m² × m² is equal to m⁴.
w³ × w² is equal to w⁵.
5k³ × 4k⁴ × k is equal to 20k⁸.
The length of each side of the square is 9x.
A simplification of the expression 28x³ ÷ 4x is 7x².
How to calculate the area of a rectangle?In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:
A = LB
Where:
A represent the area of a rectangle.B represent the breadth of a rectangle.L represent the length of a rectangle.By substituting the given parameters into the formula for the area of a rectangle, we have the following;
Area of rectangle = (27x) × (3x)
Area of rectangle = 81x²
Note: Area of square = Area of rectangle
Area of square = (side length)²
81x² = (side length)²
Side length = √(81x²)
Side length = 9x
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Using the simple interest formula, find the amount earned after 4 years with a present value of $600 and an APR of 5%. Verify that you get the same answer as in the table.
The simple interest after 4 years with the given principal and rate is $120.
Given that, principal =$600, rate=5% and time=4 years.
We know that, simple interest=(Principal×Rate×Time)/100.
Simple interest = (600×5×4)/100
= $120
Therefore, the simple interest after 4 years with the given principal and rate is $120.
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On a coordinate plane, point A is (negative 2, 3), point B is (2, 4), and point C is (0, negative 1). The points are connected with lines. Use the graph to find the coordinates of each vertex in triangle ABC. is the coordinate of Point A. is the coordinate of Point B. is the coordinate of Point C.
math hw for tonight
help solve this problem! Thank you!
ap cal bc
The position of an object is determined as (¹/₃ ln |1 + t³| + 2)i + (- ¹/₂cos(2t) + 3 )j.
None of above is the correct answer.
What is the particle's position?The position of an object is defined as the product of velocity of the object and the time of motion of the object.
So to obtain the position of the particle, we will integrate the velocity of the particle as follows;
The velocity is given as;
v(t) = t²i/(1 + t³) + sin 2t j
Integrate i component as;
Let u = 1 + t³
du/dt = 3t².
dt = du / (3t²)
∫ t²/(1 + t³) dt =∫ (1/u) x (t²/3t²) du
= (1/3) ∫ (1/u) du
= (1/3) ln |u| + C
= (1/3) ln|1 + t³| + C
Integrate j component as follows;
∫ sin(2t) dt = - ¹/₂cos(2t) + C
∫ v(t) dt = (1/3) ln|1 + t³|)i - ¹/₂cos(2t)j
So finally, we add the initial position of 2i + 3j, as follows;
x = (¹/₃ ln |1 + t³| + 2)i + (- ¹/₂cos(2t) + 3 )j
So none of the options matches this solution, the closet is B.
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A car costing $34,000 is leased for $473 monthly over 5 years with a $2,420 down payment. The car’s residual value is estimated to be $16,400. If the car is purchased with a $5,000 down payment, the monthly loan payments will be $623 for 60 months. Calculate the costs of leasing this car and buying this car. Is buying or leasing less expensive and by how much less?
The cost of leasing the car is $28,780 and the cost of buying the car is $42,380.
Buying the car is more expensive than leasing by $13,600 over the 5-year period.
We have,
To calculate the cost of leasing the car, we first need to determine the total amount paid over the lease term:
= (Monthly payment x Number of months) + Down payment
= ($473 x 60) + $2,420
= $28,780
To determine the cost of buying the car, we first need to calculate the total loan amount:
= Cost of car - Down payment + Residual value
= $34,000 - $5,000 + $16,400
= $45,400
Now,
Total loan cost = (Monthly payment x Number of months) + Down payment
Total loan cost = ($623 x 60) + $5,000
Total loan cost = $42,380
So,
The cost of leasing the car is $28,780 and the cost of buying the car is $42,380.
To determine which option is less expensive, we can subtract the cost of leasing from the cost of buying:
Cost of buying - Cost of leasing = $42,380 - $28,780
Cost of buying - Cost of leasing = $13,600
So,
Buying the car is more expensive than leasing by $13,600 over the 5-year period.
Thus,
The cost of leasing the car is $28,780 and the cost of buying the car is $42,380.
Buying the car is more expensive than leasing by $13,600 over the 5-year period.
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Let u = 2i - 3j, and w=-i-6j. Find ||w - ul.
w-ul = (Type an exact answer, using radicals as needed.)
The value of ||w - u || = 3 sqrt 2
How to solveGiven:
u = 2i - 3j
w = - i - 6j
w - u = ( - i - 2i ) + ( - 6j - (-3j))
w - u = - 3i - 3j
|| w - u || = sqrt [ - 3^2 + - 3^2 ]
||w - u || = 3 sqrt 2
The concept of a radical in mathematics refers to the symbolic representation (√) of finding the roots of an expression or a number.
The widely known and frequently used kind is the square root (√), which reveals a positive value that, when multiplied by itself at once, generates the radicand.
Other forms may include cube roots (∛) or fourth roots (∜). To simplify radicals, one can factor out those factors within it that result in perfect cubes or squares from their corresponding radicands.
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The relative locations of Marilyn's house, Bobby's house, and Kimberly's house are shown in the figure.
What is the distance from Kimberly's house to Marilyn's house?
Enter your answer in the box. Round your final answer to the nearest whole number.
The distance from Kimberly's house to Marilyn's house = 12.04 mi
Let us assume that A be the angle at Kimberly's house, B represents the angle at Bobby's house and S represents the angle at Marilyn's house.
Let a, b, c represents the sides(distance between two houses) opposite to angles A, B and C.
Using sine rule to triangle ABC,
sin A/a = sin B/b = sin C/c
Consider equation,
sin A/a = sin B/b
sin(63°) / 14 = sin(50°) / b
b = (0.766 × 14) / 0.891
b = 12.04 mi
Thus, the required distance between Kimberly's house and Marilyn's house = 12.04 mi
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Find x round your answer to nearest tenth of a deggre triangle that had 16 20 and x
In the given right triangle, the angle opposite the side of length 16 units has a measure of 49.6 degrees.
We have a right triangle with an unknown angle θ (measured in degrees), the opposite side length of 16 units, and a hypotenuse length of 21 units. We're given the formula for calculating the sine of an angle:
sin(θ) = opposite / hypotenuse
By substituting the values we know, we get:
sin(x) = 16 / 21
x = sin⁻¹(16 / 21)
x ≈ 49.6°
Therefore, in the given right triangle, the angle opposite the side of length 16 units has a measure of 49.6 degrees.
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You invest $1500 in an account at interest rate r, compounded continuously.Find the time required for the amount to double and triple.(Round your answer to two decimal places). r=0.0355
The time required for the amount to double and triple are 19.53 and 30.95 respectively.
How to find the time required for the amount to double and triple?In Mathematics and Financial accounting, continuous compounding interest can be determined or calculated by using this mathematical equation (formula):
[tex]f(t) = P_{0}e^{rt}[/tex]
Where:
f(t) represents the future value.P₀ represents the principal.r represents the interest rate.t represents the time measured in years.Based on the information provided above, we can reasonably infer and logically deduce that a function for the time required for the amount to double is given by;
[tex]2(1500) = 1500e^{0.0355t}\\\\3000= 1500e^{0.0355t}\\\\2=e^{0.0355t}[/tex]
Taking the natural log (ln) of both sides of the equation, we have:
0.0355t = ln(2)
Time, t = 19.53
Similarly, a function for the time required for the amount to triple is given by;
[tex]3(1500) = 1500e^{0.0355t}\\\\4500= 1500e^{0.0355t}\\\\3=e^{0.0355t}[/tex]
Time, t = 30.95
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A cargo container is 25 ft long, 10 ft tall, and 12 ft wide. Find its volume in cubic yards. Round to
the nearest hundredth.
Answer: ________yd3
Answer:
3,000
Step-by-step explanation:
v = lwh
v = (25)(10)(12)
v = 3000
Helping in the name of Jesus.
math hw for tonight
help solve this problem! Thank you!
ap cal bc
The vector-valued function is continuous at t=2,
are
r(t) = 3/ cos t-1(i) + sin t (j)r(t) = e^ t (i) + cos t (j)What is a vector-valued function?A vector-valued function, is described as a mathematical function of one or more variables whose range is a set of multidimensional vectors or infinite-dimensional vectors.
We are required to check if the limit of the function as t approaches 2 exists and is equal to the value of the function at t=2, in order to determine if the vector-valued function is continuous at t=2.
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Let A={a,b,k,s,u} and B={y,t,p,l,m,a}, find the least possible universal set for A and B
Answer:
The universal set is the set of all elements that can possibly belong to either set A or set B. To find the least possible universal set for A and B, we need to combine all the elements from both sets while avoiding duplicates.
The combined set of A and B is {a, b, k, s, u, y, t, p, l, m}. Therefore, this is the least possible universal set for A and B.
Step-by-step explanation:
The universal set is the set of all elements that can possibly belong to either set A or set B. To find the least possible universal set for A and B, we need to combine all the elements from both sets while avoiding duplicates.
The combined set of A and B is {a, b, k, s, u, y, t, p, l, m}. Therefore, this is the least possible universal set for A and B.
Find the line parallel to y = -9x-1 that includes the point (2, -3). y- [?] = [?] ( x - [?])
Answer:
y + 3 = - 9(x - 2)
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 9x - 1 ← is in slope- intercept form
with slope m = - 9
• Parallel lines have equal slopes
then slope of parallel line is m = - 9
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
m = - 9 and (a, b ) = (2, - 3 ) , then
y - (- 3) = - 9(x - 2) , that is
y + 3 = - 9(x - 2)
Write the mixed number as a percent.
1 9/10
190 percent. you can find this by dividing the numerator by denominater
Answer:
190%
Step-by-step explanation:
19/10 = 19 ÷ 10 = 1.9
1.9 x 100 = 190%
The Sky Train from the terminal to the rental car and long term parking center is supposed to arrive every 8 minutes. The waiting times for the train are known to follow a uniform distribution.
What is the probability of waiting less than 2 minutes or more than 6 minutes?
The probability of waiting less than 2 minutes or more than 6 minutes for the Sky Train is 0.5 or 50%.
To calculate the probability of waiting less than 2 minutes or more than 6 minutes for the Sky Train from the terminal to the rental car and long term parking center, we need to find the probability of each event separately and then add them together.
The probability of waiting less than 2 minutes can be calculated as the ratio of the time interval from 0 to 2 minutes (2 minutes) to the total time interval of 8 minutes;
P(waiting less than 2 minutes) = (2 minutes) / (8 minutes) = 0.25
The probability of waiting more than 6 minutes can be calculated as the ratio of the time interval from 6 to 8 minutes (2 minutes) to the total time interval of 8 minutes;
P(waiting more than 6 minutes) = (2 minutes) / (8 minutes) = 0.25
Now, to find the probability of waiting less than 2 minutes or more than 6 minutes, we can add the two probabilities together;
P(waiting less than 2 minutes or more than 6 minutes) = P(waiting less than 2 minutes) + P(waiting more than 6 minutes)
= 0.25 + 0.25
= 0.5
Therefore, the probability of waiting less than 2 minutes or more than 6 minutes will be 0.5 or 50%.
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A store specializing in mountain bikes is to open in one of two malls. If the first mall is selected, the store anticipates a yearly profit of $1,050,000 if successful and a yearly loss of $350,000 otherwise. The probability of success is 2 If the second mall is selected, it is estimated that the yearly profit will be $700.000 if successful; otherwise, the annual loss will be $210.000. The probability of success at the second mall is
_ Complete parts (a) through (c) below
a. What is the expected profit for the first mall?
The expected profit for the first mall is $1,750,000
Given data ,
Let the probability be represented as A and B
Now , For Event A:
Probability of success at the first mall (P(A)) = 2 (given)
Profit if successful (P(A) * Profit | Success) = 2 * $1,050,000 = $2,100,000
Loss if unsuccessful (Loss | Failure) = -$350,000
For Event B:
Probability of success at the second mall (P(B)) = unknown (to be calculated)
Profit if successful (P(B) * Profit | Success) = P(B) * $700,000
Loss if unsuccessful (Loss | Failure) = -$210,000
Expected Profit for Event A = P(A) * Profit | Success + (1 - P(A)) * Loss | Failure
Expected Profit for Event A = 2 * $1,050,000 + (1 - 2) * -$350,000
Expected Profit for Event A = $2,100,000 - $350,000
Expected Profit for Event A = $ 1,750,000
Hence , the profit is $ 1,750,000
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Need help??? With this question
I don’t think I’m solving it correctly.
Answer:
116
Step-by-step explanation:
A group of 15 athletes participated in a golf competition. Their scores are below:
Score (points) 1 2 3 4 5
Number of Athletes 1 2 3 4 5
Would a dot plot or a histogram best represent the data presented here? Why?
Histogram, because a large number of scores are reported as ranges
Histogram, because a small number of scores are reported individually
Dot plot, because a large number of scores are reported as ranges
Dot plot, because a small number of scores are reported individually
Answer:
D
Step-by-step explanation:
A dot plot would be the best representation for this data, because the number of scores reported individually is small and a dot plot is ideal for displaying individual data points.
At a local college, 82 of the male students are smokers and 328 are non-smokers. Of the female students, 148 are smokers and 252 are non-smokers. A male student and a female student from the college are randomly selected for a survey. What is the probability that both are smokers?
What is the equation of the line in slope-intercept form?
Answer:
The answer is the second choice.
Step-by-step explanation:
The slope is rise over run, which is 3/-1, which is -3, which goes before the x. The line hits the y axis at -1, so it is -3x–1
Hi is anyone good at math is so can somone please help me with thisI'm struggling with it!!
The variables to the parallelogram OPQR are;
1. coordinates of points M is (1, 2.5)
2. The length of PQ is 4
3. The length of QR is 5.4
4. The length of PM is 3.9
5. The length of OM is 2.7
6. The perimeter of the parallelogram OPQR is approximately 18.8
7. if m ∠QMR = 120° m ∠ QMP = 60°
8. If m ∠ QRO = 80° m ∠ROP = 100°
How do we calculate for every listed sides of the of parallelogram OPQR?
To calculate for every listed length of parallelogram OPQR it will be helpful to list all the coordinate for this diagram and they are;
O (0, 0)
p (-2, 5)
R (4, 0)
Q (2, 5)
To find for M, we could just get it from the diagram by looking at the points for x and then y. This is (1, 2.5). You can also calculate it like this
Mx = (Px + Rx)/2 = (-2 + 4)/ 2 = 2/2 = 1
My = (Py + Ry)/2 = ( 5 + 0)/2 = 2.5
To calculate for the length of any side, we say
LPQ = √(Qx -Px)² + (Qy - Py)² = √(2 - -2)² + (5-5)² = √8 = 4
LQR = √(Rx -Qx)² + (Ry - Qy)²
LPM = √(Mx -Px)² + (My - Py)²
LOM = √(Mx -Mx)² + (Oy - My)²
if m∠QMP = 180° - m∠QMR = 180° - 120° = 60°
The question below is as seen in the pictures provided.
The diagonals of parallelogram OPQR intersect at point M.
What are the coordinates of points M?
Find PQ
Find QR
Find PM
Find OM
Find permeter of parallelogram OPQR
if m ∠QMR = 120° what is m ∠ QMP
If m ∠ QRO = 80° what is m ∠ROP
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Suppose loga 2=r, loga 3=s, and loga 5=t Which algebraic expression represents loga 75?
The algebraic expression represents loga 75 is st²
How to determine the expression?An algebraic expression is an expression obtained by a finite number of the fundamental operations of algebra upon symbols representing numbers.
The statement reads:
loga 2=r,
loga 3=s, and
loga 5=t
Log 75 Log(3*5*5)
That log3*log5*log5
= s*t*t = st²
Therefore the expression is st²
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Find the surface area of a right square pyramid if the area of the base is 169 cm² and the slant height of the pyramid is 13 cm.
The surface area of a right square pyramid if the area of the base is 169 cm² and the slant height of the pyramid is 13 cm is 507 cm².
Calculating the surface area of square pyramidWe know that the area of the square base is 169 cm², so we can solve for the length of one side.
To find the length, we use the formula for the area of a square:
Area = length x length
169 = length²
Taking the square root of both sides, we get:
length = √169
= 13 cm
Now we can use the formula for the surface area of a square pyramid:
Surface area = area of base + (1/2)perimeter of base x slant height
The perimeter of the base is 4 times the length of one side, so it is:
perimeter of base = 4 x length = 4 x 13 cm = 52 cm
Plugging in the values we have:
Surface area = 169 cm² + (1/2)(52 cm)(13 cm)
Surface area = 169 cm² + 338 cm²
Surface area = 507 cm²
Therefore, the surface area of the right square pyramid is 507 cm².
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Solve the system of equation algebraically y =
x ^ 2 + 4x + 3 y = 2x + 6
Write an equation of a quadratic function that has been reflected in the x-axis, shifted horizontally to the right 2 units and stretched by a factor of 3.
The equation is writen in the quatradtic form as [tex]g(x) = -3a(x - 2)^2 - 3b(x - 2) - 3c[/tex]
How to write the equationQuadratic equation is of the form
[tex]f(x) = ax^2 + bx + c[/tex]
the transformations
Reflect it in the x-axis: To reflect a function in the x-axis, we change the sign of the function.
[tex]g(x) = -ax^2 - bx - c[/tex]
Shift it horizontally to the right by 2 units: Our function becomes:
[tex]g(x) = -a(x - 2)^2 - b(x - 2) - c[/tex]
Stretch the function by a factor of 3: To stretch a function vertically, we multiply the function by the stretch factor, k.
[tex]g(x) = -3a(x - 2)^2 - 3b(x - 2) - 3c[/tex]
So, the final transformed quadratic function is: [tex]g(x) = -3a(x - 2)^2 - 3b(x - 2) - 3c[/tex]
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A company's survey of 150 employees find that on average an employee drinks 10.2 cups of coffee during the workweek with a margin of error of #0.6. Using this data, it is estimated that a maximum of 6, 048 cups of coffee will be consumed during a workweek. What is the total number of employees in the company?
• 403
• 560
• 593
• 630
The total number of employees in the company is 560.
What is total number of employees?
The total number of employees in the company is calculated as follows;
the true average number of cups of coffee consumed per employee during the workweek is 10.2 ± 0.6 cups.
maximum = 10.8 cups/employee
minimum = 9.6 cups/employee
The minimum number of employees is calculated as;
n_m = 6,048 cups / 10.8
n_m = 560
The maximum number is calculated as;
n_max = 6,048 cups/9.6
n_max = 630
Based on the error margin, we take the minimum number.
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Suppose the probability of an event is 0.20. What are the odds in favor of this event?
Answer:
If the probability of an event is 0.20, the odds in favor of the event can be calculated as follows:
- Divide the probability of the event occurring by the probability of the event not occurring:
0.20 / (1 - 0.20) = 0.20 / 0.80
- Simplify the fraction:
0.20 / 0.80 = 1 / 4
Therefore, the odds in favor of the event are 1 to 4.
Step-by-step explanation:
The odds in favor of an event with a probability of 0.20 is a ratio of 1 to 4.
Explanation:The question is about calculating the odds in favor of an event with a probability of 0.20. The odds in favor of an event is defined as the ratio of the probability that the event will happen to the probability that it will not happen.
In this case, the probability of the event is 0.20, therefore the probability that it will not happen is 1 - 0.20 = 0.80. So, the odds in favor of the event are 0.20 to 0.80 or it can be simplified to 1 to 4.
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The volume of a cone is 35π cubic inches and the height is 4.2 inches. What is the radius of the cone?
The value of the radius of the cone is, 5 inches
We have to given that;
The volume of a cone is 35π cubic inches.
And, the height is 4.2 inches.
Now, We know that;
Volume of cone is,
V = πr²h/3
Hence, We get;
35π = π × r² × 4.2 / 3
105 = 4.2r²
r² = 105/4.2
r² = 25
r = 5 inches
Thus, The value of the radius of the cone is, 5 inches
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someone help me with my math problems these are my last questions
Answer:translation, 12^2+35^2, squre root the answer, thgen add it to 12
Step-by-step explanation:
Write your answer as an integer or as a decimal rounded to the nearest tenth.
The measure of WY using trigonometric identities is 5.4405.
We have,
Using trigonometric identities,
tan 33 = YW/√70
Now,
√70 = 8.37
tan 33 = 0.65
Substituting,
0.65 = YW/8.37
YW = 0.65 x 8.37
YW = 5.4405
Thus,
The measure of WY is 5.4405.
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X
What is the multiplicative inverse of 5/6
The multiplicative inverse of 5/6 as required to be determined in the given task content is 6/5.
What is multiplicative inverse?It follows from the task content that the multiplicative inverse of the given number; 5/6 is required to be determined.
By definition; it follows that the Multiplicative inverse of an expression refers to its reciprocal. It is the value that, when multiplied by the original, give a product of 1 (the multiplicative identity element).
So,
5/6 × 6/5
= 30/30
= 1
Hence, 6/5 is the multiplicative inverse of 5/6
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