For the last part, you have to find where [tex]f'(t)[/tex] attains its maximum over [tex]0\le t\le8[/tex]. We have
[tex]f'(t)=-6\sin3t+6\cos2t[/tex]
so that
[tex]f''(t)=-18\cos3t-12\sin2t[/tex]
with critical points at [tex]t[/tex] such that
[tex]-18\cos3t-12\sin2t=0[/tex]
[tex]3\cos3t+2\sin2t=0[/tex]
[tex]3(\cos^3t-3\cos t\sin^2t)+4\sin t\cos t=0[/tex]
[tex]\cos t(3\cos^2t-9\sin^2t+4\sin t)=0[/tex]
[tex]\cos t(12\sin^2t-4\sin t-3)=0[/tex]
So either
[tex]\cos t=0\implies t=\dfrac{(2n+1)\pi}2[/tex]
or
[tex]12\sin^2t-4\sin t-3=0\implies\sin t=\dfrac{1\pm\sqrt{10}}6\implies t=\sin^{-1}\dfrac{1\pm\sqrt{10}}6+2n\pi[/tex]
where [tex]n[/tex] is any integer. We get 8 solutions over the given interval with [tex]n=0,1,2[/tex] from the first set of solutions, [tex]n=0,1[/tex] from the set of solutions where [tex]\sin t=\dfrac{1+\sqrt{10}}6[/tex], and [tex]n=1[/tex] from the set of solutions where [tex]\sin t=\dfrac{1-\sqrt{10}}6[/tex]. They are approximately
[tex]\dfrac\pi2\approx2[/tex]
[tex]\dfrac{3\pi}2\approx5[/tex]
[tex]\dfrac{5\pi}2\approx8[/tex]
[tex]\sin^{-1}\dfrac{1+\sqrt{10}}6\approx1[/tex]
[tex]2\pi+\sin^{-1}\dfrac{1+\sqrt{10}}6\approx7[/tex]
[tex]2\pi+\sin^{-1}\dfrac{1-\sqrt{10}}6\approx6[/tex]
The correct answer for part (d) is: The particle is moving the fastest at [tex]\( t = 4.7 \)[/tex] with a speed of [tex]5[/tex] units per time period.
To find when the particle is moving the fastest, we need to determine the time at which the velocity of the particle is maximized. The velocity of the particle is given by the derivative of the position function with respect to time. The position function is [tex]\( f(t) = 2 \cos(3t) + 3 \sin(2t) \)[/tex]. Differentiating this with respect to [tex]\( t \)[/tex] gives the velocity function:
[tex]\[ v(t) = \frac{d}{dt}(2 \cos(3t) + 3 \sin(2t)) = -6 \sin(3t) + 6 \cos(2t) \][/tex]
To find the maximum velocity, we need to find the critical points of the velocity function by setting its derivative equal to zero:
[tex]\[ \frac{d}{dt}(-6 \sin(3t) + 6 \cos(2t)) = -18 \cos(3t) - 12 \sin(2t) = 0 \][/tex]
Solving for [tex]\( t \)[/tex] in the interval [tex]\( 0 \leq t \leq 8 \)[/tex] will give us the times at which the velocity is maximized or minimized. Let's solve for [tex]\( t \)[/tex]:
[tex]\[ -18 \cos(3t) = 12 \sin(2t) \][/tex]
This is a transcendental equation and cannot be solved algebraically. We would typically use numerical methods or graphing to find the solutions. However, since we are given that the time when the particle is moving the fastest is [tex]\( t = 4.7 \)[/tex], we can assume that this is the time at which the velocity function reaches its maximum value.
Now, to find the speed at which the particle is moving the fastest, we evaluate the velocity function at [tex]\( t = 4.7 \)[/tex]:
[tex]\[ v(4.7) = -6 \sin(3 \cdot 4.7) + 6 \cos(2 \cdot 4.7) \][/tex]
Calculating the sine and cosine values and then substituting them into the equation will give us the maximum velocity. Since we are looking for the speed, which is the absolute value of the velocity, we take the absolute value of the result.
The speed is given by the magnitude of the velocity vector, so we have:
[tex]\[ |v(4.7)| = |-6 \sin(3 \cdot 4.7) + 6 \cos(2 \cdot 4.7)| \][/tex]
Evaluating this expression will give us the speed at which the particle is moving the fastest. The correct answer, rounded to the nearest integer, is [tex]\( 5 \)[/tex] units per time period, not [tex]\( -5 \).[/tex] The negative sign in the velocity does not affect the speed, as speed is a scalar quantity and is always positive.
Therefore, the particle is moving the fastest at [tex]\( t = 4.7 \)[/tex] with a speed of [tex]\( 5 \)[/tex] units per time period.
If a sphere's volume is doubled, what is the corresponding change in its radius? A. The radius is increased to 20 times the original size. B. The radius is increased to 4 times the original size. C. The radius is increased to 2 times the original size. D. The radius is increased to 8 times the original size
Answer:
The radius is increased by 1.2599 times the original size.
Step-by-step explanation:
The volume is 3 dimensional whereas the radius is one dimensional.
Therefore the factor for the radius will be the cube root of the factor for the volume.
So the radius is increased by 1.2599.
The circumference of a circle is 28pi inches. What is the length of the radius of this circle?
[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=28\pi \end{cases}\implies 28\pi =2\pi r\implies \cfrac{28\pi }{2\pi }=r\implies 14=r[/tex]
Question 1(Multiple Choice Worth 2 points) Find the derivative of f(x) = 7 divided by x at x = 1.
-7
-1
1
7
Question 2(Multiple Choice Worth 2 points) Find the derivative of f(x) = 4x + 7 at x = 5.
4
1
5
7
Question 3(Multiple Choice Worth 2 points) Find the derivative of f(x) = 12x2 + 8x at x = 9.
256
-243
288
224
Question 4(Multiple Choice Worth 2 points) Find the derivative of f(x) = negative 11 divided by x at x = 9.
11/9
81/11
9/11
11/81
Question 5 (Essay Worth 2 points) The position of an object at time t is given by s(t) = 1 - 10t. Find the instantaneous velocity at t = 10 by finding the derivative.
Answer:
Step-by-step explanation:
Question 1:
For this case we must find the derivative of the following function:
[tex]f (x) = \frac {7} {x}[/tex] evaluated at [tex]x = 1[/tex]
We have by definition:
[tex]\frac {d} {dx} [x ^ n] = nx ^ {n-1}[/tex]
So:
[tex]\frac {df (x)} {dx} = - 1 * 7 * x ^ {- 1-1} = - 7x ^ {- 2} = - \frac {7} {x ^ 2}[/tex]
We evaluate in [tex]x = 1[/tex]
[tex]- \frac {7} {x ^ 2} = - \frac {7} {1 ^ 2} = - 7[/tex]
ANswer:
Option A
Question 2:
For this we must find the derivative of the following function:
[tex]f (x) = 4x + 7\ evaluated\ at\ x = 5[/tex]
We have by definition:
[tex]\frac {d} {dx} [x ^ n] = nx ^ {n-1}[/tex]
The derivative of a constant is 0
So:
[tex]\frac {df (x)} {dx} = 1 * 4 * x ^ {1-1} + 0 = 4 * x ^ 0 = 4[/tex]
Thus, the value of the derivative is 4.
Answer:
Option A
Question 3:
For this we must find the derivative of the following function:
[tex]f (x) = 12x ^ 2 + 8x\ evaluated\ at\ x = 9[/tex]
We have by definition:
[tex]\frac {d} {dx} [x ^ n] = nx ^ {n-1}[/tex]
So:
[tex]\frac {df (x)} {dx} = 2 * 12 * x ^ {2-1} + 1 * 8 * x ^ {1-1} = 24x + 8 * x ^ 0 = 24x + 8[/tex]
We evaluate for [tex]x = 9[/tex]we have:
[tex]24 (9) + 8 = 224[/tex]
Answer:
Option D
Question 4:
For this we must find the derivative of the following function:
[tex]f (x) = - \frac {11} {x}\ evaluated\ at\ x = 9[/tex]
We have by definition:
[tex]\frac {d} {dx} [x ^ n] = nx ^ {n-1}[/tex]
So:
[tex]\frac {df (x)} {dx} = - (- 1 * 11 * x ^ {- 1-1}) = 11x ^ {- 2} = \frac {11} {x ^ 2}[/tex]
We evaluate for [tex]x = 9[/tex] and we have:
[tex]\frac {11} {9 ^ 2} = \frac {11} {81}[/tex]
ANswer:
Option D
Question 5:
For this case we have by definition, that the derivative of the position is the velocity. That is to say:
[tex]\frac {d (s (t))} {dt} = v (t)[/tex]
Where:
s: It's the position
v: It's the velocity
t: It's time
We have the position is:
[tex]s (t) = 1-10t[/tex]
We derive:
[tex]\frac {d (s (t))} {dt} = 0- (1 * 10 * t ^ {1-1}) = - 10 * t ^ 0 = -10[/tex]
So, the instantaneous velocity is -10
Answer:
-10
Niu has decorated xxx cards. He started with 242424 stickers, and he used 444 stickers per card. Which expressions can we use to describe how many stickers Niu has left?
Answer:
The required expression is 24 - 4x
Step-by-step explanation:
Given,
Initial number of stickers she has = 24,
Also, the number of stickers she used for a card = 4,
⇒ the number of stickers she used for x cards = 4x,
So, the number of stickers she left after decorating x cards = Initial number of stickers - the number of stickers used for x cards,
= 24 - 4x
Which is the required expression.
i don't understand this ;-;
Sally can paint a room in 7 hours and John can paint the same room in 10 hours. How long should it take Sally and John to paint the room together?
Answer:
17 hours
Step-by-step explanation:
As we know altogether means how many in all or in an easier saying the total.The total is 17.Hope that help you!
If the area of a square is 64 square centimeters, what's the length of one side? A. 8 cm B. 4 cm C. 32 cm D. 16 cm
Answer:
8
Step-by-step explanation:
So a square is equal on all sides if I'm correct so. The area is pretty much the length x width. So 8 times 8 equals 64.
Hope this helps, have a good day
s = 8cm (Answer A)
Step-by-step explanation:
The area of a square, A, is the square of the length of any one side:
A = s².
If A = 64 cm², then 64 cm² = s².
Taking the square root of both sides yields s = 8cm (Answer A)
Line q goes through points (-3,3) and (-5,-3). At what point does line q cross the y-axis ?
Answer:
(0,12)
Step-by-step explanation:
To write the equation of a line, calculate the slope between points (-3,3) and (-5,-3). After, substitute the slope and a point into the point slope form. Then convert to the slope intercept form to identify the y-intercept.
[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{3--3}{-3--5}= \frac{6}{2}=3[/tex]
Substitute m = 3 and the point (-3,3) into the point slope form.
[tex]y - y_1 = m(x-x_1)\\y -3 = 3(x--3)\\y-3 = 3(x +3)\\y-3=3x + 9\\ y = 3x + 12[/tex]
This means that it crosses at (0,12) since b - 12 for y=mx+b.
Answer:(0,12)
Step-by-step explanation:
Assume that the readings on the thermometers are normally distributed with a mean of 0 degrees and standard deviation of 1.00degreesC. Assume 2.8% of the thermometers are rejected because they have readings that are too high and another 2.8% are rejected because they have readings that are too low. Draw a sketch and find the two readings that are cutoff values separating the rejected thermometers from the others.
Answer:
1.91° and -1.91°.
Step-by-step explanation:
2.8% of the thermometers are rejected on either end of the curve. The bottom end, where the readings are too far below the mean, will have an area from this point to the left tail of the curve of 0.028.
The top end, where the readings are too far above the mean, will have an area from this point to the left tail of the curve of 1-0.028 = 0.972.
We look in a z table for these values. We look within the cells of the table; the closest value to 0.028 is 0.0281, which corresponds with a z score of -1.91. The closest value to 0.972 is 0.9719, which corresponds with a z score of 1.91.
We substitute these values into the z score formula, along with our values for the mean (0) and the standard deviation (1):
[tex]-1.91=\frac{X-0}{1}[/tex]
Simplifying the right hand side, X-0 = X; X/1 = X. This means X = -1.91.
For the second value,
[tex]1.91=\frac{X-0}{1}[/tex]
Simplifying the right hand side, X-0 = X; X/1 = X. This means X = 1.91.
This means the two values are 1.91° and -1.91°.
The cutoff values separating the rejected thermometers in a normally distributed thermometer reading with a mean of 0 and a standard deviation of 1°C are -1.88°C and +1.88°C. These values are determined using the z-scores that corresponds to the tail probabilities (2.8%) of the normal distribution.
Explanation:The question involves determining the cutoff values that separate the rejected thermometers based on a normally distributed thermometer reading. We know that 2.8% of the thermometers are rejected for being too high, and another 2.8% for being too low. Here, this involves using the concept of the normal distribution and z-scores.
First, since each tail contains 2.8% of the data, the cumulative probability up to the cutoff point will be 100% - 2.8% = 97.2% for the higher cutoff and 2.8% for the lower cutoff. To find the z-scores that correspond to these areas, you can consult a standard normal distribution table or use an online tool. Typically, z-scores around ±1.88 correspond to a cumulative probability closest to 97.2% and -1.88 for 2.8%.
Since the mean (μ) is 0 and the standard deviation (σ) is 1°C, the thermometer readings the cutoff values or z-scores represent are given by z = (X - μ)/σ. Therefore, the thermometer readings for these z-scores are -1.88°C and +1.88°C. These are the cutoff values which separate the rejected thermometers.
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A rectangular prism has a volume of 729ft^3. The length width and height are the same. What is the length of each side
Answer:
9 feet
Step-by-step explanation:
If each side is the equivalent, each side of the prism is the cube root of 729
Cube root of 729 is 9
Each side is 9 feet long
What is the 101st term in the sequence 876, 869, 862, ...?
1583
176
1576
169
Answer:
176
Step-by-step explanation:
We see that it is an arithmetic sequence since we are subtracting the same number to a term to get the next term. So 876 - 7 = 869 & 869 - 7 = 862.
So the common difference d is -7
and the first term, a is 876
The nth term of an arithmetic sequence is given by a + (n-1)d
where n would be 101, since we want to figure 101st term.
So:
[tex]a+(n-1)d\\876+(101-1)(-7)\\876+(100)(-7)\\=176[/tex]
Correct answer is the 2nd choice, 176
The 101st term in the sequence 876, 869, 862, ... is 176, found by using the formula for the nth term of an arithmetic sequence with a common difference of -7.
Explanation:To find the 101st term in the sequence 876, 869, 862, ..., we first need to determine the common difference of the arithmetic sequence. Each term decreases by 7 (869 - 876 = -7 and 862 - 869 = -7), so the common difference is -7.
Now, we use the formula for the nth term of an arithmetic sequence, which is an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.
The 101st term is calculated as follows:
a1 = 876 (the first term)d = -7 (the common difference)n = 101 (the term number we want to find)So, a101 = 876 + (101 - 1)(-7)a101 = 876 - 700a101 = 176Thus, the 101st term is 176.
Simplify the irrational number 75; then estimate it to two decimal places.
Answer:
[tex]5\sqrt{3}[/tex] OR [tex]8.69[/tex]
Step-by-step explanation:
Let's first simplify [tex]\sqrt{75}[/tex].
5 and 15 multiply to get 75. 5 and 3 multiply to get 15. Since we have a pair of fives and a three leftover, we can write [tex]\sqrt{75}[/tex] as:
[tex]5\sqrt{3}[/tex]
Now, let's find the answer in decimal form. We know that:
[tex]8^2=64[/tex] and [tex]9^2=81[/tex]
With that information, we know that the answer has to be between 8 and 9.
Divide 75 by 8: [tex]\frac{75}{8}=9.375[/tex]
Take the average of that answer and 8: [tex]\frac{9.375+8}{2}=\frac{17.375}{2}=8.6875[/tex]
This answer we got is extremely close to the exact answer of [tex]\sqrt{75}[/tex], which is [tex]8.66025403...[/tex]. Since we are estimating, the answer above will do just fine.
You scored a 95% on your math quiz.The quiz was out of 60 points.How many points did you get
Find the measure of the angle with the greatest measure (picture provided)
Answer:
The measure of the greatest angle is about 81° ⇒ answer (b)
Step-by-step explanation:
* Let the given triangle is ΔABC where,
- a = 18 inches ⇒ opposite to angle A
- b = 21 inches ⇒ opposite to angle B
- c = 14 inches ⇒ opposite to angle C
∵ The greatest angle is opposite to the largest side
∴ The greatest angle will be angle B because b is the largest side
* By using cos Rule:
∵ b² = a² + c² - 2ac cos(B)
* Lets re-arrange the terms to find the measure of angle B
∴ 2ac cos(B) = a² + c² - b²
∴ cos(B) = (a² + c² - b²)/2ac
∴ cos(B) = (18² + 14² - 21²)/2(18)(14) = 79/504
∴ m∠B = 80.98 ≅ 81°
∴ The measure of the greatest angle is about 81°
How many total circles will be used if there are 20 rows of circles? Show all calculations.
Answer:
210
Step-by-step explanation:
As there is one circle in first row, 2 circles in 2nd row and three in third row, which clearly implies that the number of circles in each row is equal to the row number. So, we have to calculate sum of first 20 numbers to calculate the total number of circles.
n=20
Total Circles=(n(n+1))/2
=(20 (20+1))/2
=(20(21))/2
= 420/2
=210
So the total number of circles will be 210.
Find the missing sides.
Answer:
Part 3)
[tex]x=6\ units[/tex]
[tex]y=3\ units[/tex]
Part 4) [tex]x=18\sqrt{2}\ units[/tex]
Step-by-step explanation:
Part 3)
step 1
Find the value of x
In the right triangle of the figure we know that
The cosine of angle of 30 degrees is equal to the adjacent side to angle of 30 degrees divide by the hypotenuse
so
[tex]cos(30\°)=\frac{3\sqrt{3}}{x}[/tex]
and remember that
[tex]cos(30\°)=\frac{\sqrt{3}}{2}[/tex]
substitute
[tex]\frac{\sqrt{3}}{2}=\frac{3\sqrt{3}}{x}[/tex]
Simplify
[tex]x=(2*3)=6\ units[/tex]
step 2
Find the value of y
In the right triangle of the figure we know that
The sine of angle of 30 degrees is equal to the opposite side to angle of 30 degrees divide by the hypotenuse
so
[tex]sin(30\°)=\frac{y}{x}[/tex]
and remember that
[tex]sin(30\°)=\frac{1}{2}[/tex]
substitute
[tex]\frac{1}{2}=\frac{y}{6}[/tex]
[tex]y=6/2=3\ units[/tex]
Part 4) Find the value of x
Applying the Pythagoras Theorem
[tex]x^{2} =18^{2} +18^{2} \\ \\x^{2} = 324+324\\ \\x^{2}=648\\ \\x=\sqrt{648}\ units[/tex]
Simplify
[tex]x=18\sqrt{2}\ units[/tex]
Complete the square to transform the quadratic equation into the form (x –p)2= q.X2-8x -10 = 18
Answer:
[tex](x-4)^{2}=44[/tex]
Step-by-step explanation:
we have
[tex]x^{2}-8x-10=18[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]x^{2}-8x=18+10[/tex]
[tex]x^{2}-8x=28[/tex]
Complete the square . Remember to balance the equation by adding the same constants to each side
[tex]x^{2}-8x+16=28+16[/tex]
[tex]x^{2}-8x+16=44[/tex]
Rewrite as perfect squares
[tex](x-4)^{2}=44[/tex]
I REALLY NEED SOMEONES HELP ON THIS PLEASE!! I NEED THIS DONE TODAY!
Error analysis: Describe the error in the way the product of the two binomials is set up and/or solved. Please be specific. (Image is listed below)
Solve the problem in the question above correctly. Please show your work!
[tex]\huge\boxed{\text{The $5$ needs to be negative.}}[/tex]
Since the first binomial is [tex](x-5)[/tex], the [tex]5[/tex] is negative and must be that way when using the table.
Here's the corrected table:
[tex]\begin{array}{c|c|c|}\multicolumn{1}{c}{}&\multicolumn{1}{c}{3x}&\multicolumn{1}{c}{1}\\\cline{2-3}x&3x^2&x\\\cline{2-3}-5&-15x&-5\\\cline{2-3}\end{array}\\\\\\3x^2+x-15x-5\\3x^2-14x-5[/tex]
Find the length of side BA. Round to the nearest hundredth.
A) .42
B) .65
C) .83
D) 1.25
Answer:
Option A. [tex]0.42[/tex]
Step-by-step explanation:
we know that
Applying the law of cosines
[tex]BA^{2}=(1/2)^{2}+(1/3)^{2} -2(1/2)(1/3))cos(100)[/tex]
[tex]BA^{2}=0.1756[/tex]
[tex]BA=0.42[/tex]
WILL GIVE BRAINLIEST
Plz help me.... : /
Answer:
(-7 , 3)
Step-by-step explanation:
3x^2 + 12x = 63 //Subtract 63 on both sides.
3x^2 + 12x - 63 = 0 //Common factor 3.
3(x^2 + 4x - 21) = 0 //Divide both sides by 3.
(x^2 + 7x - 3x - 21) = 0
x(x + 7) - 3(x + 7) = 0
(x + 7) (x - 3) = 0
x = -7 and 3
Solution: (-7, 3)
Compute the exact value of the function for the given x-value without using a calculator.F(x)=6^x for x = -3
[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ f(x)=6^x\qquad \boxed{x=-3}\qquad \implies f(-3)=6^{-3}\implies f(-3)=\cfrac{1}{6^3} \\\\\\ f(-3)=\cfrac{1}{6\cdot 6\cdot 6}\implies f(-3)=\cfrac{1}{36\cdot 6}\implies f(-3)=\cfrac{1}{216}[/tex]
Answer: B on Edg
Step-by-step explanation:
Sketch a graph y = |x – 3| – 2 and describe the translations.
Answer:
Shifted horizontally to the right 3 units, and shifted vertically down 2 units
Step-by-step explanation:
The parent graph of this equation is y = |x|
There are 2 translations to this graph for the equation y = |x - 3| - 2
The "x - 3" part shifts the graph to the right 3 units
The -2 shifts the graph vertically down 2 units
See below for the parent graph, and the graph of the equation we are working with
The graph of function y = |x - 3| - 2 is shown in figure.
What is Translation?A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
The equation is,
⇒ y = |x - 3| - 2
Now,
Since, The equation is,
⇒ y = |x - 3| - 2
Clearly, The equation y = |x - 3| - 2 is the translation of y = |x| with 3 units right and 2 units up.
Thus, The graph of function y = |x - 3| - 2 is shown in figure with 3 units right and 2 units up translation of y = |x|.
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According to the Rational Root Theorem, which of the following values is a possible rational root of the polynomial p(x)=x2+3x+12?
A. 24
B. -1/2
C. -2
D. 1/6
E. 1/2
Answer:
C. -2
Step-by-step explanation:
Since the leading coefficient is 1 and rational roots are of the form ...
±(divisor of the constant)/(divisor of the leading coefficient)
all of the possible rational roots must be whole number diviors of 12. The only one on the list is -2.
The Rational Root Theorem allows us to determine that -2 is a possible rational root for the polynomial p(x)=x2+3x+12.
Explanation:According to the Rational Root Theorem, the possible rational roots of a polynomial equation can be found by taking all the factors of the constant term (in this case, 12) and dividing them by all the factors of the leading coefficient (in this case, 1 as the coefficient for x2 is 1). The factors of 12 are ±1, ±2, ±3, ±4, ±6, ±12. As our leading coefficient is 1, our possible roots can include ±1, ±2, ±3, ±4, ±6, ±12.
Looking at the list of options provided: A. 24, B. -1/2, C. -2, D. 1/6, E. 1/2, we see that only -2 is a possible rational root for the polynomial p(x)=x2+3x+12 based on the Rational Root Theorem.
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Which values of k would the product of k/3 times 12 be greater than 12? A. For any valu of k less than 1 but greater than 0. B. For any value of k less than 3 but greater than 1,. C. For any value of k equal to 3. D. For any value of k greater than 3
Answer:
k > 3
Option D
For any value of k greater than 3
Step-by-step explanation:
We ara dealing with an inequality
(k/3)*12 > 12
Dividing by 12 each side
(k/3)*12/12 > 12/12
(k/3) > 1
Multiplying by three
3*(k/3) > 3*1
k > 3
Answer:
k > 3
Option D
For any value of k greater than 3
Step-by-step explanation:
Your car gets 25 miles to the gallon, and gas prices are $3 per gallon. How much gas money will you spend on gas each week?
Answer:
whew chiile
Step-by-step explanation:
Please help quickly!
Match the following items by evaluating the expression for x = -6.
x -2
x -1
x 0
x 1
x 2
Choices;
-6
36
-1/6
1
1/36
Answer:
If those are supposed to be exponents the answers are:
1. 1/36
2. - 1/6
3. 1
4. -6
5. 36
Step-by-step explanation:
The student is provided with the correct evaluations of five expressions given the value x = -6. Each expression is computed, and the correct numerical matches are presented.
The student is attempting to solve expressions given the value of x = -6. To find the correct matches, each expression must be computed separately. Let's start by calculating the given expressions:
x - 2: When x is -6, the expression becomes (-6) - 2 = -8.
x - 1: When x is -6, the expression becomes (-6) - 1 = -7.
x + 0: When x is -6, the expression is simply -6.
x + 1: When x is -6, the expression becomes (-6) + 1 = -5.
x + 2: When x is -6, the expression becomes (-6) + 2 = -4.
With these computations, the matches would be:
x - 2 matches with -8
x - 1 matches with -7
x + 0 matches with -6
x + 1 matches with -5
x + 2 matches with -4
A two gallon container had all of its dimensions tripled. How many gallons does the new container hold?
When the dimensions of a two gallon container are tripled, the container can hold up to 54 gallons of liquid, since the volume will increase 27 times.
Explanation:The question is about how a two gallon container can hold when all of its dimensions are tripled. In mathematics, when dimensions of a cube (or a rectangular prism, which the container can be assumed to be) are increased proportionally, the volume, which is proportional to the cube of the dimensions, increases by the cube of that same factor.
In this case, the dimensions of the container have all been tripled (a three-fold increase) which results in the volume of the space inside the container increasing by 3³ = 27 times. Therefore, the two gallon container, when its dimensions are tripled, can hold 2 gallons x 27 = 54 gallons. It's important to understand this is a principle of geometry and works irrespective of the units of measurement used (gallons, liters, cubic centimeters, etc.)
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There are 11 red checkers and 5 black checkers in a bag. Checkers are selected one at a time, with replacement. Each time, the color of the checker is recorded. Find the probability of selecting a red checker exactly 6 times in 9 selections. Show your work.
Answer:
P(6 times in 9 selection) = 0.116
Step-by-step explanation:
There are 11 red checkers and 5 black checkers in a bag so
P(red) = no. of red checkers / total no. of checkers = 11/(11+5) = 11/16
Checkers are selected one at a time, with replacement. So P(red) is the same for every selection at 11/16.
Use binomial distribution to find the probability of selecting a red checker exactly 6 times in 9 selections.
In this case, n = 9 and k = 6, P(red)=11/16 so
P(6 times in 9 selection) = nCk * P(red)^k * (1-P(red))^(n-k)
where 9C7 = 9! / [7!*(9-7)!] = 9! / 7!*2! = 9*8 / 2 =36
so P(6 times in 9 selection)
= 36 * (11/16)^6 * (5/16)^3
= 0.116
The context is a binomial distribution where success is defined as drawing a red checker from the bag. With replacement, each draw is independent. Therefore, the formula for binomial probability can be used to calculate the probability of drawing a red checker exactly 6 times in 9 draws.
Explanation:This is a problem of the binomial distribution. For a binomial distribution, each trial is independent, meaning the result of the previous trial does not affect the result of the next trial. This is satisfied since the question states that the checkers are selected with replacement.
'Success' in this context is defined as selecting a red checker which occurs with a probability of 11/16 (since there are 11 red checkers out of a total of 16). Failure is defined as selecting a black checker which occurs with a success probability of 5/16.
To find the probability of selecting a red checker exactly 6 times in 9 selections, we use the formula for binomial probability: P(k; n, p) = C(n, k) * (p^k) * (1 - p)^(n-k). Here, n=9 (number of trials), k=6 (desired 'successes') and p=11/16. When you substitute these values into the formula, you get the desired probability.
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What is accurate about the scientific results learned by counting tree rings? Study of tree rings and associated geology shows that the Earth is 12,000 years old, but no older. Study of tree rings and associated geology shows that the Earth is exactly 12,429 years old. Study of tree rings by themselves shows that the Earth is 4.6 billion years old. Study of tree rings and associated geology shows that the Earth is more than 12,429 years old. Study of tree rings and associated geology proves that the Earth is 5,000 years old, but no older.
Answer:
The correct answer is "Study of tree rings and associated geology shows that the Earth is more than 12,429 years old"
Step-by-step explanation:
While tress have been growing long enough to prove the earth is more than 12,000 years old, it is not able to prove much longer than that. Luckily geology is able to show is that Earth is over 4.6 billions years old. As a result, the above is the only true statement.
The age of the Earth is approximately 4.5 billion years, as determined by radioactive dating methods and supported by other geological evidence. Although not directly determining the Earth's age, the study of tree rings provides valuable information about climate conditions in specific periods.
Explanation:The scientific study of tree rings, known as dendrochronology, can provide valuable information about the Earth's climate in different periods. However, it doesn't directly determine the overall age of the Earth.
Conversely, radioactive dating methods, like uranium-238 dating or rubidium-strontium dating, have been used to determine the Earth's age by dating the oldest rocks and minerals on Earth's crust. For example, the Jack Hills zircons from Australia were found by uranium-lead dating to be nearly 4.4 billion years old.
Using these dating methods in connection with the study of tree rings and other geological evidence, scientists have estimated that the age of the Earth is approximately 4.5 billion years.
This age is significantly older than what could be derived from tree rings alone, as the oldest living trees, like the Methuselah tree, are estimated to be just over 4,800 years old.
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Question 10 Unsaved
A real estate agent made a scatter plot with the size of homes, in square feet, on the x-axis and the homeowner's property taxes on the y-axis. The variable have a strong linear correlation and the equation for the least squares regression line is yˆ=0.392x+638.118.
Based on the equation, what should the agent expect the property tax to be for a 2,400-square foot home in the area?
Question 10 options:
$2,464.12
$1,578.92
$1,190.94
$940.80
[tex]y = 0.392x + 638.118 \\ x = 2400 \\ y = (0.392 \times 2400) + 638.118 \\ y = 1578.92[/tex]
hope u understand
I need 7,714 solar panels to power my new workshop. If each box contains 24 panels, about how many boxes should I purchase? Choose the best estimate.
If you need 7, 714 solar panels, and 1 box contains 24 panels then you'll need:
7, 714/24 = 321.4167
This answer estimated can be 321. So yuh might need 321 panels.
ANSWER = 321 PANELS
Answer:300
Step-by-step explanation:
If you need 7, 714 solar panels, and 1 box contains 24 panels then you'll need:
7, 714/24 = 321.4167
This answer estimated can be 321. So yuh might need 321 panels.
ANSWER = 321 PANELS
But the best estimate is 300 pannels