Final answer:
To find the product of (-2x^2)^3 and -3x, first calculate the cube of -2x^2 (-8x^6), then multiply it by -3x to obtain 24x^7.
Explanation:
The student has asked to find the product of two expressions, (-2x^2)^3 and -3x. To solve this, we first calculate the cube of -2x^2, which is -8x^6, then we multiply this result by -3x to find the final product.
So, let's perform these two steps:
Cube of -2x^2: (-2x^2)^3 = (-2)^3 × (x^2)^3 = -8 × x^6 = -8x^6
Multiplication by -3x: -8x^6 × -3x = 24x^7
Therefore, the product is 24x^7.
South middle school has 750?students. North middle school has 13/15 times as many students as South. Does north middle school have more or fewer than 750 students?
Answer : The north middle school have fewer than 750 students.
Step-by-step explanation:
Let the number of students in south middle school be, x
and the number of students in north middle school be, y
Given:
Number students in south middle school = x = 750
and,
North middle school has 13/15 times as many students as South. That means,
[tex]y=\frac{13}{15}\times x[/tex] ........(1)
Now put the value of 'x' in expression 1, we get:
[tex]y=\frac{13}{15}\times 750[/tex]
[tex]y=650[/tex]
Thus, number of students in north middle school = y = 650
From this we conclude that north middle school have fewer than 750 students.
Hence, the north middle school have fewer than 750 students.
Calculate cos to two decimal places
Five years ago, William bought a twelve-room apartment complex for $340,000, and he plans to sell it today. The real estate market caused William’s complex to increase in value by 1.8% every year. William charges $525 per month to rent a room, and pays $36,500 in building upkeep every year. If William has kept all of his apartments continually rented out since he bought the building, to the nearest hundred dollars, how much profit will he realize once he sells it?
a.
$195,500
b.
$227,200
c.
$226,100
d.
$245,500
Answer:
THE ANSWER IS B ON EGDE
Step-by-step explanation:
Answer:
Edging b
Step-by-step explanation:
Which number families does the number 1 belong to??
Ben wants to buy 2 blue sweaters for 119$ and 3 brown sweaters for 44$ each how much will ben spend on his five sweaters?
A Jeweler has 36 inches of silver chain. She needs 5 times much to make some necklaces and 3 times that amount to make some bracelets. How much does the jeweler need to make her necklaces and bracelets
Step-by-step explanation:
A traffic light near a museum is green for 30 seconds, yellow for 5 seconds, and red for 15 seconds.
If 8 vehicles approach the signal, the probability that 3 of them are stopped by the red light is
If 8 vehicles approach the signal, the probability that 3 of them are stopped by the red light is:
0.25412184
Step-by-step explanation:Here we need to use the binomial theorem.
i.e. the probability of k successes out of total n experiments is calculated by the formula:
[tex]P(X=k)=n_C_kp^k(1-p)^{n-k}[/tex]
where p is the probability of successes.
Here we have p=Probability that signal is red.
i.e. p=15/50=3/10=0.3
Hence, 1-p=0.7
Also we have: n=8
and k=3
Hence,
[tex]P(X=3)=8_C_3\times (0.3)^3(0.7)^{8-3}\\\\\\P(X=3)=\dfrac{8!}{3!\times (8-3)!}\times (0.3)^3\times (0.7)^5\\\\\\P(X=3)=\dfrac{8!}{3!\times 5!}\times 0.00453789\\\\\\P(X=3)=0.25412184[/tex]
Hence, the probability is:
0.25412184
A circle has a central angle measuring 3pi/4 radians that intersects an arc of length 45 in. What is the length of the radius of the circle?
The circumference of a circle is defined to be the _________.
A. the width of the circle
B. length of the radius
C. distance around the circle
D. area of the circle
Answer:
it is the distance of a circle
Step-by-step explanation:
Choose the correct simplification of (4x − 3)(3x2 − 4x − 3).
12x3 + 25x2 + 9
12x3 − 25x2 − 9
12x3 + 25x2 − 9
12x3 − 25x2 + 9 Choose the correct simplification of (4x − 3)(3x2 − 4x − 3).
12x3 + 25x2 + 9
12x3 − 25x2 − 9
12x3 + 25x2 − 9
12x3 − 25x2 + 9
Answer: [tex]12x^3-25x^2+9[/tex]
Step-by-step explanation:
Given expression: [tex](4x-3)(3x^2-4x-3)[/tex]
To simplify the above expression we apply the distributive property [ (b+c)a=ba+ca, where a,b, c be any expression] we get ,
[tex](4x-3)(3x^2-4x-3)\\\\=4x(3x^2-4x-3)-3(3x^2-4x-3)\\\\=12x^{1+2}-16x^{1+1}-12x-9x^2+12x+9.......\text{[by law of exponents]}\\\\=12x^{3}-16x^{2}-12x-9x^2+12x+9\\\\\text{Combing like terms, we get}\\\\=12x^3-(16+9)x^2-12x+12x+9\\\\=12x^3-25x^2+9[/tex]
Answer:
[tex]12x^{3}-25x^{2}+9[/tex]
Step-by-step explanation:
1. Write down the equation:
[tex](4x-3)(3x^{2}-4x-3)[/tex]
2. Multiply the first term on the left parenthesis by each term on the right parenthesis:
[tex]4x*3x^{2}=12x^{3}[/tex]
[tex]4x*(-4x)=-16x^{2}[/tex]
[tex]4x*(-3)=-12x[/tex]
3. Multiply the second term on the left parenthesis by each term on the right parenthesis:
[tex]-3*(3x^{2})=-9x^{2}[/tex]
[tex]-3*(-4x)=12x[/tex]
[tex]-3*(-3)=9[/tex]
4. Add up all the terms:
[tex]12x^{3}-16x^{2}-12x-9x^{2}+12x+9[/tex]
Simplify:
[tex]12x^{3}-25x^{2}+9[/tex]
Find all relative extrema. Use the Second Derivative Test where applicable. (If an answer does not exist, enter DNE.)
f (x) = x2 + 9x − 4 relative minimum
(x, y) =
relative maximum (x, y) =
please help me
...?
Final answer:
To find the relative minimum of the function, we first calculate its first derivative and set it to zero to find critical points. A single critical point is found at x = -9/2. Using the Second Derivative Test, we conclude that there is a relative minimum at (-9/2, -97/4) since the function's second derivative is positive, indicating the function is concave up at this point.
Explanation:
To find the relative extrema of the function f(x) = x2 + 9x − 4, we first need to determine its critical points. This is done by finding the derivative of f(x) and setting it equal to zero.
The derivative of the function, f'(x), can be calculated as follows:
f'(x) = 2x + 9
Setting the derivative equal to zero gives us:
2x + 9 = 0
x = -9/2
Now, we apply the Second Derivative Test to determine if this critical point is a relative maximum or minimum. The second derivative is:
f''(x) = 2
Since the second derivative is positive, the function is concave up at x = -9/2. Therefore, the function has a relative minimum at this point.
To find the y-coordinate, we substitute x = -9/2 into the original function:
f(-9/2) = (-9/2)2 + 9*(-9/2) − 4
Simplifying this, we get:
y = 81/4 - 81/2 - 4
y = 81/4 - 162/4 - 16/4
y = -97/4
Therefore, the relative minimum is (-9/2, -97/4). There is no relative maximum since the function is a parabola that opens upwards.
A sprinter can run 279 feet in 9 seconds. Find the sprinter's unit rate of feet per second.
To find the sprinter's unit rate of feet per second, divide the total distance by the time. In this case, the sprinter's unit rate is approximately 31 feet per second.
Explanation:To find the sprinter's unit rate of feet per second, we need to divide the total distance the sprinter can run by the time it takes. In this case, the sprinter can run 279 feet in 9 seconds. So the unit rate is 279 feet divided by 9 seconds, which is approximately 31 feet per second.
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How do you make 1 3/4 an improper fraction?
The graph of the piecewise function f(x) is shown.
What is the domain of f(x)?
{x | 1 < x < 5}
{x | 1 < x < 5}
{y | −4 < y < 1}
{y | −4 < y < 1}
Answer:
Domain is {x| 1<=x <5}
Step-by-step explanation:
The graph of the piecewise function f(x) is shown.
In the given graph of piecewise function
Domain is the set of x values for which the function is defined
first graph is from x= 1 to 3, 3 is excluded
second graph is from x= 3 to 5, 5 is excluded
So the graph of x values is from x=1 to 5 ( 5 excluded because we have open circle at 5)
Domain is {x| 1<=x <5}
The integer n3 + 2n is divisible by 3 for every positive integer n
prove it by math induction
is it my proof right ?
By the principle of mathematical induction, we have shown that for all positive integers n, n^3 + 2n is divisible by 3.
Proof by Induction: n^3 + 2n is divisible by 3 for all positive integers n.
Base Case:
For n = 1, n^3 + 2n = 1^3 + 2(1) = 3, which is divisible by 3.
Induction Hypothesis:
Assume that for some positive integer k, k^3 + 2k is divisible by 3. We can write this as: k^3 + 2k = 3m, where m is an integer.
Induction Step:
We need to show that (k + 1)^3 + 2(k + 1) is divisible by 3. Expanding the expression:
(k + 1)^3 + 2(k + 1) = k^3 + 3k^2 + 3k + 1 + 2k + 2
= (k^3 + 2k) + (3k^2 + 3k + 3)
Substituting the induction hypothesis:
= 3m + 3(k^2 + k + 1)
= 3(m + k^2 + k + 1)
Since k^2 + k + 1 is an integer (sum of three integers), and m is an integer, their sum (m + k^2 + k + 1) is also an integer. Therefore, (k + 1)^3 + 2(k + 1) is divisible by 3.
the 6 a.m. temperatures for Four constructed days in the town of Lincoln were -12.1 Celsius -7.8 Celsius -14.3 Celsius and -7.2 Celsius what was the average 6 a.m. temperature for the four days
Related Rates
A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 2.1 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building?
once you have that relation, then you can replace the variables by the numbers given. by similar triangles that relation is
y12=2x then differentiate both sidesIn a basic sine curve, where can the zeros NOT be found
a thermometer is guaranteed to give a temperature no more than 1.2 degrees farenheit from the actual temperature. if thermometer reads 28 degrees farenheit, write and solve equation to find max and min temps could be
Copycats copies charges $.18 for the first copy and $.12 for each additional copy what is the greatest number of copies you can get for three dollars
SOLVE. (2ax + 1/2 bx)2 ...?
Explanation of how to expand and simplify the given quadratic expression Hence answer is 4a²x² + abx² + 1/4b²x²,
Solve the equation: (2ax + 1/2 bx)²
Expanding the given expression:
(2ax + 1/2 bx)²
= (2ax)² + (2ax) (1/2 bx) + (1/2 bx)²
= 4a²x² + 2abx² + 1/4b²x²
= 4a²x² + abx² + 1/4b²x²
Answer: 4a²x² + abx² + 1/4b²x²
TRUE or FALSE.
Based only on the information given in the diagram, it is guaranteed that ΔABC ≈ ΔXYZ.
It is a true statement that it is guaranteed that ΔABC ≈ ΔXYZ in the diagram given.
Why will ΔABC equals ΔXYZ?In this context, all triangles have 180 degrees altogether in as much they have a standard size of the shape.
The triangles have the sames standard size although the letters of the angles are different.
Therefore, the statement is a true statement.
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Given the function, f(x)=[square root] x+3-2 , calculate the average rate of change between x=6 and x=13.
Answer:
Average rate for the given function is 1 / 7
Step-by-step explanation:
The average exchange rate corresponds to the ratio between the variation of the function and the variation of the variable. That is to say,
Average rate = [f (x2) - f (x1)] / (x2 -x1). Since x1 = 6 and x2 = 13, you have:
f (x1) = f (6) = sqrt (6 + 3) - 2 = 3 - 2 = 1
f (x2) = f (13) = sqrt (13 + 3) - 2 = 4 - 2 = 2
In this way,
Average rate = (2 -1) / (13 - 6) = 1/7
Math question: Write the equation of the line with an undefined slope, passing through the point (2, 5).
The equation of a line with an undefined slope passing through the point (2, 5) can be written as x = 2.
When the slope of a line is undefined, it means that the line is vertical. In a vertical line, the x-coordinate remains constant while the y-coordinate can take any value.
So, for this line passing through the point (2, 5), the x-coordinate will always be 2, regardless of the value of y. Therefore, we can represent this line with the equation x = 2.
Donald earns a commission of 3.7% on all sales above his weekly quota of $12,500. his sales last week totaled $32,480. what commission amount did Donald earn last week?
Donald earned a commission of $739.26 last week.
Explanation:To calculate the commission amount earned by Donald last week, we need to find the sales above his weekly quota first. Sales above the quota is calculated by subtracting the weekly quota from the total sales. In this case, $32,480 - $12,500 = $19,980. Next, we can calculate the commission amount by multiplying the sales above the quota by the commission rate. The commission amount earned by Donald last week is $19,980 * 0.037 = $739.26.
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For exercises 19-24, y varies directly with x
if y = 25 when x = 15, find y when x = 6.
Help me explain how to do it step by step !
Ms. Purdy bought coffee and orange juice for her coworkers in her office.She bought X cups of coffee at $2 per cup and Y cups of orange juice at $1.50 per cup. Altogether she spent $30. Interpret the X- and the Y- Intercepts
Final answer:
The X-intercept of the equation 2X + 1.5Y = 30 represents the maximum number of cups of coffee that can be bought with $30 if no orange juice is purchased (15 cups), and the Y-intercept represents the maximum number of orange juice cups that can be bought with $30 if no coffee is purchased (20 cups).
Explanation:
When Ms. Purdy purchased coffee and orange juice for her coworkers, she created a budget constraint based on the respective prices and her total spending. With X representing the number of cups of coffee purchased at $2 each and Y representing the cups of orange juice purchased at $1.50 each, the equation for her total expenditure is 2X + 1.5Y = 30.
The X-intercept occurs when no orange juice is purchased (Y=0), and the total budget is spent on coffee.
This can be calculated by setting Y to 0 in the equation, resulting in X = 15.
The Y-intercept occurs when no coffee is purchased (X=0), which can be found by setting X to 0, leading to Y = 20.
Thus, the X-intercept represents the maximum number of cups of coffee that can be purchased with the $30 budget if no orange juice is bought, while the Y-intercept shows the maximum number of cups of orange juice that could be purchased with the same budget if no coffee is bought.
. Evaluate 9C5
126
24
3024
120
...?
Answer:
126 is the answer please give me brainliest.
Step-by-step explanation:
The sum of two numbers is 27. the larger number is 6 more than twice the smaller number. what are the numbers?
Suppose you went to a carnival. The price to get in was $6, and you paid $0.50 to get on each ride. If you went to the carnival and rode 11 rides, how much did you spend?
The total money that would be spent for 11 rides in the carnival be $11.5
As mentioned in the question, the price to get in was $6, and you paid $0.50 to get on each ride.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Let the total money paid for 11 rides,
= 0.5 × 11 = $5.5
Total money spent on the carnival,
= 6 + 5.5 = $11.5
Thus, the total money that would be spent for 11 rides in the carnival be $11.5.
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A ball bearing is shaped like a sphere and has a diameter os 2.5 centimeters l. What is the volume contained inside the ball bearing? Use 3.14 pi. Round your answer to the nearest hundredth
The volume of the ball bearing, which is a sphere, would be approximately 8.18 cm³. This is calculated using the formula for the volume of a sphere and the given diameter, which is halved to get the radius for the calculation
Explanation:The volume of a sphere can be calculated using the formula V = 4/3 * π * r³, where r is the radius of the sphere. In this case, the diameter of the ball bearing is 2.5 cm, so the radius would be half of that (diameter/2), which is 1.25 cm. Substituting the radius value to the volume formula, we get: V = 4/3 * π * (1.25cm)³ = 4/3 * 3.14 * 1.95cm³ = approximately 8.18 cm³, rounded to the nearest hundredth.
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