Which is the graph of the cube root function f(x) = cube root of x
Answers
Answer:
The function is given below as
\(f(x)=\sqrt[3]{x}\)Step 1:
We will generate table of values for when x=0
\(\begin{gathered} f(x)=\sqrt[3]{x} \\ when\text{ x=1} \\ y=\sqrt[3]{1} \\ y=1 \\ (1,1) \end{gathered}\)When x=-1
\(\begin{gathered} f(x)=\sqrt[3]{x} \\ y=\sqrt[3]{-1} \\ y=-1 \\ (-1,-1) \end{gathered}\)when x=0
\(\begin{gathered} y=\sqrt[3]{0} \\ y=0 \\ (0,0) \end{gathered}\)When x=8
\(\begin{gathered} y=\sqrt[3]{x} \\ y=\sqrt[3]{8} \\ y=2 \\ (8,2) \end{gathered}\)When x=-8
\(\begin{gathered} y=\sqrt[3]{-8} \\ y=-2 \\ (-8,-2) \end{gathered}\)The table of values is given below as
Using a graphing calculator, we will have the graph be
Related Questions
Find the volume of this sphere use three
Answers
2916 ft³
Step-by-step explanation:Volume helps describe the amount of space that a shape takes up.
Volume of a Sphere
Volume describes the 3-dimensional size of a shape. Since volume is a 3-D measurement, the units should be cubed; this explains why the answer is given in feet cubed. In order to find the volume, we need to use the radius. The radius of a sphere is the distance from the center to the outside. In this case, we are told that the radius is 9 ft.
Volume Formula
Every regular shape has its own volume formula. For a sphere, the formula is:
\(V = \frac{4}{3}\pi r^{3}\)So, to find the volume, all we need to do is plug in the radius. For this sphere, r = 9.
V = 4/3 * 3 * 9³V = 2916When using 3 for pi, the volume of the sphere is 2916 ft³.
Erika's toy is valued at €450. Its value increased by 10% then decreases by 10% the year after. What is the value of Erika's toy after these two changes?
Answers
Answer:
€445.50-------------------------
Initial value of the toy is €450.
After 10% increase the value is:
€450 + 10% = €450*1.1 = €495After further 10% decrease the value becomes:
€495 - 10% = €495*0.9 = €445.50The final value of the toy is €445.50.
A figure is shown, where lines CE and FD intersect at point B.
.
A figure is shown, where lines CE and FD intersect at point B.
.
Angle ABC is complementary to angle DBC.
What is the measure, in degrees of ?
Answers
Answer:
Step-by-step explanation:
Its 4.51
a bag of rice has a mass of 3 kilogram s. Jackie buys 17 bags of rice for the school cafeteria . How many grams of rice did jackie buy?
Answers
Answer:51,000
Step-by-step explanation:
ther is 1000 grams every kilogram so 17x3 is 51 and 51x1000 is 51,000
Eugene's grandmother is teaching him how to make her salsa recipe. Each batch of salsa requires 1 4 of a cup of red onions. If they have 1 1 2 cups of red onions, how many batches of salsa can they make?
Answers
Answer:
they can make 6 batches
Step-by-step explanation:
1/2 = 2/4 1 = 4/4
so if one batch is 1/4, and 4+2 is 6, they can make 6 batches
Answer:
6 Batches
Step-by-step explanation:
The graph of the function f shown in the figure above has horizontal tangents atx=3 and x=6. Ifg(x)=∫02xf(t)dtwhat is the value ofg′(3)?(A) 0 (B)−1(C)−2(D)−3(E)−6
Answers
The horizontal tangents at x=3 and x=6 on the graph of the function f are shown in the given image. If \(g(x)=\int\limits^{2x}_0 {f(t)}\;dt\), then g'(3) is -2. Then, option (C) is correct.
A function's zero slopes is indicated by a horizontal tangent line that runs parallel to the x-axis. The given graph of function f has horizontal tangents at x =3 and x = 6. Then, the given function is \(g(x)=\int\limits^{2x}_0 {f(t)}\;dt\). Then, we have to find g'(3). It is clear from the graph that f(3) = -3 and f(6) = -1.
Then, applying the Leibnitz rule for differentiation of the given function, we get,
\(\begin{aligned} g(x) &= \int^{2x}_0 f(t)\;dt\\g'(x)&=f(2x)\cdot\frac{d}{dx}(2x)-f(0)\cdot\frac{d}{dx}(0)\\&=2f(2x)\end{aligned}\)
Now, substituting x = 3 in the above equation, we get,
\(\begin{aligned}g'(3)&=2f(2\times3)\\&=2f(6)\\&=2\times -1\\&=-2\end{aligned}\)
The required answer is -2.
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An experiment on the teaching of reading compares two methods, A and B. The response variable is the Degree of Reading Power (DRP) score. The experimenter uses Method A in a class of 100 students and Method B in a comparable class of 100 students. Students are assigned to the two classes at random. Suppose that in the population of all children of this age the DRP score has the N(75, 30) distribution if Method A is used and the N(74, 40) distribution if Method B is used. Let us call the mean DRP score for 100 students in the A group. Let us call the mean DRP score for 100 students in the B group ý.
Required:
What is the probability that the mean score for the B group will be at least five points higher than the mean score for the A group?
Answers
Answer:
0% probability that the mean score for the B group will be at least five points higher than the mean score for the A group
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution, the central limit theorem, and subtraction of normal variables:
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction of normal variables:
When we subtract two normal variables, the mean is the subtraction of the mean of each variable, while the standard deviation is the square root of the sum of each variance.
Method A:
One student: N(75,30), so \(\mu = 75, \sigma = 30\)
Samples of 100 students: \(n = 100, s = \frac{30}{\sqrt{100}} = 0.3\)
Method B:
One student: N(74,40), so \(\mu = 74, \sigma = 40\)
Samples of 100 students: \(n = 100, s = \frac{40}{\sqrt{100}} = 0.4\)
What is the probability that the mean score for the B group will be at least five points higher than the mean score for the A group?
This is the probability that B - A >= 5. So
\(\mu_{B-A} = \mu_B - \mu_A = 74 - 75 = -1\)
\(s_{B-A} = \sqrt{s_A^{2}+S_B^{2}} = \sqrt{(0.3)^2+(0.4)^2} = 0.5\)
We have to find 1 subtracted by the pvalue of Z when X = 5. So
\(Z = \frac{X - \mu}{\sigma}\)
By the Central Limit Theorem
\(Z = \frac{X - \mu}{s}\)
\(Z = \frac{5 - (-1)}{0.5}\)
\(Z = 12\)
\(Z = 12\) has a pvalue of 1
1 - 1 = 0, so
0% probability that the mean score for the B group will be at least five points higher than the mean score for the A group
A six-sided die is rolled 120 times. Fill in the expected frequency column. Then, conduct a hypothesis test at the 5% level to determine if the die is fair. The data below are the result of the 120 rolls. (Enter exact numbers as integers, fractions, or decimals.)
Face Value Frequency Expected Frequency
1 14 ?
2 33 ?
3 15 ?
4 14 ?
5 30 ?
6 14 ?
Required:
a. State the null hypothesis.
b. State the alternative hypothesis.
c. What are the degrees of freedom?
Answers
Answer:
Die is not fair given that Pvalue< 0.05, hence we reject Null hypothesis
a) H0: Die = fair
b) Ha : Die ≠ fair
c) df = 5
Step-by-step explanation:
The expected frequency of every face values = 20
a) state Null hypothesis
H0: Die = fair
b) Alternate Hypothesis
Ha : Die ≠ fair
c) degree of freedom
df = ( n - 1 )
= ( 6 - 1 ) = 5
n = sample size ( number of faces a die has )
Note : After conducting hypothesis test
Pvalue ≈ 0.0026
test statistic ≈ 18.30
Hence we can conclude that die is not fair given that Pvalue < 0.05, hence we reject Null hypothesis
Solve the equation for w.
4w + 2 + 0.6w = −3.4w − 6
No solution
w = 0
w = 1
w = −1
Answers
Answer:
w = -1
Step-by-step explanation:
Given equation:
\(4w + 2 + 0.6w=-3.4w-6\)
Add 3.4w to both sides:
\(\implies 4w + 2 + 0.6w+3.4w=-3.4w-6+3.4w\)
\(\implies 4w + 2 + 0.6w+3.4w=-6\)
Subtract 2 from both sides:
\(\implies 4w + 2 + 0.6w+3.4w-2=-6-2\)
\(\implies 4w +0.6w+3.4w=-6-2\)
Combine the terms in w on the left side of the equation and subtract the numbers on the right side of the equation:
\(\implies 8w=-8\)
Divide both sides by 8:
\(\implies \dfrac{8w}{8}=\dfrac{-8}{8}\)
\(\implies w=-1\)
Therefore, the solution to the given equation is:
\(\boxed{w=-1}\)
Given that,
→ 4w + 2 + 0.6w = -3.4w - 6
Now the value of w will be,
→ 4w + 2 + 0.6w = -3.4w - 6
→ 4.6w + 2 = -3.4w - 6
→ 4.6w + 3.4w = -6 - 2
→ 8w = -8
→ w = -8/8
→ [ w = -1 ]
Hence, the value of w is -1.
PLEASE HELP ME QUICK!!A train moves at a constant speed of 8 miles every 6 minutes. Fill in the table below to show how far the train travels according to different
amounts of time.
Answers
Answer:
1. 4
2. 20
3. 80
Step-by-step explanation:
A drawing class was assigned a final project where students had to choose one art medium and one subject. The teacher kept track of the types of projects submitted. A plant An insect Acrylic paint 21 5 Chalk 5 7 Charcoal 7 11 What is the probability that a randomly selected student chose to draw a plant or did not use acrylic paint? Simplify any fractions.
Answers
Answer:
The probability that a randomly selected student chose to draw a plant or did not use acrylic paint is;
\(P(A\cup B^{\prime})=\frac{51}{56}\)Explanation:
Given the table in the attached image;
Let A represent the event that a randomly selected student chose to draw a plant, and B' represent the event that a randomly selected student did not use acrylic paint;
\(\begin{gathered} P(A)=\frac{n(A)}{n(T)}=\frac{33}{56} \\ P(B^{\prime})=\frac{n(B^{\prime})}{n(T)}=\frac{30}{56} \end{gathered}\)Recall that the probability that a randomly selected student chose to draw a plant or did not use acrylic paint will be;
\(P(A\cup B^{\prime})=P(A)+P(B^{\prime})-P(A\cap B^{\prime})\)The probability of A and B' is;
\(P(A\cap B^{\prime})=\frac{n(A\cap B^{\prime})}{n(T)}=\frac{12}{56}\)Substituting the values;
\(\begin{gathered} P(A\cup B^{\prime})=P(A)+P(B^{\prime})-P(A\cap B^{\prime}) \\ P(A\cup B^{\prime})=\frac{33}{56}+\frac{30}{56}-\frac{12}{56}=\frac{63-12}{56} \\ P(A\cup B^{\prime})=\frac{51}{56} \end{gathered}\)Therefore, the probability that a randomly selected student chose to draw a plant or did not use acrylic paint is;
\(P(A\cup B^{\prime})=\frac{51}{56}\)PLEASE HELP FAST !!!!!
The distribution of pitches thrown in the
80 at-bats in a baseball game is as follows.
Pitches 1 2 3 4 5
Frequency 12 16 32 12 8
Find the relative frequency that the pitcher
will throw exactly 4 pitches in an at-bat.
?
Relative Frequency =
Do NOT simplify your answer.
Answers
The relative frequency of the pitcher throwing exactly 4 pitches in an at-bat is given as follows:
3/20.
How to calculate a relative frequency?A relative frequency is calculated as the division of the number of desired outcomes by the number of total outcomes.
The total number of at bats in this problem is given as follows:
80.
In 12 of them, the pitcher threw exactly four pitches, hence the relative frequency of the pitcher throwing exactly 4 pitches in an at-bat is given as follows:
12/80 = 3/20.
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Alicia borrowed $3000 from the bank at a rate of 12% simple interest per year. She earned 1440. How many years was the loan.?
Answers
Answer:
1440 $
Step-by-step explanation:
3000 - 100%
x - 12%
360 - 1 years
mia is six years older than her sister Natalie the sum of their age is 48 how old is Natalie
Answers
Answer: 21,
Step-by-step explanation: Her sister is 27, so she’s 21. = 48.
The age of Natalie based on the given condition will be 21 years old while Mia's is 27 years old.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
Suppose the age Mia is M while Natalie is N.
As per the given, Mia is six years older than her sister Natalie.
M = N + 6
Sum, M + N = 48
Substitute,
N + 6 + N = 48
2N = 42
N = 21
M = 21 + 6 = 27
Hence "According to the conditions, Natalie will be 21 years old, whilst Mia would be 27 years old".
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Compare the algebraically expressed function f(x) = 1 4 x2 - 2x to the function shown in the graph to determine which statement is true. A) The algebraic function has a greater maximum value. B) The algebraic function has a lower minimum value. C) The graphed function has a greater maximum value. D) The graphed function has a lower minimum value.
Answers
The correct statement regarding the minimum value of the quadratic functions is given as follows:
D) The graphed function has a lower minimum value.
How to obtain the minimum value of the quadratic functions?From the graph, the minimum value of the quadratic function is given as follows:
y = -8.
The algebraic function is defined as follows:
f(x) = 0.25x² - 2x.
Hence the coefficients are given as follows:
a = 0.25 and b = -2.
The x-coordinate of the vertex is given as follows:
x = -b/2a
x = 2/0.5
x = 4.
Then the y-coordinate of the vertex, representing the minimum value, is given as follows:
f(4) = 0.25(4)² - 2(4)
f(4) = -4 -> meaning that the graphed function has a lower minimum value.
Missing InformationThe graph is given by the image presented at the end of the answer.
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Which of the following gives a valid reason for using the given solution method to solve the system of equations shown?
Equation 1: 4x - 5y = 4
Equation Il: 2x + 3y = 2
A. Elimination; a coefficient in Equation I is an integer multiple of a coefficient in Equation II.
B
Elimination; a coefficient in Equation II is an integer multiple of a coefficient in Equation I
0
Substitution: Equation I can be solved for x in one step by dividing both sides by 4.
D.
Substitution: Equation Il can be solved for x in one step by subtracting 3y from both sides.
Answers
Answer:
C
Step-by-step explanation:
The probability of selecting 3 female employees and 7 male employees to win a promotional trip a company with 10 female and 50 male employees would best be modeled with the _______.
Answers
Answer:
The best model is hypergeometric distribution.
Step-by-step explanation:
The probability would be best modeled with hypergeometric distribution.
Hypergeometric distribution is a discrete probability distribution that describes the probability of successes in draws, without replacement, which is often employed in random sampling for statistical quality control.
The hypergeometric distribution differs from the binomial distribution in the lack of replacements.
Thus, the best model is hypergeometric distribution.
Point Z is the incenter of ΔSRT.
Point Z is the incenter of triangle S R T. Lines are drawn from the points of the triangle to point Z. Lines are drawn from point Z to the sides of the triangle to form right angles and line segments Z A, Z B, and Z C. Angle A Z R is 35 degrees. Angle Z R C is 35 degrees. Angle B S Z is 24 degrees. Angle Z S A is 24 degrees.
What is mAngleZTB?
24°
31°
35°
62°
Point H is the center of the circle that passes through points D, E, and F.
Point H is the center of the circle that passes through points L, M, and N.
Line segment H E is-congruent-to line segment H D
Line segment L H is-congruent-to line segment N H
Line segment F L is-congruent-to line segment F N
Answers
Answer:
The answer is 31
Step-by-step explanation:
ZTB= 31
The measure of angle ∠ZTB of triangle SRT is 31°.
What is a triangle?A triangle is a flat geometric figure that has three sides and three angles. The sum of the interior angles of a triangle is equal to 180°. The exterior angles sum up to 360°.
For the given situation,
Let S R T be a triangle, and point Z is the in center of triangle S R T.
Lines are drawn from point Z to the sides of the triangle to form right angles and line segments Z A, Z B, and Z C as shown in the below figure.
Here, ∠ AZR = 35°, ∠ZRC = 35°, ∠ BSZ = 24°, ∠ZSA = 24°, ∠ZTB = ?
The in center of a triangle is the intersection point of all the three interior angle bisectors of the triangle. It can be defined as the point where the internal angle bisectors of the triangle cross.
According to the angle bisector theorem,
⇒ \(\angle ZRC = \angle ARZ\)
⇒ \(\angle ARZ = 35\degree\)
Let the unknown angle, ∠ZTB be x. Then ∠BTC = 2x
The sum of the interior angles of a triangle is equal to 180°,
So, \(24+24+35+35+2x=180\)
⇒ \(118+2x=180\)
⇒ \(2x=180-118\)
⇒ \(x=\frac{62}{2}\)
⇒ \(x=31\)
Hence we can conclude that the measure of angle ∠ZTB of triangle SRT is 31°.
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pleaseeee help !!!!!!!!!
Answers
Answer:
p < -20/13Step-by-step explanation:
Given the inequality expression -2/3p - 4/3 > 1/5 p
Collect like terms;
-2/3 p - 1/5 p > 4/3
Find the LCM
(-10-3/15) p > 4/3
-13/15p > 4/3
Cross multiply
-13p * 3 > 15 * 4
-39p > 60
p < -60/39
p < -20/13
Hence the required result is p < -20/13
Aris and Josiah are reading a 50-page book for their ELA class. Aris wants to know what page Josiah is reading. Josiah gives her two hints: 1. The product of the two page numbers he can see is 930. 2. The page he is reading is an odd numbered page.
Answers
Answer:
31
Step-by-step explanation:
Let x and (x + 1) be the page numbers Josiah can see
Hint 1: x(x + 1) = 930
⇒ x² + x = 930
⇒ x² + x - 930 = 0
Using quadratic formula,
\(x = \frac{-b\pm\sqrt{b^2 -4ac} }{2a}\)
a = 1, b = 1 and c = -930
\(x = \frac{-1\pm\sqrt{1^2 -4(1)(-930)} }{2(1)}\\\\= \frac{-1\pm\sqrt{1 +3720} }{2}\\\\= \frac{-1\pm\sqrt{3721} }{2}\\\\= \frac{-1\pm61 }{2}\\\)
\(x = \frac{-1-61 }{2}\;\;\;\;or\;\;\;\;x= \frac{-1+61 }{2}\\\\\implies x = \frac{-62 }{2}\;\;\;\;or\;\;\;\;x= \frac{60 }{2}\\\\\implies x = -31\;\;\;\;or\;\;\;\;x= 30\)
Sice x is a page number, it cannot be negative
⇒ x = 30 and
x + 1 = 31
The two pages Josiah can see are pg.30 and pg.31
Hint 2: The page he is reading is an odd number
Out of the pages 30 and 31, 31 is an odd number
Thereofre, Josiah is reading page 31
The length of a rectangle is 5 cm more than its width. If the perimeter is 58cm, calculate:
(a) Write an equation to show the perimeter of the rectangle ?
(b) calculate:
I.width
II.length
III. the area of the rectangle
Answers
The equation to show the perimeter of the rectangle is P = 2(2w + 5)
Writing an equation to show the perimeter of the rectangleFrom the question, we have the following parameters that can be used in our computation:
Length = 5 more than the width
Also, we have
Perimeter = 58
This means that
P = 2(w + 5 + w)
P = 2(2w + 5)
Calculating the dimensions and the areaIn (a), we have
P = 2(2w + 5)
This gives
2(2w + 5) = 58
So, we have
2w + 5 = 29
2w = 24
w = 12
Next, we have
l = 12 + 5
l = 17
Lastly, we have
Area = 17 * 12
Area = 204
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Lucy and Zaki each throw a ball at a target. an image What is the probability that both Lucy and Zaki miss the target?
Answers
The Probability of both Zack and Lucy missing the target will be 0.48
Let the probability of Lucy and Zack missing the target be = P(L) and P(Z), respectively. So, If the probabilities of Zack and Lucy missing the target are as follows-
P(L) = 0.6 and
P(Z) = 0.8
then, the probability of both Lucy and Zack missing the target will be,
P(L) × P(Z) i.e.
0.6×0.8 = 0.48
Probability is basically a method to find out the possibility of likelihood of a certain outcome. In mathematics, it was introduced by Pierre and Cardano in the seventeenth century.
The complete question is-
The probabilities of Lucy and Zack hitting or missing the target are given in the following image. As per that, what will be the probability of both Lucy and Zack missing the target?
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what 2 plus 2 u gotta answer this right if not that is sad ok so what is 2 plus 2 use your finger thats why u got them
Answers
2 + 2 = 4
* * + * *
* * * *
Answer:
4
Step-by-step explanation:
2 + 2 is 4 cause if you add 2 two two’s it would be 4
Is the following function even, odd, or neither? f(x)=x^4-2x^2
Answers
The given function, f(x) = x⁴ - 2x², is even function.
What is the function?The nature of the function, whether it is even or odd can be determined by applying the following rules.
Even function, f(x) = f(-x)
Odd function; f(x) = -f(-x)
The given function, f(x) = x⁴ - 2x²
Test of for even function;
f(-x) = (-x)⁴ - 2(-x)²
f(-x) = x⁴ - 2x²
so f(x) = f(-x), the function is even.
Test for odd function;
-f(-x) = - [(-x)⁴ - 2(-x)²]
-f(-x) = -x⁴ + 2x²
so, f(x) ≠ -f(-x), the function is not odd.
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The amount of money Karen will have in her savings account after 15 weeks can be determined using the expression below:
d + 15x
where d represents the dollar amount currently in the account, and x represents the dollar amount Karen will add to the account each week.
If Karen currently has $20 in the account and adds $3 to it each week, how much should Karen have in the account after 15 weeks?
A)S38
B) $65
C) S105
D) $303
Answers
3x15 = 45
45+20 = 65
To be competitive for admission to four-year universities (UCF, UF, FSU, FAU, FIU, UCF, USF, etc.) what courses should you try to have each year of high school no matter the intended college major or current status of high school graduation requirements?
Answers
Answer:
Ask your guidance counselor or a college admissions counselor
Step-by-step explanation:
square root of 1/9
Answers
fred explained to his friend nicole 5x8/6 is the step it takes to multiply 5/8 x 6 a fraction by a whole number. is fred correct?
explain your reasoning.
Answers
Answer:
no fred is not correct
Step-by-step explanation:
so u say
5/8×6/1
then u say 5×6=30
then u say 8×1=8
then u say 30÷8= 3.75
so yr answer is =3.75
hope u understand
Please help this is due in 20 mins, I will give brainliest
Answers
Answer:
L = 5\(\sqrt{10}\)
Step-by-step explanation:
use Pythagorean Theorem:
L² + (5\(\sqrt{2}\))² = (10\(\sqrt{3}\))²
L² + 25(2) = 100(3)
L² + 50 = 300
L² = 250
L = \(\sqrt{250}\) = \(\sqrt{25}\) · \(\sqrt{10}\) = 5\(\sqrt{10}\)
Answer:
by Pythagoras law
(10√3)²=l²+(5√2)²
100×3-25×2=l²
l²=25o
l=√250=5√10
:.l=5√10
find the perimeter of rectangle whose length is 5m 20 cm and breadth 3.5m
Answers
Answer:
17.4 sq.mStep-by-step explanation:
Given,
Length of the rectangle = 5m 20cm = 5.2m
Breadth of the rectangle = 3.5m
Therefore,
Perimeter of the rectangle
= 2(Length + Breadth)
= 2(5.2m + 3.5m)
= 2 × 8.7m
= 17.4m
Hence,
Area of the given rectangle is 17.4 sq.m (Ans)