The final function for slinky displacement is: 24 sin(t/2 - /2) d(t). This offers the displacement in inches as a function of time in seconds.
How to Solve the Problem?A sinusoidal function of the form: can be used to describe the slinky's displacement.
A sin(t + ) = d(t).
where A is the greatest displacement, is the angular frequency (2 divided by the period), and is the phase angle (starting phase).
We know the slinky's greatest displacement (amplitude) occurs at t=0, thus we have:
24 inches = d(0) = A sin()
We also know that the period is T=2 seconds because the time for one oscillation (i.e., one complete cycle) is 2 seconds. As a result, the angular frequency is:
ω = 2π / T = π radians/second
The phase angle can be calculated using the fact that the slinky is at its equilibrium position at t=T/4=0.5 seconds. At this time, the sine function's argument is:
= 2 / T = radians per second
The phase angle can be calculated using the fact that the slinky is at its equilibrium position (zero displacement) at t=T/4=0.5 seconds. At this time, the sine function's argument is:
ωt + φ = π/2
When we substitute the known values, we get:
π/2 + φ = 0.5π
φ = -π/2
As a result, the slinky's displacement function is:
A sin(t/2 - /2) = d(t).
We may utilize the information that the amplitude is 24 inches to calculate A:
A = |24| = 24
As a result, the final function for slinky displacement is:
24 sin(t/2 - /2) d(t)
This offers the displacement in inches as a function of time in seconds.
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Mrs. Garza is buying boxes of crayons for her classroom. The table below shows the
number of crayons she can buy.
Which equation will help Mrs. Garza determine the number of crayons she will get with 7 boxes?
A N=16+B
B. N-=16-B
C. N=16B
D. N=16/B
Factor the polynomial completely. If the polynomial is prime, so state.
x2 - x - 35
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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Read the paragraph and choose a sentence that describes it best. Because of the association with TERFs, many feminists have stopped identifying with radical feminism. Though some of their views may be similar to the original tenets of radical feminism, many feminists no longer associate with the term because they are trans-inclusive. TERF is not just transphobic feminism; it is a violent international movement that often compromises its feminist stances to partner with conservatives, with a goal to endanger and get rid of trans people, especially transfeminine people.
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:
The paragraph discusses the impact of TERFs on radical feminism and their transphobic and violent agenda.The paragraph analyzes why many feminists have distanced themselves from radical feminism due to TERFs and how TERFs are not true feminists but transphobes.Need help on question 20. Plsss help
The calculated distance between the tree and the zip line is 9.21 units
Evaluating the distance between the tree and the zip lineFrom 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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Which expression is equivalent to 5^3 × 10^-2?
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 mean age of students in a Large math class is less than 30. A simple random sample of the students has a mean age of 29.3
Choose the correct answer
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.
How to get the correct optionWe 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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This question has two parts. First, answer Part A. Then, answer Part B.
Part A
Mrs. Miller is ordering an L-shaped countertop with the dimensions shown for her kitchen.
34
9-ft
3-A
15 ft
3 ft
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.
What is surface area?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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Using the graphing Method, find the value of x in the system of equations y=4x-1 and y=-x+4
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.
Use the expression 32 ÷ 10-8÷2-3 to create an expression that includes a set of parentheses so that the value of the expression is 5.
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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If y varies directly as x, and y= 2 when x = 3, find y when x = 1.
a. y = 2x; y(1)=2
C.
b.
3
A
B
C
D
(1)
2
d.
4
3; P(1) - 4
3
-
2
y = x; y(1) -
3
Please select the best answer from the choices provided
2/
3
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.
how many teams completed the escape room in 45 minutes or less
The answer to the question about how many teams completed the escape room in 45 minutes or less is 6.
What is a Dot Plot?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
How did we find this answer?If we count the amount of dots on 45 and before 45 and add them up, the answer is 6
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A man earned wages of 38,800 received 1600 in interest from savings account and contributed to 3200 to tax deferred retirement plan he was entitled to personal exemption of 2900 and had had deductions totaling 4950 find his gross income adjust gross income and taxable income
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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Find value of X and BD
Look at picture
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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The list below gives the number of people who made the trip for a selection of nine summer days 2756 64 36 40 29 2756 and 30 find the range of the data set
Answer:
The range is 37
Step-by-step explanation:
highest - lowest = range
64-27= 37
Hope it helped! :)
CAN SOMEONE HELP WITH THIS QUESTION?
Sin-1 (-1/2) exact value
Step-by-step explanation:
Just use your calculator
arcsin( -1/2) = -30 degrees ( or 330 degrees or 210 degrees)
Guadalupe's credit card has an APR of 23%, calculated on the previous monthly balance, and a minimum payment of 2%, starting the month after the first purchase. Her credit card record for the last 7 months is shown in the table below. End of month 2 3 5 6 7 Previous balance $0.00 $900.00 $899.25 $898.50 $897.75 $897.00 $896 26 New charges $900.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 Payment Finance Principal received charges paid $0.00 $0.00 $0.00 $18.00 $17.99 $17.97 $17.96 $17.94 $17.93 How is the new balance calculated? $17.25 $17.24 $17.22 $17.21 $17.19 $17.18 $0.75 $0.75 $0.75 $0.75 $0.75 $0.75 New balance $900.00 $899.25 $898.50 $897.75 $897.00 $896.26 $895.51
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
-(4-8)+(-3-7)−(−1+6) + (−2+5)=
Answer: -8
Step-by-step explanation:
Simple math. Your welcome glad to help
I know I asked this before but i need help asap
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!
4. Which set of data could be represented by the box-and-whisker plot? (1 point)
O0, 3, 9, 9, 11, 14, 15, 16, 16, 18, 19, 25, 25, 28, 28, 30
O2, 3, 4, 7, 13, 15, 15, 15, 16, 17, 20, 22, 25, 25, 26, 28
O2, 6, 7, 8, 10, 11, 12, 14, 18, 20, 22, 24, 26, 27, 27, 28
O2, 2, 7, 10, 10, 11, 13, 15, 17, 20, 20, 24, 26, 27, 27, 28
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.
What is a box-and-whisker plot?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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In this figure, ∠1 and ∠2 are located on a line.
Let m∠1=x° and m∠2=(4/5 x)°.
What is the value of x?
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
Please see the attached
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.
What are the ratios?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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(-6,-4), (0, -4), and (2,-4)
What is the equation of this line?
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.
What is the area of sector GHJ , given that θ=pi/4 radians. Express your answer in terms of pi and as a decimal rounded to the nearest tenth. Show your work.
The area of sector GHJ is:
3.125π cm² (in terms of pi)
9.8 cm² (As a decimal rounded to the nearest tenth)
How to find the area of sector GHJ?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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what is the area of a parallelogram if base is 1 1/4 mi and the heigh is 3/4 mi.
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
A group of students worked out the mean and range of their ages. The mean was 12 years and 3 months. The range was 2 years and 7 months. a) What was the mean of the ages of the same group of students exactly one year later? b) What was the range of their ages exactly one year later? Write a sentence to explain each of your answers.
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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C & J Realty has received 16 inquiries from prospective home buyers. In how many ways can the inquiries be directed to any two of the firm's real estate agents if each agent handles eight inquiries?
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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ALPHABET Which of the following letters
contain at least one acute angle? Which
contain vertical angles? Which contain
adjacent angles?
A E L X
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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Solve the quadratic equation by completing the square.
2
x² - 4x-10=0
First, choose the appropriate form and fill in the blanks with the correct num
Then, solve the equation. Round your answer to the nearest hundredth.
If there is more than one solution, separate them with commas.
A bag contains 605 red, 342 blue, 518 green, and 535 yellow tokens. A token is selected at random and then replaced.this is performed 2,000 times
The probability of randomly selecting a red token would be 0. 30.
How to find the probability ?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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