countertop, and any additional fees associated with the purchase. Once all of these factors are taken into account, Mrs. Miller can then calculate the total cost of the countertop.

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Answer:

x = 100

Step-by-step explanation:

1 and 2 are a linear pair and sum to 180° , that is

x + [tex]\frac{4}{5}[/tex] x = 180 ( multiply through by 5 to clear the fraction )

5x + 4x = 900

9x = 900 ( divide both sides by 9 )

x = 100

The given polynomial is a prime polynomial.

The given polynomial is

x² - x + 35

Since we know that discriminant of quadratic polynomial

p(x)= ax² + bx + c  is b² - 4ac

Therefore, discriminant of the given polynomial be,

⇒ (-1)² - 4x1x35

⇒ - 139

Since discriminant is negative number so it has no real roots.

And an irreducible or primal polynomial is a polynomial with integer coefficients that cannot be factored into polynomials of lower degree and also with integer coefficients.

Hence it is not factored completely.

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Answer:

The range is 37

Step-by-step explanation:

highest - lowest = range

64-27= 37

Hope it helped! :)

Answer:

15h-6k+12m

Step-by-step explanation:

The perimeter of the triangle is the sum of all of its side lengths

P=a+b+c

If a=5h-4k

b=10h+7m

c=5m-2k

Then the formula would be

P=(5h-4k)+(10h+7m)+(5m-2k)

P=15h-6k+12m

Hope this helps!

The expression (32 ÷ (10 - 8)) ÷ 2 - 3 evaluates to 5 and includes the necessary parentheses to achieve this result.

What is an algebraic expression?

An algebraic expression is a mathematical phrase that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

To make the value of the expression equal to 5, we can use parentheses to change the order of operations. One possible way to do this is:

32 ÷ (10 - (8 ÷ 2) - 3)

First, we evaluate the expression inside the parentheses:

8 ÷ 2 = 4

10 - 4 - 3 = 3

So now the expression becomes:

32 ÷ 3

=10.67

This is not equal to 5.

To make the value of the expression equal to 5, we need to modify the expression inside the parentheses. One way to do this is:

32 ÷ (10 - (8 ÷ (2 - 3)))

Here, we use the parentheses to change the order of operations so that we subtract 3 from 2 before dividing 8 by the result. This gives us:

8 ÷ (-1) = -8

So now the expression inside the parentheses becomes:

10 - (-8) = 18

So the entire expression becomes:

32 ÷ 18 = 1.78

This is still not equal to 5.

Another way to make the value of the expression equal to 5 is:

(32 ÷ (10 - 8)) ÷ 2 - 3

Here, we use the parentheses to ensure that we divide 32 by the result of (10 - 8) before dividing the whole expression by 2 and subtracting 3. This gives us:

32 ÷ 2 - 3 = 13

So the entire expression becomes:

13

And this is equal to 5.

Therefore, one possible expression that includes a set of parentheses so that the value of the expression is 5 is:

(32 ÷ (10 - 8)) ÷ 2 - 3

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Option B is correct. The sample is not unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is not sufficient evidence to support the claim.

We are utilizing the rare event rule and subjective estimation to verify the legitimacy of a claim. The assertion states that, within a considerable math class, the mean age of pupils is below 30. When selecting students at random, we observe that their average age is 29.3 years.

Given that the sample's mean age only subtlety fluctuates from the value expected (i.e., 30), the result obtained is not improbable if the premise holds true (thus validating the claim). Furthermore, it would be non-ambiguous even if the proposition is false due to the minuscule difference between 29.3 and 30 years of age.

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Using the ratios, 1 yd/3 feet, 1 mi/5,280 feet, and 200 yards/1 feet, the number of flags required to mark the racecourse with a flag every 200 yards is 22.

Ratios are relative sizes of one quantity or value compared to another.

Ratios are depicted as fractional values using decimals, percentages, or fractions, including the standard ratio form (:).

The total distance of the racecourse = 2.5 miles

The common distance between each flag = 200 yards

1 mile = 1,760 yards

2.5 miles = 4,400 yards

1 yard = 3 feel

The number of flags required to cover the distance = 22 (4,400 ÷ 200)

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A set of data that could be represented by the box-and-whisker plot include the following: D.

The median of the set of data is equal to 10.

In Mathematics and Statistics, a box-and-whisker plot is a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the information provided about the data set (2, 2, 7, 10, 10, 11, 13, 15, 17, 20, 20, 24, 26, 27, 27, 28), the five-number summary for the given data set include the following:

Minimum (Min) = 2.

First quartile (Q₁) = 16.

Median (Med) = 10.

Third quartile (Q₃) = 25.5.

Maximum (Max) = 28.

In conclusion, we can logically deduce that the median of the data set is 10 and it has no outlier.

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The letters "L" and "X" both contain adjacent angles, as adjacent angles are angles that share a common vertex and side. In both letters, there are two angles that share a vertex and a side.

What is Acute angle ?

An acute angle is an angle that measures between 0 and 90 degrees. In other words, an acute angle is an angle that is smaller than a right angle, which measures exactly 90 degrees.

The letter "A" contains an acute angle, as the angle between the two lines that form the letter is less than 90 degrees.

None of the letters A, E, L, or X contain vertical angles, as vertical angles are formed by two intersecting lines and none of these letters contain intersecting lines.

Therefore, The letters "L" and "X" both contain adjacent angles, as adjacent angles are angles that share a common vertex and side. In both letters, there are two angles that share a vertex and a side.

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Answer: y = -4

Step-by-step explanation:

Based on these three given points, we can tell that this line is a horizontal line because there is no slope. All of the points have the same y-value, -4.

This means the equation of the line is:

       y = -4

See attached for a visual representation. I have graphed the given points over the top of the equation we wrote for the line.

Explanation:

The paragraph explains how TERFs have alienated many feminists from radical feminism and why TERF is a harmful and anti-trans movement.

Some other possible sentences are:

Answer:

[tex]5 {}^{3} \times 10 {}^{ - 2} \\ = 5 {}^{3} \times \frac{1}{10 {}^{2} } \\ = 5 {}^{3} \times \frac{1}{2 {}^{2} 5 {}^{2} } \\ = 5 \times \frac{1}{4 \\ } \\ = \frac{5}{4} [/tex]

hope it helps

The measure of length of x of the parallelogram is x = 2.36 units

Given data ,

Let the parallelogram be represented as ABCD

Now , the measure of lengths of the sides are

The measure of AB = 13x - 20

The measure of CD = 2x + 6

The measure of BC = 5x + 4

Opposite sides are parallel

Opposite sides are congruent

So , AB = CD

13x - 20 = 2x + 6

Subtracting 2x on both sides , we get

11x = 26

Divide by 11 on both sides , we get

x = 2.36 units

Hence , the parallelogram is solved and x = 2.36 units

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Exactly one-year later,

(a) Mean of the ages will be 13 years and 3 months.

(b) Range of the ages will be same 2 years and 7 months.

Part (a) : To find the mean of the ages of the same group of students exactly one year later, we add one year to each student's age and find the new mean.

New mean is : 12 years and 3 months + 1 year = 13 years and 3 months;

So the mean of the ages of the same group of students exactly one year later is 13 years and 3 months.

Part (b) : The range of their ages would still be 2 years and 7 months because we are adding the same amount to all of their ages, the difference between the youngest and oldest member of the group would remain the same.

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Answer: To solve the system of equations graphically, we need to graph both equations on the same coordinate system and find the point where they intersect. This point will give us the values of x and y that satisfy both equations.

First, we can rewrite the two equations in slope-intercept form:

y = 4x - 1 (equation 1)

y = -x + 4 (equation 2)

Now we can graph both equations on the same coordinate system. To do this, we can plot a few points for each equation and then draw a line through the points. Alternatively, we can use the y-intercept and slope of each equation to graph the lines. For equation 1, the y-intercept is -1 and the slope is 4. For equation 2, the y-intercept is 4 and the slope is -1.

We can see that the two lines intersect at the point (1, 3). Therefore, the solution to the system of equations is x = 1.

The calculated distance between the tree and the zip line is 9.21 units

From the question, we have the following parameters that can be used in our computation:

y = -6/7x + 7

This represents the zip line

Convert the equation to standard form

This gives

7y = -6x + 49

So, we have

6x + 7y - 49 = 0

This means that

A = 6, B = 7 and C = -49

From the point (6, 14), we have

x = 6 and y = 14

The distance between the tree and the zip line is then calculated as

[tex]d = \frac{|ax + by + c|}{\sqrt{a^2 + b^2}}[/tex]

By substitution, we have

[tex]d = \frac{|6 * 6 + 7 * 14 - 49|}{\sqrt{6^2 + 7^2}}[/tex]

This gives

[tex]d = \frac{85}{9.22}[/tex]

Divide

d = 9.21

Hence, the distance between the tree and the zip line is 9.21 units

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The gross income amount is $35,750

Given data ,

To find the gross income, we add up all of the man's income sources:

Gross Income = Wages + Interest + Retirement Plan Contribution

Gross Income = 38,800 + 1,600 + 3,200

Gross Income = 43,600

To find the Adjusted Gross Income (AGI), we subtract any eligible deductions from the gross income. In this case, the personal exemption and deductions are eligible.

AGI = Gross Income - Personal Exemption - Deductions

AGI = 43,600 - 2,900 - 4,950

AGI = 35,750

Finally, to find the taxable income, we subtract any additional deductions or exemptions from the AGI. We will assume that there are no additional deductions or exemptions in this case.

Taxable Income = AGI

Taxable Income = 35,750

Hence , the gross income is $43,600, the adjusted gross income is $35,750, and the taxable income is $35,750

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The answer to the question about how many teams completed the escape room in 45 minutes or less is 6.

A dot plot is a type of chart used to display the distribution of a dataset. It is also known as a dot chart, strip plot, or dot graph. In a dot plot, each data point is represented by a dot placed along a horizontal or vertical axis.

Dot plots are useful for showing the distribution of a small to moderate-sized dataset, and are especially helpful when you want to compare the distribution of two or more datasets side by side. They are also useful for identifying outliers or gaps in the data

If we count the amount of dots on 45 and before 45 and add them up, the answer is 6

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Answer:$909.03

Step-by-step explanation:he new balance on Guadalupe's credit card is calculated as follows:

First, we calculate the interest charged on the previous balance. Since the APR is 23%, the monthly interest rate is 23%/12 = 1.92%. So the interest charged on the previous balance for the month is:

Interest = Previous balance x Monthly interest rate

= $900.00 x 1.92%

= $17.28

Next, we add the finance charge, which is calculated as 1% of the previous balance plus any new charges. So the finance charge for the month is:

Finance charge = 1% x (Previous balance + New charges)

= 1% x ($900.00 + $0.00)

= $9.00

The total amount due is the sum of the previous balance, the interest charged, and the finance charge:

Total amount due = Previous balance + Interest + Finance charge

= $900.00 + $17.28 + $9.00

= $926.28

The minimum payment due is 2% of the total amount due, which is:

Minimum payment = 2% x Total amount due

= 2% x $926.28

= $18.53

If the minimum payment is less than $25, the minimum payment due is $25. So in this case, the minimum payment due is $25.

Guadalupe made a payment of $18.00, which is less than the minimum payment due, so she will be charged a late fee in addition to the interest on the unpaid balance.

The principal paid is the difference between the payment made and the interest charged, which is:

Principal paid = Payment - Interest

= $18.00 - $17.28

= $0.72

The new balance is the sum of the previous balance, any new charges, and the interest charged, minus the payment made, plus any finance charge and late fee:

New balance = Previous balance + New charges + Interest - Payment + Finance charge + Late fee

= $900.00 + $0.00 + $17.28 - $18.00 + $9.00 + $0.75

Answer:

Step-by-step explanation:

A=4

b Base

1

h Height

4

b

h

a

h

h

b

a

a

P

A

b

Solution

A=bh=1·4=4 hope helps  byee

Answer:

Step-by-step explanation:

If y varies directly as x, it means that y is directly proportional to x, and we can express this relationship using a proportionality constant k:

y = kx

To find the value of k, we can use the given information that y = 2 when x = 3:

2 = k(3)

Solving for k, we get:

k = 2/3

Now that we know the value of k, we can use the formula to find y when x = 1:

y = (2/3)x

y = (2/3)(1)

y = 2/3

Therefore, when x = 1, y = 2/3.

The probability of randomly selecting a red token would be 0. 30.

First, we know that the experiment was done 2, 000 times;

605 + 342 + 518 + 535 = 2000

The probability that a red token is randomly selected is therefore:

= Red token / Total times

= 605 / 2, 000

= 0. 3025

In fractions, we can make this:

= 605 / 2, 000

= 121 / 400

This is closest to the fraction 3 / 10 which is 0. 30.

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Answer: -8

Step-by-step explanation:

Simple math. Your welcome glad to help

There are 6435 ways to direct the inquiries to any two of the firm's real estate agents.

What is combinations?

Combinations are a mathematical concept used to count the number of ways that a certain number of items can be selected from a larger set of items without regard to the order in which they are selected.

We can use combinations to solve this problem. We need to choose 8 inquiries out of 16 for the first agent, and the remaining 8 inquiries will be handled by the second agent.

The number of ways to choose 8 inquiries out of 16 is:

C(16, 8) = 16! ÷ (8! * (16-8)!) = 12870

This is the number of ways the inquiries can be directed to one agent. Since there are two agents and each handles 8 inquiries, we need to divide this number by 2 to avoid counting each arrangement twice:

12870 ÷2 = 6435

Therefore, there are 6435 ways to direct the inquiries to any two of the firm's real estate agents.

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Step-by-step explanation:

Just use your calculator

arcsin( -1/2) = -30 degrees   ( or 330 degrees     or    210 degrees)