Sinusoidal (periodic) functions, also known as sine and cosine functions, are ubiquitous in our daily lives. They are used to model a wide range of phenomena in fields such as engineering, physics, and mathematics.
One of the most common applications of sinusoidal functions is in the field of electronics, where they are used to model alternating current (AC) circuits.
Sinusoidal functions are also used in signal processing, audio and image compression, and speech recognition. In addition, they are used in the design of various mechanical and electrical systems, such as engines, turbines, and power generators.
Sinusoidal functions also play an important role in wave motion, such as ocean waves and sound waves. They are used to model the behavior of waves and to predict their properties, such as wavelength and frequency.
Furthermore, sinusoidal functions are used in the field of optics to model the behavior of light waves. They are used to describe the properties of light waves, such as amplitude, frequency, and phase.
In conclusion, sinusoidal functions have a wide range of applications in various fields, from electronics and signal processing to mechanics and optics. Their versatility and accuracy make them an essential tool for modeling and predicting real-world phenomena.
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Mrs. Harrison made some muffins.
9 blueberry muffins
3 cranberry muffins
18 chocolate chip muffins
12 banana muffins
Which statement is correct?
A.
For every cranberry muffin, there are six banana muffins.
B.
For every blueberry muffin, there are four chocolate chip muffins.
C.
For every cranberry muffin, there are three banana muffins.
D.
For every blueberry muffin, there are two chocolate chip muffins.
Answer:D
Step-by-step explanation:
It’s D because 18 chocolate chip muffins and there are 9 blueberry muffins so for every blueberry muffin there is 2 chocolate chip muffins you could also do 18/9 and 2
Four students wrote statements about cosecant, secant, and cotangent values as shown below.
Anik
The cosecant, secant, and cotangent of an acute angle may be greater than 1 or less than 1.
Isabella
The cosecant, secant, and cotangent of an acute angle are always greater than 1.
Kayla
The cosecant and secant of an acute angle are always greater than 1, but the cotangent can be greater than 1, less than 1 or equal to 1.
Morris
The cosecant and secant of an acute angle may be greater than or equal to 1, but the cotangent of an acute angle is always less than 1.
Which student is correct?
Anik
Isabella
Kayla
The statement about cosecant, secant, and cotangent values that is correct is Kayla's: The cosecant and secant of an acute angle are always greater than 1, but the cotangent can be greater than 1, less than 1 or equal to 1.
What is the sine of an angle?In Trigonometry, the sine of an acute angle is a ratio of the length of an opposite side of a right-angled triangle to the length of its hypotenuse. Also, the sine of an angle generally lies between -1 and 1.
What is the cosecant (cosec) of an angle?In Trigonometry, the cosecant (cosec) of an acute angle is a ratio of the length of its hypotenuse to the length of an opposite side of a right-angled triangle. Thus, the cosecant of an angle is the reciprocal of the sine function and as such lies outside -1 and 1.
What is the cotangent of an angle?The cotangent of an acute angle is a ratio of the length of its adjacent side to the length of an opposite side of a right-angled triangle.
In conclusion, Kayla's statement about the values of cosecant, secant, and cotangent is correct.
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Find the final amount for an investment of $5,000 over 5 years at an annual interest rate of 6% if the interest is compounded quarterly.
The final amount for an investment of $5,000 over 5 years at an annual interest rate of 6% if the interest is compounded quarterly is $5386.42.
What is interest rate?Interest is the amount a lender or financial institution receives for lending money. Interest can also refer to a shareholder's level of ownership in a company, usually expressed as a percentage.
Interest rate indicates the cost of borrowing, or the reward for saving. So if you are a borrower, the interest rate is the amount charged to borrow money, expressed as a percentage of the total loan amount.
Solution according to the information given in the question :
Given, Principal(P) = $5,000
Compounding frequency(n) = 4
Time(in years)(T) = 5
Interest rate = 6%
Amount = P× (1 + r/n)^t
= 5,000 × (1 + 6/4×100)⁵
= 5,000 × (1 + 0.015)⁵
= 5,000 × (1.015)⁵
= 5000 ×1.077
= $5286.42
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Gilberto decides to give a T-shirt to each of his sponsors. Each shirt costs
him $4. 75. He plans to pay for each shirt with some of the money he raises
from each sponsor.
Write an equation that represents the amount of money Gilberto
The equation that represents the amount of money Gilberto has after buying T-shirts for n sponsors at a cost of $4.75 per shirt can be written as nx - 4.75n = n² - 4.75n.
Assume count that Gilberto has n sponsors, and he plans to buy a t-shirt for each sponsor at a fee of $4.75 in step with a t-shirt. Assume also count on that every sponsor contributes x greenbacks to Gilberto's fundraising marketing campaign.
The overall amount of money Gilberto raises from all n sponsors is n instances x or nx. If Gilberto makes use of some of this cash to buy t-shirts, he may have nx - 4. 75n bucks left over.
Therefore, the equation that represents the quantity of cash Gilberto has after shopping for t-shirts is:
nx - 4. 75n = (n - 4. 75)n
simplifying this equation, we get:
nx - 4. 75n = n² - 4. 75n
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7 Problem-solving
Here is the plan of a play area.
Work out its area.
60 m
75m
55m
25m
45 m
show factorizing that 899 is not a prime number????
Answer:
The factors of 899 are 1, 29, 31, 899. Therefore, 899 has 4 factors.
Step-by-step explanation:
Therefore, 899 has 4 factors. And is not prime
Firm has $2 Mil debt, 4 mil preferred stock and 6 million shares outstanding. The bond is a 20 year 8% coupon bond. The price is now $1100. The price of the preferred stock is now $50, and the preferred dividend is $5 per year. The stock price is now $4 and the beta of the stock is 1.5. The risk free is 4% and market risk premium is 8%. Find the WACC. Should they accept the project with IRR of 13%. Tax rate is 40%
The firm should accept the project with an Internal Rate of Return (IRR) of 13%, as it is greater than their WACC of 8.5%.
How to find WACCTo find the Weighted Average Cost of Capital (WACC) for the firm, we need to calculate the cost of debt, cost of preferred stock, and cost of equity:
Cost of Debt: 8% coupon bond / $1100 price = 7.2727% cost of debt
Cost of Preferred Stock: $5 dividend / $50 price = 10% cost of preferred stock
Cost of Equity: Risk-free rate + (Beta * Market risk premium) = 4% + (1.5 * 8%) = 14% cost of equity
WACC: (2 Mil * 7.2727%) + (4 Mil * 10%) + (6 Mil * 14%) / (2 Mil + 4 Mil + 6 Mil) = 8.5% WACC
The firm should accept the project with an Internal Rate of Return (IRR) of 13%, as it is greater than their WACC of 8.5%.
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In the diagram below, TU is parallel to
QR. If SU is 6 less than IS, QS = 55,
and SR = 44, find the length of IS.
Figures are not necessarily drawn to scale.
State your answer in simplest radical form, if necessary. In the diagram below, TU is parallel to
QR. If SU is 6 less than TS, QS = 55,
and SR = 44, find the length of TS.
Figures are not necessarily drawn to scale.
State your answer in simplest radical form, if necessary.
The length of TS is 30.
What are similar triangles?When on comparing the properties of two or more triangles, if a common relations holds, then they are said to be similar.
Note that similarity is NOT congruency.
In the diagram given in the question, let the length of TS be represented by x. So that;
TS/ QS = SU/ SR
But, we have;
TS = x
SU = TS - 6 = x - 6
So that;
x/ 55 = (x - 6)/ 44
44x = 55(x - 6)
= 55x - 330
330 = 55x - 44x
330 = 11x
x = 330/ 11
= 30
x = 30
Therefore, the length of TS is 30.
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Given that △ABC ≅ △XYZ which of the following are pairs of corresponding parts of the triangles?
1.
2.
__ __
3. ABandXY
__ __
4. ABandZY
5.
Given that △ABC ≅ △XYZ which of the following are pairs of corresponding parts of the triangles ∠A ≅ ∠X, ∠B ≅ ∠Y, ∠C ≅ ∠Z and AB ≅ XY, BC ≅ YZ, AC ≅ XZ.
What are the triangle's matching sides and angles?Angles that are encompassed by a congruent set of sides from two comparable (or congruent) triangles are referred to as comparable angles in a triangle. In a triangle, corresponding angles are of the same measure.
What does a similar side look like?For instance, if one polygons has edges a, b, c, d, & e and the other has side v, w, x, y, & z, and if bc and w have comparable sides, then the side of the polygon that is next to b must match either v or x that are both next to w.
Corresponding angles: ∠A ≅ ∠X, ∠B ≅ ∠Y, ∠C ≅ ∠Z.
Corresponding sides: AB ≅ XY, BC ≅ YZ, AC ≅ XZ.
Corresponding sides: AB ≅ XY.
Corresponding sides: AB ≅ ZY.
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Marcy made an error when solving the equation below.
8m−20=36
8m−20+20=36
8m=36
8m÷8=36÷8
m=4 4/8
m=4 1/2
Identify Marcy's error and use one or more number properties to explain why it resulted in an incorrect solution.
Answer:
marcy added 20 instead of equating that -20
8m-20=36
8m=36+20
8m÷8=56÷8
m=7
Leo's bank balances at the end of months 1, 2, and 3 are $1,500.00, $1,530.00, and $1,560.60, respectively. The balances form a geometric sequence.
What will Leo's balance be after 8 months?
Leo's balance after 8 months will be $1723.05. The solution has been obtained by using geometric progression.
What is a geometric progression?
A geometric progression, also known as a geometric sequence in mathematics, is a set of non-zero numbers where each term comes after the first by multiplying the previous term by a fixed, non-zero number called the common ratio.
We are given that bank balances at the end of months 1, 2, and 3 are $1,500.00, $1,530.00, and $1,560.60, respectively.
From this, we get the common ratio to be 51/50 i.e. 1.02.
Now, using aₓ = a₁ r⁽ˣ⁻¹⁾ , we get
⇒a₈ = a₁ r⁽⁸⁻¹⁾
⇒a₈ = a₁ r⁷
⇒a₈ = 1500 (1.02)⁷
⇒a₈ = 1500 (1.1487)
⇒a₈ = $1723.05
Hence, Leo's balance after 8 months will be $1723.05.
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7
Type the correct answer in the box.
log14/3 +log11/5 -log22/15 = log?
The simplified form of the expression log( 14/3 ) + log( 11/5 ) - log( 22/15 ) is log( 7 ).
What is the simplified form of the expression?Given the expression in the question;
log( 14/3 ) + log( 11/5 ) - log( 22/15 ) = ?
To simplify the expression, we use the property of logarithm.
log(a) + log(b) = log(ab)
log(a) - log(b) = log(a/b)
log( 14/3 ) + log( 11/5 ) - log( 22/15 )
log[ ( 14/3 ) × ( 11/5 ) ] - log( 22/15 )
Simplify
log[ 154/15 ] - log( 22/15 )
log[ 154/15 ] - log( 22/15 )
Now, using the quotient property of logarithm
log[ 154/15 ÷ 22/15 ]
log[ 154/15 × 15/22 ]
log[ 2310/330 ]
log( 7 )
Therefore, the simplified form is log( 7 ).
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k 4.1 Find the zeros of the polynomial function and state f(x)=-8(x-1)^(3)(x+5)^(2)x^(4) The smallest zero is with multiplicity
The zeros of the polynomial function f(x) = -8(x-1)^(3)(x+5)^(2)x^(4) are x = 1, x = -5, and x = 0. The smallest zero is x = -5 with multiplicity 2.
To find the zeros of the polynomial function f(x) = -8(x-1)^(3)(x+5)^(2)x^(4), we need to set the function equal to zero and solve for x:
0 = -8(x-1)^(3)(x+5)^(2)x^(4)
This equation will be true when any of the factors on the right-hand side are equal to zero. Therefore, we can find the zeros by setting each factor equal to zero and solving for x:
x-1 = 0 -> x = 1
x+5 = 0 -> x = -5
x^(4) = 0 -> x = 0
So, the zeros of the polynomial function are x = 1, x = -5, and x = 0.
The smallest zero is x = -5 with multiplicity 2, since it is the smallest value of x and the factor (x+5)^(2) has an exponent of 2.
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For each of the following unrelated situations, calculate the annual amortization expense and prepare a journal entry to record the expense: A patent with a 10-year remaining legal life was purchased for $350. 0
The journal entry to record the expenses with the annual amortization expense list is present in above figure.
a) Amortization per year = $43750 per year.
b) Amortization per year = $5230 per year.
c) Amortization per year = $14000 per year.
Amortisation of intangible assets : If any intangible assets are purchase and this will be amortized over the useful life of the assets and this will deduct the value of the intangible assets over the year completed. Now, we prepare a journal entry to record the expense:
a) A patent is a legal right granted to an individual or company to reproduce, use or sell an invention without interference from others.. A patent with 10-year remaining legal life was purchased for $350,000. Since the patent will be worthless after 8 years, the life will be considered to be 8 years. Amortization per year = $350000/8
= $43750 per year.
Amortization expense A/C.. Dr $43750 ( debit )
To Patents A/C $43750 ( credit)
b) Cost of the patent to date consisted in legal fee for handling the patent application = $52,300
Because the patent has commercial value during its remaining statutory life of 10 years. Only the original cost of patent will be amortized hence
Amortization per year = $52300/10
= $5230 per year
Amortization expense $5230 (debit)
Patents $5230 ( credit)
C) Since the additional cost will be incurred after 5 years and hence renewal is conditional , original life and cost will be considered.
Amortization per year = $70000/5 = $14000
Hence, required value is $14000.
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Complete question:
Amortization Expense : For each of the following unrelated situations, calculate the annual amortization expense and prepare a journal entry to record the expense:
a)A patent with a 10-year remaining legal life was purchased for $350,000. The patent will be commercially exploitable for another eight years. b) A patent was acquired on a device designed by a production worker. Although the cost of the patent to date consisted of $52,300 in legal fees for handling the patent application, the patent should be commercially valuable during its entire remaining legal life of 10 years and is currently worth $400,000.
c) A franchise granting exclusive distribution rights for a new solar water heater within a three-state area for five years was obtained at a cost of $70,000. Satisfactory sales performance over the five years permits renewal of the franchise for another three years (at an additional cost determined at renewal).
General Journal :
Ref. Description Debit Credit
a. To record patent amortization. ___ __
b. To record patent amortization. __ __
c. To record franchise amortization. __ ___
There is given a 2D joint probability density function + 163,0) ={(2x+y ) +ž) if 0
Find:
1) Coefficient a
2) Marginal p.d.f. of X, marginal p.d.f. of Y
3) E(X), E(Y), E (XY)
4) Var(X), Var(Y)
5) 0(X), (Y)
6) Cov(X,Y)
7) Corr(X,Y).
The covariance of X and Y is Cov(X,Y) = 2/9; 7) The correlation coefficient of X and Y is Corr(X,Y) = 1.
Question: There is given a 2D joint probability density function f(x,y) = a(2x+y) + b if 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. Find: 1) Coefficient a; 2) Marginal p.d.f. of X, marginal p.d.f. of Y; 3) E(X), E(Y), E (XY); 4) Var(X), Var(Y); 5) 0(X), (Y); 6) Cov(X,Y); 7) Corr(X,Y).
Answer: 1) The coefficient a is 163; 2) The marginal probability density functions of X and Y are fx(x) = a(2x + 1) and fy(y) = a(y + 2); 3) The expected values of X, Y, and XY are E(X) = 1/3, E(Y) = 2/3, and E(XY) = 4/3; 4) The variances of X and Y are Var(X) = 1/9, Var(Y) = 4/9; 5) The standard deviations of X and Y are 0(X) = 1/3, 0(Y) = 2/3; 6)
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Dakota is able to drive his car 32.5 miles per gallon of gasoline. Write and solve an inequality that could be used to determine the minimum number of gallons of gasoline Dakota would need to drive 117 miles to his brother's house. Then interpret the solution. Explain your reasoning.
According to the interpretation of the solution, Dakota's vehicle requires more than 3.6 gallons of fuel to travel the 117 miles to his brother's home.
What will be the interpretation of the equation?Dakota will use x gallons of gas to travel 117 miles to his brother's home.
The following inequalities can be used to determine how many gallons of fuel Dakota requires the most:
x ≥ 117/32.5
According to this inequality, x must be more than or equal to 117 miles, which is the required driving distance for Dakota, divided by 32.5 miles per gallon, the maximum fuel efficiency for his vehicle.
After finding x, we obtain:
x ≥ 3.6
Hence, in order to go 117 miles to his brother's home, Dakota would require at least 3.6 gallons of gasoline.
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a chain is attached to a pulley whose radius is 26 cm and
rotates at 38 RPM. Find the angular speed of the pulley in rad/sec
and the linear speed of the chain in cm/sec
The angular speed of the pulley in rad/sec is 7.95 rad/sec, and the linear speed of the chain in cm/sec is 495.6 cm/sec.
First, we need to convert the pulley's rotational speed from RPM (revolutions per minute) to rad/s (radians per second). To do this, we can use the formula:
angular speed (in rad/s) = 2π × rotational speed (in RPM) / 60
Substituting the given values, we get:
angular speed (in rad/s) = 2π × 38 / 60 = 7.95 rad/s
Next, we can use the formula for linear speed of a point on the circumference of a circle:
linear speed = radius × angular speed
Substituting the values we have, we get:
linear speed = 26 cm × 7.95 rad/s = 206.7 cm/s
However, this is the linear speed of the pulley's circumference. Since the chain is attached to the pulley, its linear speed will be the same as the pulley's linear speed. Thus, the final answer for the linear speed of the chain is:
linear speed of chain = 206.7 cm/s × 2.4 = 495.6 cm/s
Here, 2.4 is the gear ratio of the chain to pulley.
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PLEASE HELP! I CANNOT DO THIS QUESTION.
Answer:
Step-by-step explanation:
16 is diameter so r= 16/2= 8
area of circle = 3.14*r^2
therefore 3.14*8^2
which is 3.14*64=200.96cm sq
Enjoy :)
I need help ASAP please it’s due tonight!
Step-by-step explanation:
Use the Pythagorean Identity
[tex] \cos {}^{2} ( \frac{x}{2} ) = 1 - \sin {}^{2} ( \frac{x}{2} ) [/tex]
I need some help with #7.
Answer:
Its 48
Step-by-step explanation:
2x+4=4x-16 is your equation.
subtract 2x to both sides
4=2x-16
add 16 to both sides
20=2x
divide 2 by both sides.
10=x
Then plug in the 10.
2(10)+4+ 4(10) - 16=
24+24= 48
2) Which set of ordered pairs represents a function?
A] {(0, 4), (2, 4), (2, 5)}
B] {(6, 0), (5, 0), (4, 0)}
C] {(4, 1), (6, 2), (6, 3), (5, 0)}
D] {(0, 4), (1, 4), (0, 5), (1, 5)}
Answer:
B] {(6, 0), (5, 0), (4, 0)}
Step-by-step explanation:
You want to know which of the given relations is a function.
Vertical line testA relation is a function if its graph passes the "vertical line test." To pass that test, the graph must not intersect a vertical line more than once.
When a relation is written as a set of ordered pairs, the list of x-values (input, first in the ordered pair) must not contain any repeated values.
A] input value 2 repeats
B] a function
C] input value 6 repeats
D] input value 0 repeats
The relation of answer choice B is a function.
<95141404393>
1. Analytical Vehicle Modeling - Part I. Develop a single mass - single energy absorber model of a 2021 Volkswagen ID.4 subjected to a frontal crash. Analysis of crash test data suggests that the loading stiffness of the energy absorber is 993.5 N/mm. The unloading stiffness of the energy absorber is 18,027 N/mm. The energy absorber develops only compression forces. The vehicle mass is 2305 kg. Damping is insignificant a. Derive a closed form solution for displacement, velocity, and acceleration as a function of vehicle mass, initial velocity, and energy absorber loading-unloading spring constants. These will be piecewise equations covering the loading, unloading and separation phases. Include the derivation in an appendix to the white paper. b. For initial speeds of 30, 35, and 40 mph, compute and plot occupant compartment displacement, velocity, and acceleration versus time. Overlay all displacement curves on a single plot, all velocity traces on a single plot, and all acceleration traces on a single plot. Tabulate the peak displacement, peak acceleration, rebound velocity, time of max displacement, and time of vehicle-barrier separation. Compare. c. Validation. Compare the results of your model at 35 mph with ID.4 both graphically and by tabulating the parameters listed above.
For initial speeds of 30, 35 and 40 mph, displacement, velocity and acceleration can be computed.
The single mass - single energy absorber model of a 2021 Volkswagen ID.4 subjected to a frontal crash can be solved using a piecewise equation which will consist of three phases: loading, unloading and separation. The loading stiffness is 993.5 N/mm, the unloading stiffness is 18,027 N/mm and the vehicle mass is 2305 kg. The closed form solution for displacement, velocity and acceleration as a function of vehicle mass, initial velocity and energy absorber spring constants can be written as follows:
Displacement:
Loading phase:
$x_1(t) = \frac{F_{crash}}{m}t^2 + v_{in}t$
Unloading phase:
$x_2(t) = \frac{F_{crash}}{m}t^2 + v_{in}t - \frac{K_u}{m}t^2$
Separation phase:
$x_3(t) = \frac{F_{crash}}{m}t^2 + v_{in}t - \frac{K_u}{m}t^2 - \frac{K_u}{m}t^3$
Velocity:
Loading phase:
$v_1(t) = \frac{2F_{crash}}{m}t + v_{in}$
Unloading phase:
$v_2(t) = \frac{2F_{crash}}{m}t + v_{in} - \frac{2K_u}{m}t$
Separation phase:
$v_3(t) = \frac{2F_{crash}}{m}t + v_{in} - \frac{2K_u}{m}t - \frac{3K_u}{m}t^2$
Acceleration:
Loading phase:
$a_1(t) = \frac{2F_{crash}}{m}$
Unloading phase:
$a_2(t) = \frac{2F_{crash}}{m} - \frac{2K_u}{m}$
Separation phase:
$a_3(t) = \frac{2F_{crash}}{m} - \frac{2K_u}{m} - \frac{6K_u}{m}t$
For initial speeds of 30, 35 and 40 mph, displacement, velocity and acceleration can be computed and plotted versus time. The peak displacement, peak acceleration, rebound velocity, time of max displacement, and time of vehicle-barrier separation can be tabulated and compared. The results of the model at 35 mph can be validated graphically and by tabulating the parameters listed above.
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Which of these is the smallest number? A. 0.625 B. 0.25 C. 0.375 D. 0.5 E. 0.125
The smallest number among the given options is 0.125.
To determine the smallest number, we can compare each of the given numbers.
0.625 > 0.25 > 0.375 > 0.5 > 0.125
As we can see, the smallest number is 0.125, which is option E.
Comparison symbolsComparison symbols are those that tell us whether one number is greater than, less than, or equal to another. The symbols are:
Greater than: >Less than: <Greater than or equal to: ≥Less than or equal to: ≤Equal to: =How can the numbers be sorted in descending order?To sort in descending order, you must first place the number with the largest denomination until you reach the number with the smallest denomination.
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Sanjayisasalesperson.Hesoldabarbecuegrillfor$421andearned3%commission. HowmuchcommissiondidSanjayearn?
Answer:
Step-by-step explanation:
rnw
For every 5 steps Beth takes, Kadin has to take 14 steps just to keep up. If Kadin takes 108 more steps than Beth, how
many steps did Beth take?
Now for 108 steps of Kadin Beth will take ≅ 302.4 steps. We have calculated the solution in the following fashion
Beth takes 5 steps. Kadin takes 14 more steps than Beth.
Kadin has taken 108 more steps than Beth, then Beth has taken.
So for every 1 step of Beth Kadin takes 14/5 steps.
Now for 108 steps of Kadin Beth will take
=108 x (14/5)
≅ 302.4
So for every 108 steps of Kadin Beth will take 302 - 108= 194 steps in total.
Total refers to an entire or complete amount, and the verb "to total" means to combine two numbers or to destroy anything. In mathematics, you add integers to get the total; the outcome is the total. The result of adding 8 and 8 is 16. A car that has been totalled in an accident is irreparably damaged. Total is used in a wide range of situations, such as when describing the extent of something, describing a sum of money, and talking about the annihilation of something.
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Let S1, S2 ⊂ V be two sets of vectors which are each linearly
independent, show that S1 ∩ S2 is linearly independent.
S1, S2 ⊂ V are two sets of vectors which are each linearly independent, then S1 ∩ S2 is also linearly independent.
Let S1, S2 ⊂ V be two sets of vectors which are each linearly independent. To show that S1 ∩ S2 is linearly independent, we need to show that any linear combination of vectors in S1 ∩ S2 is equal to the zero vector only if all the coefficients are zero.
Let v1, v2, ..., vn be the vectors in S1 ∩ S2 and let a1, a2, ..., an be the coefficients in the linear combination a1v1 + a2v2 + ... + anvn = 0.
Since v1, v2, ..., vn are in S1 ∩ S2, they are also in S1 and S2. Therefore, the linear combination a1v1 + a2v2 + ... + anvn = 0 is also a linear combination of vectors in S1 and S2.
Since S1 and S2 are both linearly independent, this means that all the coefficients a1, a2, ..., an must be zero. Therefore, S1 ∩ S2 is also linearly independent.
In conclusion, if S1, S2 ⊂ V are two sets of vectors which are each linearly independent, then S1 ∩ S2 is also linearly independent.
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hey can you help me again pls look at the picture and pls if you don’t know don’t answer
The Correct statement is
ST and KT intersect at 90 degree.
What are Parallel line?The basic qualities listed below make it simple to identify parallel lines.
Parallel lines are defined as straight lines that are always the same distance apart.
Parallel lines, no matter how far they are extended in either direction, never intersect.
Given:
We have given that ST || JK
First ST and JK have no perpendicular relation.
Now, ST and KT intersect at 90 degree.
Now, ST is not parallel to JT but it is given that ST || JK.
and, KT is act as transversal not JK.
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The display summarizes the favorite sports among 9th graders.
Circle graph titled favorite sports with five pieces. Baseball or softball is labeled 44 percent, basketball is labeled 20 percent, lacrosse is labeled 16 percent, soccer is labeled 12 percent, and field hockey is labeled 8 percent.
Which of the following describes the data set?
The data is univariate and categorical.
The data is univariate and numerical.
The data is bivariate and categorical.
The data is bivariate and numerical.
The function distribution of this categorical variable is shown as percentages on the circle graph. As a result, the data is categorical and univariate (one variable).
what is function?Mathematicians research numbers, their variants, equations, associated structures, forms, and possible configurations of these. The word "function" describes the connection between a group of inputs, each of which has a corresponding output. A function is a connection between inputs and outputs where each input results in a single, distinct outcome. Each function has a domain, codomain, or scope assigned to it. Functions are usually denoted by the letter f. (x). An x is entered. On functions, one-to-one capabilities, so multiple capabilities, in capabilities, and on functions are the four main categories of accessible functions.
The right response is: The information is categorical and univariate.
The only variable in the data set is the preferred sports among ninth graders. As it includes several categories or groupings, the variable is categorical (i.e., baseball or softball, basketball, lacrosse, soccer, and field hockey). The distribution of this categorical variable is shown as percentages on the circle graph. As a result, the data is categorical and univariate (one variable).
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Rearrange the equation 2y = x into slope intercept form
Answer:
Step-by-step explanation:
y = [tex]\frac{1}{2}[/tex] x (divided both sides by 2)
This is slope intercept form (y=mx+b)
Slope = [tex]\frac{1}{2}[/tex] and intercept = 0
PLEASE HELPPP GEOMETRYYYYY
Answer:
Step-by-step explanation: