Q.2 The lengths of a triangle are 7 cm, 8 cm and 10 cm correct to the nearest cm. Work out maximum possible perimeter of the triangle.
Step-by-step explanation:
7+8+10=25cm is the possibile perimeter of this
triangle.
Please hurry! Marking brainliest!
Answer:
Step-by-step explanation:
when dividing we really are only multiplying when we flip the second fraction
so keep the first fracion the same and just flip the second one
a = 6
b = 5
c = 3
if a person gives you their card number and they say you can spend a certain amount of money and u spend more is it considered stealing? or is it not because they gave u their card willingly and all u did was go over the limit.
Answer:
It would be considered stealing.
Step-by-step explanation:
They did willingly give you their card BUT, they trusted you to only spend a certain amount and not go over that certain limit. You went over the limit even though they specifically told you not to go over it so yes, it would be classified as stealing.
Find the slope of every that is perpendicular to (0,4) and (-3,0)
The slope of a line perpendicular to the line passing through the points (0,4) and (-3,0) is -3/4.
To find the slope of a line perpendicular to a given line, we need to take the negative reciprocal of the slope of the given line.
Given the points (0,4) and (-3,0), we can calculate the slope of the given line using the slope formula:
slope = (y2 - y1) / (x2 - x1)
Let's substitute the values:
slope = (0 - 4) / (-3 - 0)
= -4 / -3
= 4/3
The slope of the given line is 4/3.
To find the slope of a line perpendicular to this line, we take the negative reciprocal of 4/3:
slope of perpendicular line = -1 / (4/3)
= -1 * (3/4)
= -3/4
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A soil sample contains 20 percent sand, 10 percent clay, and 70 percent silt. What type of soil is present in the sample?.
The type of soil present in the sample is Silty loam.
A classification tool called soil texture is used in both the field and the lab to identify different soil types based on their physical textures. Both qualitative and quantitative techniques, including the hydrometer method, can be used to determine the texture of the soil.We have silty loam present in the soil sample because it contains 20% sand, 10% clay, and 70% silt.
Silty loam is the term used to describe soil that has 20% sand, 70% silt, and 10% clay. Sandy Clay loam is a soil type that has 60% sand, 10% silt, and 30% clay.The material will be made up of 40% Silt, 30% Sand, and 30% Clay higher; muggy
Alkaline soils are common in arid climates, making the area wet and becoming more acidic as the pH value decreases.
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solve the given initial-value problem. d2x dt2 4x = −2 sin(2t) 5 cos(2t), x(0) = −1, x'(0) = 1
Given : Initial value problemd
²x/dt² + 4x
= -2sin(2t) + 5cos(2t)x(0)
= -1, x'(0)
= 1
The solution for the differential equation
d²x/dt² + 4x = -2sin(2t) + 5cos(2t)
is given by,
x(t)
= xh(t) + xp(t)
where, xh(t)
= c₁ cos(2t) + c₂ sin(2t)
is the solution of the homogeneous equation. And, xp(t) is the solution of the non-homogeneous equation. Solution of the homogeneous equation is given by finding the roots of the auxiliary equation,
m² + 4 = 0
Or, m² = -4, m = ± 2i
∴xh(t) = c₁ cos(2t) + c₂ sin(2t)
is the general solution of the homogeneous equation.
The particular integral can be found by using undetermined coefficients.
For the term -2sin(2t),
Let, xp(t) = A sin(2t) + B cos(2t)
Putting in the equation,
d²x/dt² + 4x
= -2sin(2t) + 5cos(2t)
We get, 4(A sin(2t) + B cos(2t)) + 4(A sin(2t) + B cos(2t))
= -2sin(2t) + 5cos(2t)Or, 8Asin(2t) + 8Bcos(2t)
= 5cos(2t) - 2sin(2t)
Comparing the coefficients of sin(2t) and cos(2t),
we get,
8A = -2,
8B = 5Or,
A = -1/4, B = 5/8
∴ xp(t) = -1/4 sin(2t) + 5/8 cos(2t)
Putting the values of xh(t) and xp(t) in the general solution, we get the particular solution,
x(t) = xh(t) + xp(t
)= c₁ cos(2t) + c₂ sin(2t) - 1/4 sin(2t) + 5/8 cos(2t)
= (c₁ - 1/4) cos(2t) + (c₂ + 5/8) sin(2t)
Putting the initial conditions,
x(0) = -1, x'(0) = 1 in the particular solution,
we get, c₁ - 1/4 = -1, c₂ + 5/8 = 1Or, c₁ = -3/4, c₂ = 3/8
∴ The solution of the differential equation is given byx(t)
= (-3/4)cos(2t) + (3/8)sin(2t) - 1/4 sin(2t) + 5/8 cos(2t)
= (-1/4)cos(2t) + (7/8)sin(2t)
Therefore, x(t) = (-1/4)cos(2t) + (7/8)sin(2t).
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Which expression is equivalent to 10 - 8?
A) 10+8
B) 8-10
C) 10-(-8)
evaluate the integral by reversing the order of integration. 4 0 12 5ex2 dx dy 3y
To reverse the order of integration, we need to rewrite the limits of integration in terms of the other variable.
The value of the given integral by reversing the order of integration is (5/12)(\(e^{24}\) - 1).
The given integral is ∫∫ \(5e^{(2x)}\) dx dy, where the limits of x are from 0 to 4 and the limits of y are from 0 to 3y.
To integrate with respect to y first, we need to express the limits of y in terms of x.
From the limits of y given, we have 0 ≤ y ≤ 3y, which simplifies to 0 ≤ y.
Now we need to find the upper limit of y. To do this, we set the expression for the upper limit equal to the constant 12, which is the upper limit of x.
So we have 3y = 12, which gives y = 4.
Thus, the limits of integration become ∫∫ \(5e^{(2x)}\) dy dx, where the limits of y are from 0 to 4 and the limits of x are from 0 to 3y.
Now we can integrate with respect to y:
∫∫ \(5e^{(2x)}\) dy dx = ∫ 0^4 ∫ 0^(3y) \(\int\limits^4_0 \int\limits^{(3y)}_0 5e^{(2x)} dx dy\)
= \(\int\limits^4_0 [5/2 e^{(2x)}]_0^{(3y)} dy\)
= \(\int\limits^4_0 [5/2 (e^{(6y)} - 1)] dy\)
= \([5/12 (e^{(6y)} - 1)]_0^4\)
= \((5/12)(e^{24} - 1)\)
Note that the order of integration can be reversed if the integrand is continuous on a rectangular region that contains the original region of integration.
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please help urgent
Use the formula A = P(1 + rt) to find the indicated quantity. P=$7996; r = 6%; t = 10 months; Find A. OA. $8475.76 OB. $8395.80 OC. $399.80 OD. $6663.33
Answer:
B) \(\$8395.80\)
Step-by-step explanation:
\(A=P(1+rt)\\A=7996(1+0.06\cdot\frac{10}{12})\\A=7996(1+0.05)\\A=7996(1.05)\\A=\$8395.80\)
This is all assuming that r=6% is an annual rate, making t=10/12 years
An object is launched directly in the air at a speed of 16 feet per second from a platform located 4 feet above the ground. The position of the object can be modeled using the function f(t)=−16t2+16t+4, where t is the time in seconds and f(t) is the height, in feet, of the object. What is the maximum height, in feet, that the object will reach?
The maximum height that the object will reach is 8 feet.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Here, The function of height is,
⇒ f (t) = -16t² + 16t + 4
Notice that, the function is a negative parabola. The maximum of the function is located at the vertex of the parabola. At the vertex, the line tangent to that point is horizontal, i.e., its slope is zero. The slope of the tangent line is the derivative of the function and it also expresses the velocity of the object:
Hence, We get;
df/dt = -32t + 16
At the maximum point, the slope of the tangent line is zero (it is the same as to say that at the maximum height, the velocity of the object is zero), then:
df/dt = 0
0 = -32t + 16
Solving the equation for t:
32t = 16
t = 16/32
t = 0.5 s
Then, the maximum height will be f (0.5):
f (t) = -16 t² + 16t + 4
f (0.5) = -16(0.5)² + 16(0.5) + 4
f (0.5) = - 16 × 0.25 + 8 + 4
f (0.5) = - 4 + 8 + 4
f (0.5) = 8 feet
Thus, The maximum height that the object will reach is 8 feet.
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Help mehhhhh. ❗️The number of tickets sold on Friday at a movie theater was 2,000 more than the number of tickets sold on Tuesday. 1,250 tickets were sold on Tuesday. Which integer represents the number of tickets sold on Friday?
Answer:
3,250
Step-by-step explanation:
1,250 + 2,000 = 3,250I hope this helps!
Answer:
The integer number is
3,250
Step-by-step explanation:
Tuesday ticket solds : 1,250
Friday ticket solds = 2000 + 1250 = 3250
given z1 = 8(cos 45° i sin 45°) and z2 = 4(cos 210° i sin 210°), what is z1z2?
For the required value of the given complex numbers z₁z₂ = 32(cos 255° + isin 255°).
What are complex numbers?Complex numbers are those that expand on the idea of real numbers by incorporating an illogical element.
The formula for a complex number is "a + bi," where "a" and "b" are real numbers and "i" is the imaginary unit, which is equal to the square root of -1.
"A" stands for the complex number's real component, and "b" stands for the imaginary component.
We multiply the magnitudes of two complex numbers and add their arguments to determine their product.
Let's compute z₁z₂ with the supplied values.
Given:
z₁ = 8(cos 45° + isin 45°)
z₂ = 4(cos 210° + isin 210°)
We add the arguments and multiply the magnitudes to find z₁z₂:
Magnitude of z₁ = 8
Magnitude of z₂ = 4
Argument of z₁ = 45°
Argument of z₂ = 210°
Now, let's calculate z₁z₂:
Magnitude of z₁z₂ = (Magnitude of z₁) × (Magnitude of z₂) = 8 × 4 = 32
Argument of z₁z₂ = (Argument of z₁) + (Argument of z₂) = 45° + 210° = 255°
Therefore, z₁z₂ = 32(cos 255° + isin 255°).
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The correct question =
Given z₁ = 8(cos 45° + isin 45°) and z₂ = 4(cos 210° + isin 210°), what is z₁z₂?
Evaluate m – n if m = –16 and n = 28
Answer:-44
Step-by-step explanation:
-16-(28)=-44
Answer:
-44
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
m - n
m = -16
n = 28
Step 2: Evaluate
Substitute: -16 - 28Subtract: -44What initial investment must be made to accumulate $120000 in 12 years if the money is invested in a mutual fund that pays 14%annual interest, compounded monthly? Use the analytical solution to find the answer.
What initial investment must be made to accumulate $120000 in 12 years if the money is invested in a mutual fund that pays 14%
annual interest, compounded monthly?
Remember that
The compound interest formula is equal to
\(A=P(1+\frac{r}{n})^{nt}\)where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
A=$120,000
t=12 years
r=14%=14/100=0.14
n=12
substitute in the given formula
\(120,000=P(1+\frac{0.14}{12})^{12\cdot12}\)Solve for P
P=$22,583.42what does it mean if the slope of a line is undefined
The slope of a line is undefined when the line is vertical. In this case, the line does not have a well-defined slope because its rise (change in y) would be infinite while its run (change in x) would be zero.
In general, the slope of a line represents the rate at which the line rises or falls as it moves from left to right. It is defined as the change in y divided by the change in x between any two points on the line.
If the slope of a line is positive, the line is sloping upward from left to right, and if the slope is negative, the line is sloping downward from left to right. If the slope is zero, the line is horizontal. When the slope is undefined, it means that the line is vertical, and it has no well-defined rate of rise or fall as it moves from left to right.
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What is the y-coordinate of the
midpoint of the line segment
which has endpoints
(-1,4) and (-3, -1)?
Step-by-step explanation:
h
PLSSS HELP IF YOU TRULY KNOW THISSS
Answer: 1/50
Step-by-step explanation:
Step 1: We need to multiply the numerator and denominator by 100 since there are 2 digits after the decimal.
0.02 = (0.02 × 100) / 100
= 2 / 100 [ since 0.02 × 100 = 2 ]
Step 2: Reduce the obtained fraction to the lowest term
Since 2 is the common factor of 2 and 100 so we divide both the numerator and denominator by 2.
2/100 = (2 ÷ 2) / (100 ÷ 2) = 1/50
Probability sampling is when individuals are picked through random selection from a larger population. Which probability sampling method involves selecting large, broad groups rather than individuals
Systematic Sampling is the probability sampling method involves selecting large, broad groups rather than individuals.
Systematic sampling is a type of probabilistic sampling technique that selects sample members from a larger population according to random starting points, but with regular periodic intervals. This interval, called the sampling interval, is calculated by dividing the population size by the desired sample size.
Systematic sampling is a type of probabilistic sampling technique that selects sample members from a larger population at regular periodic intervals according to random starting points. This interval, called the sampling interval, is calculated by dividing the population size by the desired sample size. Systematic sampling is considered random if the regular intervals are predetermined and the starting point is random, even though it preselects the sample population.
Systematic sampling, when performed correctly on large populations of a defined size, allows researchers, including marketing and sales professionals, to obtain representative results on large groups of people. without having to contact each individual. Example, if we select a random group of 1,000 people from a population of 50,000 by systematic sampling, we should list all potential participants and choose a starting point. When the list is created, every 50th of her on the list (starting counting from the starting point you chose) will be selected as participants because 50,000 ÷ 1,000 = 50.
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In 2009 Usain bolt set the world record for sprinting 100 m in approximately 9 3over5 seconds
Answer:
10.41 seconds meters per second
1. divide 5 by 3 you get 0.6
2. he ran 9.6 seconds
3. divide 100 by 9.6 seconds getting 10.41 meters per second
Step-by-step explanation:
Hopefully this helped, if not HMU and I wwill get you a better answer.
-Have a great day! :)
When 293 college students are randomly selected and surveyed, it is found that 114 own a car. The upper limit for the 90% confidence interval for the percentage of all college students who own a car is __
O 31.6% O 46.3% O 44.5% O43.6%
When 293 college students are randomly selected and surveyed, it is found that 114 own a car. The upper limit for the 90% confidence interval for the percentage of all college students who own a car is 46.3%.
The given problem is an example of confidence intervals in statistics. The formula for finding the confidence interval in percentage is given below:
Confidence Interval in Percentage = P ± Z Score x √ (PQ/n)
where
P = Sample proportion
Q = 1 - P
n = Sample Size
Z Score is obtained from the Z-Table where the confidence level is given.
To obtain the upper limit, the following formula should be used:
Upper Limit of the Confidence Interval = P + Z Score x √ (PQ/n)
Substitute the given values of the question into the formula:
P = 114/293 = 0.3891
Q = 1 - 0.3891 = 0.6109
n = 293
The upper limit for the 90% confidence interval is given by the Z-Table at 1.645:
Upper Limit of the Confidence Interval = 0.3891 + 1.645 x √ [(0.3891 x 0.6109)/293]
≈ 0.3891 + 1.645 x 0.0467
≈ 0.3891 + 0.07701
≈ 0.4661 = 46.3%
Therefore, the answer is 46.3%.
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A clothing store offers a 50% discount at the end of
each week that an item remains unsold. Patrick
wants to buy a shirt at the store and he says, "I've
got a great idea! I'll wait two weeks, have 100%
off, and get it for free!" Explain to your friend
Patrick why he is incorrect and find the correct
percent of discount on the original price of a shirt.
Let the original price of the item be X.
In one week, the price is halved and becomes (1/2)X.
In two weeks, the price is halved again and becomes (1/4)X, which is only 75% off.
What is the equation?
3.7 = 5x + 12.2
Answer:
x= -1.7
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
x = -1.7.
Step-by-step explanation:
3.7 = 5x + 12.2
Subtract 3.7 from both sides:
0 = 5x + 12.2 - 3.7
0 = 5x + 8.5
Subtract 5x from both sides:
-5x = 8.5
x = 8.5 / -5
x = -1.7.
2x+3y=15 x+y=6 find values for x and y
Answer:
(x, y) = (3, 3)
Step-by-step explanation:
Subtract double the second equation from the first.
(2x +3y) -2(x +y) = (15) -2(6)
y = 3 . . . . . . . . simplify
Use the second equation to find x.
x = 6 -y = 6 -3 = 3
The values of x and y are both 3.
Cancel down the following fractions: 9/72
If segment CD is congruent to segment XY, what is true about the two segments? PLEASE ILL GIVE BRAINIEST IF CORRECT
Answer:
CD overbar is congruent to XY overbar
Could i get some help with these math questions?
Help!!! Please HELP!!!
Answer:
D
Step-by-step explanation:
that's where they cross
the chance of getting a rare disease is .03 per person. out of 1,000 people, how many of them are expected to get the disease?
Answer:
I believe the answer would be 30 people.
Step-by-step explanation:
To calculate the percentage out of a group of people or items, you just multiply the percent (in decimal form) by the amount of people you want it out of. For example: A 0.1% chance out of 1,000 people would be a chance and expectancy of 1 person out of those 1,000 people. In this case it's 3% for every person. 0.03 • 1,000 is 30.
find an example that meets the given specifications. a linear transformation t : r2 → r2 such that t 2 1 = 0 11 and t 1 5 = −9 10 . t(x) = x
The example that meets the given specifications. a linear transformation t : r2 → r2 such that t 2 1 = 0 11 and t 1 5 = −9 10 . t(x) = x is:
t: R2 → R2 such that t(2,1) = (0,11) and t(1,5) = (-9,10):
The following is an example of a linear transformation t: R2 → R2 such that t(2,1) = (0,11) and t(1,5) = (-9,10):
t(x, y) = (x, -9x + 10y)
A linear transformation is a function between two vector spaces that preserves the structure of the space, namely the operations of addition and scalar multiplication. More specifically, a function T:V->W is a linear transformation if it satisfies the following properties:
T(u+v) = T(u) + T(v) for all u,v in V (additivity)
T(cu) = cT(u) for all u in V and scalar c (homogeneity)
In other words, a linear transformation preserves vector addition and scalar multiplication. It takes vectors as inputs and outputs new vectors that are also in the vector space. Additionally, a linear transformation must satisfy the following properties:
T(0) = 0, where 0 is the zero vector in V (preservation of the zero vector)
If T is a linear transformation from V to W, then T must map the basis vectors of V to linearly independent vectors in W.
Some examples of linear transformations include rotation, scaling, and projection.
Linear transformations are important in many areas of mathematics and science, including linear algebra, calculus, and physics. They are used to study a wide variety of phenomena, from the motion of planets to the behavior of complex systems.
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At the beginning of a population study, a city had 380,000 people. Each year since, the population has grown by 9.8%.
Let t be the number of years since start of the study. Let y be the city's population.
Write an exponential function showing the relationship between y and t.
The exponential function that shows the relationship between y and t is y = 380,000 x 1.098^t.
What is the exponential function?An exponential equation can be described as an equation with exponents.
The general form of exponential equation is f(x) = \(e^{x}\)
Where:
x = the variable e = constantThe form of the exponential function that represents the city's population in t years is:
Future population = present population x (1 + growth rate)^number of years
y = 380,000 x (1 + 0.098)^t
y = 380,000 x 1.098^t
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