Answers
Answer:
(c) x³·∛x
Step-by-step explanation:
You want the simplified form of ∛(x¹⁰).
Cube rootsThe first part of the problem tells you how to get there. After you have that expression, you need to bring the x⁹ term from under the radical.
[tex]\sqrt[3]{x^{10}}=\sqrt[3]{x^9\cdot x}=\sqrt[3]{x^9}\cdot\sqrt[3]{x}=\boxed{x^3\cdot\sqrt[3]{x}}\qquad\text{matches choice C}[/tex]
<95141404393>
Related Questions
ahmed throws a ball to john. The ball travels 10m in x m/s.
a) write an expression in terms of x for the time taken for the ball to reach john
john throws the ball to pierre over a distanxce of 15m in 0.5 m/s less than the timw taken for the ball to reach john from ahmed.
b) write an expression in terms of x for the time taken for the ball to go from john to pierre.
the time taken between john catching the ball and then throwing it to pierre is 2 seconds . the total time taken from ahmed to pierre in 7 seconds. write an equation to show that it simplifies to 2x^2-9x-2=0
Answers
Answer:
a) The time taken for the ball to reach John is: 10/x seconds.
b) The time taken for the ball to go from John to Pierre is: 15/(x - 0.5) seconds.
c) The equation that shows the total time taken from Ahmed to Pierre simplifies to 2x^2 - 9x - 2 = 0.
Step-by-step explanation:
a) The time taken for the ball to reach John can be calculated using the formula:
time = distance / speed
Since the distance traveled by the ball is 10m and the speed is x m/s, the time taken can be expressed as:
time = 10 / x seconds
b) The time taken for the ball to go from John to Pierre can be expressed as:
time = distance / speed
Since the distance traveled by the ball is 15m and the speed is 0.5 m/s less than the speed at which the ball traveled from Ahmed to John (i.e. x - 0.5 m/s), the time taken can be expressed as:
time = 15 / (x - 0.5) seconds
c) Let's use the information given to write an equation for the total time taken from Ahmed to Pierre. We know that the time taken for the ball to travel from Ahmed to John is 10/x seconds, the time taken for the ball to travel from John to Pierre is 15/(x-0.5) seconds, and the time taken between John catching the ball and throwing it to Pierre is 2 seconds. Therefore, the total time taken can be expressed as:
10/x + 15/(x-0.5) + 2 = 7
Multiplying both sides by x(x-0.5) to get rid of the denominators, we get:
10(x-0.5) + 15x + 2x(x-0.5) = 7x(x-0.5)
Simplifying and rearranging, we get:
2x^2 - 9x - 2 = 0
Therefore, the equation simplifies to 2x^2 - 9x - 2 = 0.
Please help !!!!!!!!!!!!!!!
Answers
Okay!
In the given diagram, we have two intersecting lines. To determine the relationship between the angles and solve for x, we can use the properties of angles formed by intersecting lines.
From the diagram, we can see that angle K is vertically opposite to the angle (4x-10)°. In a case of intersecting lines, vertically opposite angles are equal.
So, we can write:
K = (4x-10)°
To solve for x, we need more information or another equation involving x. Without any additional equations or information, we cannot determine the value of x.
If you have any additional equations or information related to the problem, please provide them, and I'll be happy to assist you further in solving for x.
How to get the answer to this problem and explain how you got it so I can understand
Answers
well, let's notice that A F, B G and C E all converge at point D, without much fuss, that simply means they're all medians, because all medians in a triangle meet at the centroid.
someone give me answers please!
Answers
Answer:
Area is 140
Step-by-step explanation:
This might be hard at first, but if you can figure out that the triangle on the left can be moved to the right, it forms a rectangle!
So, 10 x 14 = 140 Square units
Explain the difference between an indefinite integral and a definite integral.
A) An indefinite integral, after evaluating it at the limits of integration, results in a particular number. A definite integral results in a set of functions that share the same derivative and uses an arbitrary constant of integration.
B) A definite integral, after evaluating it at the limits of integration, results in a particular number. An indefinite integral results in a set of functions that share the same derivative and uses an arbitrary constant of integration.
C) An indefinte integral cannot always be integrated analytically and may require numeric integration, while it is always possible to integrate a definite integral. Definite integrals always return a real number after evaluation at its limits of integration.
D) A definite integral is defined and continuous over the interval of integration and has finite limits of integration. An indefinite integral is also defined and continuous over the interval of integration, but may have as a limit of integration.
Answers
The answer is A.
An indefinite integral is a function that, when differentiated, equals the original function. It is denoted by ∫f(x)dx, where f(x) is the function to be integrated. An indefinite integral always has an arbitrary constant of integration, which is denoted by C. This is because the derivative of any constant is zero, so the derivative of ∫f(x)dx+C is still equal to f(x).
A definite integral is the limit of a Riemann sum as the number of terms tends to infinity. It is denoted by ∫
a
b
f(x)dx, where a and b are the limits of integration. A definite integral does not have an arbitrary constant of integration, because the limits of integration specify a unique value for the integral.
In other words, an indefinite integral is a family of functions that share the same derivative, while a definite integral is a single number.
Carlos has a collection of old vinyl records. To play some of the records, the turntable rotates through an angle of 3/2pi radians in 1 second. How many revolutions does the record make in one minute?
A. 33 1/3 revolutions per minute
B. 45 revolutions per minute
C. 78 revolutions per minute
D. 16 2/3 revolutions per minute
Answers
Step-by-step explanation:
We know that the turntable rotates through an angle of 3/2pi radians in 1 second.
To find the number of revolutions in one minute, we need to convert the angle to revolutions per minute.
There are 2π radians in one revolution, so we can set up a proportion:
(3/2π radians) / (1 second) = (x revolutions) / (1 minute)
To solve for x, we can cross-multiply and simplify:
(3/2π) * (1 minute) = x * (1 second) * (2π)
x = (3/2π) * (60/1)
x = 45 revolutions per minute
Therefore, the answer is B. 45 revolutions per minute.
I hope it helps!!
_m 6. A sphere has a volume of 123 cm³. Find its radius to the nearest cm. (Use m = 3.14) (1 mark) Answer:
Answers
Step-by-step explanation:
Formula for sphere volume = 4/3 pi r^3
V = 4/3 pi r^3 solve for 'r'
r = cubrt ( 3/4 v / pi ) = cubrt ( 3/4 * 123 / 3.14) = 3 cm
Use the Intermediate Value Theorem to show that the given function has a zero in the interval [0, 2].
Answers
Answer:
See below for answer and explanation
Step-by-step explanation:
The Intermediate Value Theorem (IVT) states that there is a value [tex]c[/tex] in [tex][a,b][/tex] such that [tex]f(c)=0[/tex]. Because [tex]f(0)=0^2+5(0)-4=-4[/tex] and [tex]f(2)=2^2+5(2)-4=10[/tex], this must mean that 0 is in between -4 and 10, which concludes that there is a zero over the interval [0,2] for the given function by IVT.
78.95*0.3
Can someone please show me a step by step of how I would write this out and solve it? (No calculators)
Answers
Answer:
23.685
Step-by-step explanation:
Ok, lets convert them into fractions
78.95=7895/100
0.3=3/10
7895*3/1000
7895*3=21000+2400+270+15=23685
23685/1000=23.685
Pls help due tomorrow
Your keys drop from the top of the tower and fall straight to the ground. You want to know how far from the base of the tower the keys landed. Draw a right triangle that will help you solve the problem. label each triangle with the information you know. (the tower is 150 meters tall with a 72-degree angle )
2. using the known angle, what side is known? What side is unknown? Use opposite, adjacent, or hypotenuse in your answer.
known side ___
unknown side ___
3. What trigonometric ratio would you use to find the distance from the base of the tower to your keys? identify your choice, and then calculate the distance.
Trigonometric ratio (name) ___
Calculation (Show your work): ___
4. While you're at the top of the tower, you see an ant walking along the edge of the building. if the ant were to walk straight down the side of the tower until it reached the ground, how far would the ant travel? Which trigonometric ratio would you use to find this distance? use the ratio to find the measurement.
5. confirm that your answer to question 5 is correct using the Pythagorean theorem instead of trigonometric ratios.
6. The leaning tower of Niles, in Illinois, is a replica of the famous Leaning tower of Pisa. it was completed in 1934. the tower of Niles is 94 feet high and makes an angle of 85.5 degrees from the ground to the top of the tower. if you drop your keys from the top of this tower, how far from the base of the tower would they land?
Answers
Answer:
know side: 3
Unknown side: 5
Answer: The trigonometric ratio that I would use to find the distance from the base of the tower to the keys is the tangent; tan (86°) = height / distance.
Explanation and calculation:
You can draw a right triangle with angle 86°, opposite leg equal to the height (50 meter) and adjacent leg equal to the distance from the base of the tower to the keys: tan (86°) = 50 m / x
=> x = 50 m / tan(86°)
x = 50 m / 14.30 = 0.98 m
Answer: 0.98 m
sovle this this an hard one
Answers
Answer:
B, line B
Step-by-step explanation:
Line B closest fits the plotted points (dots). That's the best fit.
1. Which shape does not belong? Find as many reasons for each shape why it does not belong. Triangle, diamond, rectangle, pentagon
Answers
Triangle:
It might not belong because it does not have any parallel sides, unlike the other shapes.
Diamond:
It might not belong because it is the only shape that is not a quadrilateral.
Rectangle:
It might not belong because it is the only shape with opposite sides that are equal in length.
Pentagon:
It might not belong because it is the only shape that does not have any right angles.
To determine which shape does not belong among the triangle, diamond, rectangle, and pentagon, we can analyze each shape and identify reasons why it may not belong in comparison to the others.
Here are some possible reasons for each shape:
Triangle:
It could be the odd one out because it is the only shape with three sides.
It might not belong because it does not have any parallel sides, unlike the other shapes.
Diamond:
It could be the odd one out because it is the only shape that is not a polygon (since it does not have straight sides).
Rectangle:
It could be the odd one out because it is the only shape with four right angles.
Pentagon:
It could be the odd one out because it is the only shape with five sides.
It might not belong because it is the only shape that does not have any right angles.
The determination of which shape does not belong ultimately depends on the specific criteria or rules set for the given set of shapes.
Without further context or specific criteria, it is difficult to definitively say which shape does not belong.
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Andrei, Amit and Andrew were each asked to factor the term 20x^620x
6
20, x, start superscript, 6, end superscript as the product of two monomials. Their responses are shown below.
Andrei Amit Andrew
20x^6=(2x)(10x^5)20x
6
=(2x)(10x
5
)20, x, start superscript, 6, end superscript, equals, left parenthesis, 2, x, right parenthesis, left parenthesis, 10, x, start superscript, 5, end superscript, right parenthesis 20x^6=(4x^3)(5x^3)20x
6
=(4x
3
)(5x
3
)20, x, start superscript, 6, end superscript, equals, left parenthesis, 4, x, cubed, right parenthesis, left parenthesis, 5, x, cubed, right parenthesis 20x^6=(20x^2)(x^3)20x
6
=(20x
2
)(x
3
)20, x, start superscript, 6, end superscript, equals, left parenthesis, 20, x, squared, right parenthesis, left parenthesis, x, cubed, right parenthesis
1) Which of the students factored 20x^620x
6
20, x, start superscript, 6, end superscript correctly?
Choose all answers that apply:
Choose all answers that apply:
(Choice A) Andrei
A
Andrei
(Choice B) Amit
B
Amit
(Choice C) Andrew
C
Andrew
(Choice D) None of the above
D
None of the above
Answers
Based on the given responses, the student who factored 20x^6 = (2x)(10x^5) correctly is Andrei. Therefore, the correct answer is (Choice A) Andrei.
Among the given responses, the student who factored 20x^6 = 20, x to the power of 6 correctly is Andrei. Andrei's factorization is (2x)(10x^5), which correctly represents the original term 20x^6. Therefore, the correct answer is (Choice A) Andrei.
Amit's factorization is (4x^3)(5x^3), which is incorrect because it breaks down the term into two factors with the same exponent, while the original term has an exponent of 6.
Andrew's factorization is (20x^2)(x^3), which is also incorrect as it does not accurately represent the original term 20x^6.
Hence, the only student who correctly factored 20x^6 = 20, x to the power of 6 is Andrei.
The right answer is A. Andrei who factored 20x^6 = (2x)(10x^5) correctly.
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There are 140 students in the seventh grade, and 20% are in the Environmental Club. How many students are in the Environmental Club?
Answers
Answer:
28
Step-by-step explanation:
You want to know what 20% of 140 is.
PercentThe % symbol can be considered to mean "/100". This means ...
20% = 20/100
and 20% of 140 is ...
20% × 140 = 20/100 × 140 = 2800/100 = 28
There are 28 students in the Environmental Club.
__
Additional comment
You know that 10% is 1/10. This fraction can of 140 can be found by moving the decimal point one place left:
10% of 140. = 14.0
Of course, 20% is twice as much, so ...
20% of 140 = 2 × (10% of 140) = 2 × 14 = 28
In this context, "of" means "times": 20% of 140 means 20% × 140.
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In a normal distribution of 1027 values, the mean is 75 and the standard deviation is 8. What is the closest number of values that would be above 91?
A) 26
B) 2567
C) 976
D) 51
Answers
Answer: 26
Step-by-step explanation:
The closest number of values above 91 is 23.
We have,
To find the closest number of values that would be above 91 in a normal distribution with a mean of 75 and a standard deviation of 8, we need to calculate the z-score for the value 91 and then find the proportion of values above that z-score.
The formula for calculating the z-score is:
z = (x - mean) / standard deviation
where x is the value of interest, the mean is the mean of the distribution, and the standard deviation is the standard deviation of the distribution.
In this case,
x = 91, mean = 75, and standard deviation = 8.
Plugging these values into the formula, we get:
z = (91 - 75) / 8 = 2
To find the proportion of values above a z-score of 2, we can refer to the z-table or use a calculator that provides the cumulative distribution function (CDF) for the standard normal distribution.
Looking up the z-score of 2 in the z-table or using a calculator, we find that the proportion of values above a z-score of 2 is approximately 0.0228.
To determine the number of values above 91 in a distribution of 1027 values, we multiply the proportion above 91 (0.0228) by the total number of values (1027):
Number of values above 91 = 0.0228 x 1027 ≈ 23.47
Since we are looking for the closest whole number, the closest number of values above 91 would be 23.
Therefore,
The closest number of values above 91 is 23.
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PLEASE HELP!!!
The inside of the cylindrical swimming pool shown must be covered with a vinyl liner. The liner must cover the side and bottom of the swimming pool.
The diameter of the pool is 20 feet and the height is 3 feet, as shown.
What is closest to the minimum amount of vinyl needed for the liner?
O 1320 sq ft
O 817 sq ft
O 503 sq ft
O 126 sq ft
Answers
The minimum amount of vinyl needed for the liner is 502.4 sq. feet.
We have,
An open cylinder is a type of cylinder in which one of its circular surfaces has been removed.
Thus its area can be determined as:
area of an open cylinder = πr² + 2πrh
where r is the radius, and h is the height.
The area of the swimming pool that will be covered by vinyl liner resembles an open cylinder. So that;
area of the open swimming pool = πr² + 2πrh
= πr(r + 2h)
we have,
r = diameter/ 2
= 20/ 2
r = 10 feet
area of the open swimming pool = 3.14×10(10 + 2×3)
= 31.4×16
= 502.4
The minimum amount of vinyl needed for the liner is 502.4 sq. feet.
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Question 6
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>
Suppose you want to have $300,000.00 for retirement in 35 years. You plan to make regular quarterly
deposits into an account earning 8% interest compounded quarterly.
How much would you need to deposit in the account each quarter?
You need to deposit
each quarter.
Submit Question
How much money will you have put into the account? Hint
You will have put
How much interest will you have earned? Hint
You will have earned
into the acou
in interest.
over the 35 years.
Answers
you will have put approximately $1,014,706.40 into the account over the 35 years. The interest will you have earned is -$714,706.40.
To calculate the amount you need to deposit each quarter, we can use the formula for the future value of a series of regular deposits:
FV = P * ((1 + r)^n - 1) / r
Where:
FV is the future value (target amount) you want to achieve ($300,000.00)
P is the deposit amount per quarter (what we need to find)
r is the interest rate per quarter (8% or 0.08)
n is the number of quarters (35 years * 4 quarters per year = 140 quarters)
Now, let's substitute the values into the formula and solve for P:
$300,000.00 = P * ((1 + 0.08)^140 - 1) / 0.08
$300,000.00 * 0.08 = P * ((1.08)^140 - 1)
$24,000.00 = P * (4.31793257 - 1)
$24,000.00 = P * 3.31793257
P = $24,000.00 / 3.31793257
P ≈ $7,243.21
Therefore, you would need to deposit approximately $7,243.21 into the account each quarter to accumulate $300,000.00 for retirement in 35 years.
To calculate the total amount of money you will have put into the account over the 35 years, you can multiply the deposit amount per quarter by the number of quarters:
Total deposit = P * n = $7,243.21 * 140 = $1,014,706.40
Therefore, you will have put approximately $1,014,706.40 into the account over the 35 years.
To calculate the interest earned, you can subtract the total deposit amount from the target amount:
Interest earned = Future value - Total deposit = $300,000.00 - $1,014,706.40 = -$714,706.40
The negative value indicates that the interest earned is negative, meaning that you will have fallen short of your target amount by $714,706.40 due to the interest earned being less than the total deposit made.
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
mentum. All rights reserved.
Answers
The slope of a line is positive with a value of 3/2 or 1.5.
What is the slope of the line?The slope of the line is the ratio of the rise to the run, or rise divided by the run.
The slope of a line is used to describe the steepness and direction of the line.
Mathematically, the formula for the slope of a line is given as;
slope = Δy / Δx
where;
Δy is the change in the y valuesΔx is the change in x valuesThe slope equation is expanded as follows;
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
From the graph, the values of x and y is determined as;
( x₁, y₁ ) = ( - 2, 0 )
( x₂, y₂) = ( 0, 3 )
The slope of the line is calculated as follows;
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
m = ( 3 - 0 ) / ( 0 - - 2)
m = 3 / 2
m = 1.5
Thus, the line has a positive slope.
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The complete question is below:
What is the slope of the line? type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
use parenthesis to makeveach equation true 8×9-2-3
Answers
Using the parentheses to rewrite the equation 8×9-2-3 gives 67.
How to use parenthesis to make equation true?
In mathematics, the order of operations are the rules that tell the sequence in which the multiple operations in an expression should be solved.
A way to remember the order of the operations is PEMDAS, where each letter stands for a mathematical operation. There is also another version called BODMAS but the principles are the same
Parenthesis ( )
Exponent a⁷
Multiplication ×
Division ÷
Addition +
Subtraction -
Given: 8×9-2-3
We can rewrite the equation using parenthesis using PEMDAS:
Multiplication first, then followed by addition/subtraction:
8×9-2-3 = (8 × 9) - 2 - 3
= 72 - 2 - 3
= 67
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16) In the given picture, line / is parallel to line m. if m<1 = 35°
(A) Find m<3
(B) Find m<7
(C) Find m<8
(D) Find m<5
Answers
Answer:
∠ 3 = 35° , ∠ 7 = 145° , ∠ 8 = 35° , ∠ 5 = 145°
Step-by-step explanation:
∠ 3 and ∠ 1 are vertically opposite angles and are congruent , then
∠ 3 = 35°
-----------------
∠ 3 and ∠ 5 are same- side interior angles and sum to 180°, that is
∠ 5 + ∠ 3 = 180°
∠ 5 + 35° = 180° ( subtract 35° from both sides )
∠ 5 = 145°
------------------
∠ 5 and ∠ 7 are vertically opposite angles and are congruent , then
∠ 7 = 145°
--------------
∠ 1 and ∠ 8 are corresponding angles and are congruent , then
∠ 8 = 35°
---------------
A company manufactures two types of electrical components A and B. The total revenue from x units of A and y units of B is given by R(x,y)=-5x2-8y2-2xy + 42x+102y, where x and y are in thousands of units. Find the values of x and y to maximize the total revenue.
Answers
The values of x and y that maximize the total revenue are approximately 3600 units of A and 3200 units of B.
We are given that;
Function R(x,y)=-5x2-8y2-2xy + 42x+102y
Now,
To maximize the total revenue from x units of A and y units of B, we need to find the values of x and y that maximize the function R(x,y)=-5x2-8y2-2xy + 42x+102y. This is an optimization problem with two variables.
To solve this problem, we need to find the critical points of R(x,y) by taking partial derivatives with respect to x and y and setting them equal to zero.
R_x = -10x - 2y + 42 = 0
R_y = -16y - 2x + 102 = 0
Solving these equations simultaneously gives us:
x = 3.6
y = 3.2
Therefore, by the given function the answer will be 3600 units of A and 3200 units of B.
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can i get help with this finding volume
Answers
Answer:
[tex]\huge\boxed{\sf 148\ in\³}[/tex]
Step-by-step explanation:
Formula to be used:Volume of cuboid = length × width × height
Solution:Volume of smaller box:= length × width × height
= 8 × 4 × 2
= 64 in³
Total volume:= Volume of larger box + Volume of smaller box
= 212 in³
Volume of larger box:= Total volume - Smaller box
= 212 - 64
= 148 in³[tex]\rule[225]{225}{2}[/tex]
(question 8) Find the critical points of the function
Answers
Answer:
[tex]\textsf{A.} \quad \dfrac{-3}{2}[/tex]
Step-by-step explanation:
The critical points of a function are the points where the derivative of the function is either zero or undefined.
We can find the derivative of the given function using the product rule.
[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}[/tex]
Given function:
[tex]f(x)=(2x+1)e^x[/tex]
[tex]\textsf{Let}\; u=2x+1 \implies \dfrac{\text{d}u}{\text{d}x}=2[/tex]
[tex]\textsf{Let}\; v=e^x \implies \dfrac{\text{d}v}{\text{d}x}=e^x[/tex]
Apply the product rule:
[tex]\begin{aligned}f'(x)&=(2x+1)e^x+e^x(2)\\&=(2x+1)e^x+2e^x\\&=e^x(2x+1+2)\\&=e^x(2x+3)\end{aligned}[/tex]
Set the derivative equal to zero and solve for x:
[tex]\begin{aligned}f'(x)&=0\\e^x(2x+3)&=0\\2x+3&=0\\2x&=-3\\x&=-\dfrac{3}{2}\end{aligned}[/tex]
Therefore, the critical point of the function f(x) is when x = -3/2.
“Financial statements are a vital communication tool for key stakeholders”. Discuss this statement considering
the role of financial record keeping in the survival and growth of small businesses.
Answers
Financial statements can help small businesses pinpoint their weak points, plan for expansion, and find new partners or investors.
The roles of financial recordsFinancial statements are an essential tool for communicating with important parties, such as lenders, suppliers, and investors. Maintaining accurate financial records is essential to the survival and expansion of small businesses.
The financial health, performance, and profitability of the organization are shown by accurate and trustworthy financial accounts. Stakeholders can use them to make well-informed decisions on the business's creditworthiness, investment prospects, and loan repayment capacity.
Financial statements can help small businesses pinpoint their weak points, plan for expansion, and find new partners or investors.
Small firms may find it difficult to win the trust and support of stakeholders without appropriate financial record keeping and transparent statements, which will impede their chances of survival and expansion.
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Pleaseeeeee help with these two questions:
A car accelerates for 4.5 seconds at a rate of 2 m/s^2. If the car was driving at 10 m/s initially, what is it's final velocity? The car is moving on a straight path.
12.25 m/s
22.5 m/s
4.44 m/s
19 m/s
QUESTION 2
If a 5000 kg car hits a 500 kg motorcycle, which of the following is true? Assume they collide and cleanly bounce off of each other.
-The motorcycle will have a greater acceleration after the collision due to the greater force exerted by the car on
impact.
-The forces are equal and opposite so both vehicles will have the same acceleration after the impact.
-The motorcycle will have a greater acceleration after the collision due to its lower inertia.
Answers
Answer:
Last choice: 19m/s
Reasoning:
Velocity can be described by the Kinematic Equation: vf=u+at. The equation is a linear relationship in the form y=mx+b, so it contains a rate of change (slope) and a starting point (y-intercept). In the equation, vf=final velocity, u=initial velocity, a=acceleration, and t=time.
Let’s solve for the final velocity (vf) using the Kinematic Equation:
Vf=(2m/s²)(4.5s)+(10m/s)
Vf=9m/s+10m/2
Vf=19m/s
Question 2:
Choice A.)
Simplify by writing without the absolute value sign.
|x-5| if x<5
Please help!
Answers
when x < 5, we can simplify it as -(x - 5) because (x - 5) is negative.
We have,
Absolute value:
The absolute value of a number represents its distance from zero on the number line. It is always a non-negative value.
For example, the absolute value of 3 is 3, and the absolute value of -3 is also 3.
|x - 5|:
In this expression, we have the absolute value of the quantity (x - 5).
It means that we are looking at the distance between x and 5 on the number line.
x < 5:
The condition x < 5 states that x is less than 5.
It means that x is located to the left of 5 on the number line.
Simplification:
When x is less than 5, it implies that x is located to the left of 5.
In this case,
The quantity (x - 5) becomes negative because we are subtracting a larger value (5) from a smaller value (x).
Now,
The expression |x - 5| can be simplified to -(x - 5), which means taking the negation of (x - 5).
- If x = 3, which is less than 5, we can substitute it into the expression:
|x - 5| = |3 - 5| = |-2| = 2
- If x = 7, which is greater than 5:
|x - 5| = |7 - 5| = |2| = 2
In both cases,
The value of |x - 5| is 2.
However, when x < 5, we can simplify it as -(x - 5) because (x - 5) is negative.
Thus,
when x < 5, we can simplify it as -(x - 5) because (x - 5) is negative.
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color blindness occurs in 4% of the male population. design a simulation that can be used to estimate the probablitiy that a randomly chose male will be color blind
Answers
To design a simulation to estimate the probability that a randomly chosen male will be color blind, you can follow these steps:
Set up the simulation: Determine the number of males to include in your simulation. Let's say you choose to simulate 10,000 males.
Generate random color blindness: Use a random number generator to assign color blindness status to each simulated male. Since color blindness occurs in 4% of the male population, you can randomly assign color blindness to approximately 4% of the males in your simulation.
Count the number of color-blind males: Iterate through the simulated males and count the number of males who are color blind.
Calculate the probability: Divide the count of color-blind males by the total number of males in the simulation to obtain the estimated probability. Multiply the result by 100 to express it as a percentage.
Here's a Python code snippet to illustrate this simulation:
import random
num_simulated_males = 10000
num_color_blind_males = 0
for _ in range(num_simulated_males):
if random.random() <= 0.04: # Probability of being color blind
num_color_blind_males += 1
probability_color_blind = (num_color_blind_males / num_simulated_males) * 100
print(f"Estimated probability of a randomly chosen male being color blind: {probability_color_blind:.2f}%")
Keep in mind that this simulation provides an estimate based on the assumed probability of 4% for color blindness in the male population. The actual probability may vary slightly, but running the simulation with a large number of simulated males should yield a reasonably accurate estimate.
The formula for continuously compounded interest is given by
, where
is the account balance,
is the principal,
is the annual interest rate (expressed as a decimal), and
is the time in years.
If $5000 is deposited into an account earning an annual interest rate of 2.5%, compounded continuously, then what is the account balance after 12 years?
Round your answer to the nearest dollar and do not include the $ symbol in your answer.
Answers
The balance of the account after 12 years is given as follows:
$9,111.
How to obtain the balance of the account?The balance of an account after t years, using continuous compounding, is given by the exponential equation presented as follows:
[tex]A(t) = A(0)e^{kt}[/tex]
In which the parameters are given as follows:
A(0) is the initial deposit.k is the interest rate, as a decimal.The parameter values for this problem are given as follows:
A(0) = 5000, k = 0.025, t = 12.
Hence the balance of the account after 12 years is given as follows:
[tex]A(t) = A(0)e^{kt}[/tex]
[tex]A(12) = 5000e^{0.025 \times 24}[/tex]
A(12) = $9,111.
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Translate each question into mathematical expression and at part II write the right letter
Answers
Answer:
Step-by-step explanation:
5. Priest and Sons, is a local manufacturer of a product that sells for $13.50 per unit. Variable costper unit is $7.85 and fixed cost per period is $1 220. Capacity per period is 1100 units. Perform a break-even analysis showing an algebraic statement of:
a. the revenue function
b. the cost function
c. calculate the break-even point in units
Answers
The break-even point is approximately 217 units.
We are given that;
Cost of local product= $13.50
Variable cost per unit= $7.85
Fixed cost per period= $1
Now,
The revenue function is the product of the price per unit and the number of units sold:
R(x)=13.50x
where x is the number of units sold.
The cost function is the sum of the fixed cost and the variable cost per unit multiplied by the number of units sold:
C(x)=1220+7.85x
where x is the number of units sold.
The break-even point is the point at which revenue equals cost. We can find this point by setting R(x) equal to C(x) and solving for x:
13.50x=1220+7.85x
5.65x=1220
x≈216.81
Therefore, by the function the answer will be 217 units.
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