In this sequence, the first term is [tex]a_1[/tex] and every successive term is determined by
[tex]a_n=a_{n-1}+d[/tex]
where [tex]d[/tex] is the common difference between terms. We have
[tex]a_{11}=a_{10}+d=a_{9}+2d=\cdots=a_5+6d[/tex]
so that
[tex]41=11+6d\implies6d=30\implies d=5[/tex]
Then
[tex]a_5=a_4+5=a_3+2\cdot5=\cdots=a_1+4\cdot5[/tex]
[tex]\implies11=a_1+20\implies a_1=-9[/tex]
Answer:
The first term is -13.
Step-by-step explanation:
The general rule of an arithmetic sequence is the following:
[tex]a_{n+1} = a_{n} + d[/tex]
In which d is the common diference between each term.
This is the case going from one term to the next. However, when, as in this problem, we have the fifth and the tenth term, this formula can be expanded, as the following way:
[tex]a_{n + m} = a_{n} + m*d[/tex]
So
[tex]a_{10} = a_{5} + 5*d[/tex]
[tex]41 = 11 + 5d[/tex]
[tex]5d = 30[/tex]
[tex]d = 6[/tex]
The common diference is 6.
To find the first term, we do:
[tex]a_{5} = a_{1} + 4*d[/tex]
[tex]11 = a_{1} + 4*6[/tex]
[tex]a_{1} = -13[/tex]
The first term is -13.
what is the equation of the graphed line written in standard form?x-4y=4. x+4y=4. y=1/4x-1. y=-1/4x-1
Answer:
y=1/4x-1
Step-by-step explanation:
First step to determine the equation of a line is is to determine its slope.
We see the line passes through points (4,0) and (0,-1), that means its slope is:
S = (0 - -1) / (4 - 0) = 1/4
Since there's only one choice with a slope of 1/4, the choice is easy :-)
But we can also verify the equation by checking if it validates the given points. So, what's the value of y if x = 0?
y = (1/4)0 - 1 = 0 - 1 = -1 Validated.
And when x = 4?
y = (1/4)4 - 1 = 1 - 1 = 0 Validated too.
Answer:
[tex]x-4y=4[/tex]
Step-by-step explanation:
The given function passes through: (4,0) and (0,-1).
The equation is of the form;
y=mx+b
where b=-1 is the y-intercept.
The equation now becomes:
y=mx-1
We substitute the point (4,0) into the function to obtain;
0=m(4)-1
0+1=4m
1=4m
[tex]m=\frac{1}{4}[/tex]
Therefore the equation is:
[tex]y=\frac{1}{4}x-1[/tex]
Multiply through by 4 to get;
[tex]4y=x-4[/tex]
The equation in standard form is;
[tex]x-4y=4[/tex]
A spinner has five equal sections that are numbered 1-5. In which distributions does the variable X have a binomial distribution? Select each correct answer.
A.) When the spinner is spun multiple times, X is the number of spins until it lands on 5.
B.) When the spinner is spun four times, X is the number of times the spinner does not land on an odd number.
C.) When the spinner is spun three times, X is the sum of the numbers the spinner lands on.
D.) When the spinner is spun five times, X is the number of times the spinner lands on 1.
Answer: The answer is C
Step-by-step explanation: If you think about it the spinner only spun 3 times and when that happens them you sum up X
(C) When the spinner is spun three times, X is the sum of the numbers the spinner lands on.
Binomial Distribution:The binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability [tex]q=1p[/tex]). This distribution is used in probability theory and statistics. A Bernoulli trial, or experiment, is another name for a single success-or-failure experiment, and a Bernoulli process is another name for a series of results. For a single trial, or [tex]n=1[/tex], the binomial distribution is a Bernoulli distribution. The popular binomial test of statistical significance is based on the binomial distribution.Therefore, the correct option is (C) When the spinner is spun three times, X is the sum of the numbers the spinner lands on.
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write a polynomial function in standard form with the given roots: -4i
Answer:
[tex]f(x)=x^2+16[/tex]
Step-by-step explanation:
By the conjugate rule, if -4i is a root, then so is +4i. So we have 2 roots, thus, we have a second degree polynomial (namely, a quadratic). If
x = -4i, then
x + 4i is a root.
If
x = 4i, then
x - 4i is a root.
Having (x - 4i)(x + 4i) as roots, we can now FOIL them together to get a polynomial of least degree.
FOILing gives us
[tex]x^2+4ix-4ix-16i^2[/tex]
Notice that the +4ix and the -4ix cancel each other out, leaving you with
[tex]x^2-16i^2[/tex]
Since
[tex]i^2=-1[/tex]
we can make the substitution:
[tex]x^2-16(-1)[/tex]
which simplifies to
[tex]x^2+16[/tex]
In function notation form:
[tex]f(x)=x^2+16[/tex]
Final answer:
The polynomial function in standard form with the root -4i is f(x) = x² + 16. We derive this by realizing that the conjugate, 4i, is also a root and multiplying the factors (x + 4i)(x - 4i), simplifying to the quadratic polynomial.
Explanation:
To write a polynomial function with the given root -4i, we must take into consideration that complex roots come in conjugate pairs for polynomials with real coefficients. Hence, if -4i is a root, then its conjugate 4i must also be a root. The factors of the polynomial corresponding to these roots are (x + 4i) and (x - 4i).
We can find the polynomial by multiplying these two factors:
(x + 4i)(x - 4i)
Applying the difference of squares, we get:
x² - (4i)²
x² - (-16)
x² + 16
The polynomial function in standard form with the given root -4i is:
f(x) = x² + 16
50 POINTS
Which of the following can be determined from the table above?
A.
Events B and C are independent.
B.
Events D and A are independent.
C.
Events C and A are independent.
D.
Events E and B are independent.
Answer: Option 'B' is correct.
Step-by-step explanation:
Since we have given that
P(A) = 0.5
P(B) = 0.5
P(C) = 0.15
P(D) = 0.7
P(E) = 0.15
We need to find the independent events.
When we consider,
P(A∩D) = P(Event A and Event D) = 0.35
and
P(A) × P(D) = 0.7 × 0.5 = 0.35
We get that
P(A∩D)= P(A) × P(D) = 0.35
All other options are not satisfying the conditions of "Independent events".
Hence, Option 'B' is correct.
Answer:
option b would be the correct answer
Step-by-step explanation:
In the equation 3x^2-10x=8 please solve for x and show work ty !
Answer:
x=4,-2/3
Step-by-step explanation:
To solve for x, we first subtract 8 from both sides.
So 3x^2-10x-8=0
Using the quadratic formula, we get
X=(10+sqrt(100+96))/6 or x = (10-sqrt(100+96))/6
So x=(10+14)/6 or x=(10-14)/6
So x=4 or x=-2/3.
Answer:
x=4 or x=-2/3.
Step-by-step explanation:
[tex]4(x - 8) {}^{3} - 18 = 846[/tex]
need help solving it
Answer:
x=14
Step-by-step explanation:
4(x - 8)³ - 18 = 846
4(x - 8)³ = 864
(x - 8)³ =216
∛(x - 8)³ =∛216
x-8 = 6
x= 6+8
x=14
Answer:
x=14
Step-by-step explanation:
look this solution :
How many times as bigger is it? Picture shown above
2 * 10^2
Divide the first numbers, which are 6 and 3, to get 2. Then, subtract the powers of the exponents, which are 5 and 3, to get 2.
HELP PLEASE MATH!! A company is testing tires for wear and tear. A given tire is said to either pass the test (P) or fail the test (F). Enter the missing outcome possibilities in each box to show the possible results if three tires are tested.
{PPP,( ), PFP, FPP, FFP, FPF,( )FFF}
Answer:
PPF, PFF
Step-by-step explanation:
There are several ways you can list all the possible combinations. A couple of my favorite are a) use a binary counting sequence; b) use a gray code counting sequence.
Using the first method, the binary numbers 000 to 111 can be listed in numerical order as 000, 001, 010, 011, 100, 101, 110, 111. Letting 0=P and 1=F, the ones missing from your list are the ones in italics in my list.
Using the second method, we change the right-most character, then the middle one, and finally the left-most character so there is one change at a time: 000, 001, 011, 010, 110, 111, 101, 100.
After you have a list of all possible combinations, it is a simple matter to compare the given list to the list of possibilities to see which are missing.
The correct outcome possibilities for the missing boxes in the given scenario are:
1. PPP (all three tires pass)
2. PPF (two tires pass, one fails)
3. PFP (two tires pass, one fails)
4. FPP (two tires pass, one fails)
5. FFP (two tires pass, one fails)
6. FPF (two tires pass, one fails)
7. FFF (all three tires fail)
To determine the missing outcomes, we must consider all possible combinations of passes (P) and failures (F) for three tires. Since each tire can either pass or fail, there are [tex]2^3 = 8[/tex] possible outcomes. We already have five of these outcomes listed, and we need to find the remaining two.
The missing outcomes must include all combinations of passes and failures that have not been listed yet. Since we have all combinations with exactly two passes and one fail, and we have the combination with three passes and three fails, the remaining combinations must have exactly one pass and two fails. These combinations are:
- PFF (one tire passes, two fail)
- FPF (one tire passes, two fail)
Therefore, the complete list of outcomes is:
1. PPP (all three tires pass)
2. PPF (two tires pass, one fails)
3. PFP (two tires pass, one fails)
4. FPP (two tires pass, one fails)
5. FFP (two tires pass, one fails)
6. FPF (two tires pass, one fails)
7. PFF (one tire passes, two fail)
8. FFF (all three tires fail)
Each of these outcomes represents a distinct possibility when testing three tires, and together they account for every possible result of the wear and tear test for the three tires.
Compare Standard Deviations
Place data sets in order from the smallest standard deviation to the largest standard deviation.
A = {9, 10, 11, 7, 13}
B = {7, 10, 11, 10, 12}
C = {10, 10, 10, 10, 10}
D = {1, 1, 10, 19, 19}
E = {1, 5, 6, 19, 19}
_________________
1 -
2 -
3 -
4 -
5 -
Answer:
1-C, 2-B, 3-A, 4-E, 5-D
Step-by-step explanation:
It is convenient to let a graphing calculator or spreadsheet compute the standard deviations for you. (Some will compute sample standard deviation; some will compute population standard deviation. It makes no difference to the ordering, as long as the same computation is used for all data sets.)
The correct order of the data sets from smallest to largest standard deviation is: C, B, A, E, D.
Explanation:Calculate the standard deviation for each data set. A = 2.2361, B = 1.5492, C = 0, D = 8.8818, E = 7.7277.Arrange the data sets in order from smallest to largest standard deviation: C, B, A, E, D.Therefore, "the correct order is: C, B, A, E, D".Learn more about ordering data sets by standard deviation here:https://brainly.com/question/37740206
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Which of these is a key feature of an experimental study? A. The treatment in the experiment should be simple enough for each individual in the experimental group to understand. B. The treatment in the experiment must vary for each individual in the experimental group. C. The treatment in the experiment must be applied to each of the individuals in the experimental group. D. The treatment in the experiment should be short so that each individual is tested quickly.
Answer:
I believe it is "E"
Step-by-step explanation:
E-series can eat my memes
Kill me please I'm Swedish ree
Answer: The key feature in the experimental study is C. The treatment in the experiment must be applied to each of the individuals in the experimental group. This is because it is made sure that the variables and conditions in different correspondents are applied so that actual results may be concluded.
Step-by-step explanation:
Which of the following is a zero for the function f(x) = (x + 3)(x − 7)(x + 5)? x = −7 x = −3 x = 3 x = 5
Answer:
x = −3
Step-by-step explanation:
A zero of a function is a value that makes one of the factors be zero.
To make x+3 = 0, x = -3.
To make x-7 = 0, x = 7.
To make x+5 = 0, x = -5.
Of these values that make the factors zero, only x = -3 is on your choices list.
Answer: The correct option is
(B) x = - 3.
Step-by-step explanation: We are given to select the correct zero of the following polynomial function :
[tex]f(x)=(x+3)(x-7)(x+5)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
The zeroes of the function f(x) are given by
[tex]f(x)=0\\\\\Rightarrow (x+3)(x-7)(x+5)=0\\\\\Rightarrow x+3=0,~~x-7=0,~~x+5=0\\\\\Rightarrow x=-3,7,-5.[/tex]
Therefore, the zeroes of the given function are
x = -3, x = 7 and x = -5.
Thus, the correct option is
(B) x = -3.
State whether the given equation or function is linear. Write yes or no. Explain your reasoning.
5x^4 + 5y = 9
Yes, the equation is in linear form. It is in the form xy = C.
Yes, the equation is linear. 0
No, the equation is not linear. It is not in the form Ax + By = C.
No, the equation is not linear. It is in the form x + y = c.
Answer:
Option C is correct.
Step-by-step explanation:
The given equation or function is linear if the variables x and y have degree zero or 1.
The given equation is 5x^4+5y =9
here x has degree =4 and y has degree = 1, but for linear equation both x and y variables must have degree zero or 1.
So, Option C is correct.
Plz help ASAP!! Explain your answer! I will mark at brainliest!!!
Answer:
A. 16.12 ft B. 9.64 ft
Step-by-step explanation:
For both of these, you need Pythagorean's Theorem because we have right triangles. In part A, we are given 2 legs and are asked to find the length of the hypotenuse:
[tex]14^2+8^2=PR^2[/tex] and
[tex]196+64=PR^2[/tex]
and PR = 16.12 ft
In part B, we are given the length of the hypotenuse and side PQ remains the same:
[tex]14^2+QR^2=17^2[/tex] and
[tex]196+QR^2=289[/tex]
[tex]QR^2=289-196[/tex] so
QR = 9.64 ft
A software designer is mapping the streets for a new racing game. All of the streets are depicted as either perpendicular or parallel lines. The equation of the lane passing through A and B is -7x + 3y = -21.5. What is the equation of the central street PQ?
A.
-3x + 4y = 3
B.
-1.5x − 3.5y = -31.5
C.
2x + y = 20
D.
-2.25x + y = -9.75
This is a PLATO math question, will give 15 pts to the best answer
Answer:
B. -1.5x − 3.5y = -31.5
Step-by-step explanation:
You forgot to provide the reference image which is essential to answer the question, but I managed to find it... and attach it to my answer.
In the given equation for AB, if we place the y term on the left and x term on the right, we see the slope of that line is 7/3 (y = (7x - 21.5)/3 ==> 7/3x).
We see on the image that the line PQ is perpendicular to AB. That means that its slope is -3/7.
If we quickly check the slopes of each of the possible answers...
A. -3x + 4y = 3 ----> 4y = 3x - 3 ==> y = (3x-3)/4 => slope = 3/4
Not what we're looking for.
B. -1.5x - 3.5y = -31.5 ==> 3.5y = -1.5x + 31 ===> y = (-1.5x +31)/3.5
that gives us a slope of -1.5/3.5... We can simplify it... -3(0.5)/7(0.5) = -3/7
Exactly as predicted.
Since we have the point P (7,6), we can enter it in the equation to verify:
-1.5x - 3.5y = -31.5
-1.5 (7) - 3.5 (6) = -10.5 - 21 = -31.5 --- Verified
C. 2x + y = 20 ==> y = 20 - 2x ===> slope is -2, not what we want.
D. -2.25x + y = -9.75 ==> y = 2.25x - 9.75 ==> slop is 2.25 cannot be it.
Answer: B. -1.5x − 3.5y = -31.5
Step-by-step explanation:
An object is launched from a launching pad 144 ft. above the ground at a velocity of 128ft/sec. what is the maximum height reached by the rocket?
Answer:
18) a. h(x) = -16x² + vx + h(0) ⇒ h(x) = -16x² + 128x + 144
b. The maximum height = 400 feet
c. Attached graph
19) The rocket will reach the maximum height after 4 seconds
20) The rocket hits the ground after 9 seconds
Step-by-step explanation:
* Lets study the rule of motion for an object with constant acceleration
# The distance S = ut ± 1/2 at², where u is the initial velocity, t is the time
and a is the acceleration of gravity
# The vertical distances h in x second is h(x) - h(0), where h(0)
is the initial height of the object above the ground
∵ h(x) = vx + 1/2 ax², where h is the vrtical distance, v is the initial
velocity, a is the acceleration of gravity (32 feet/second²) and x
is the time
18)a.
∵ The value of a = -32 ft/sec² ⇒ negative because the direction
of the motion
is upward
∴ h(x) - h(0) = vx - (1/2)(32)(x²) ⇒ (1/2)(32) = 16
∴ h(x) = vx - 16x² + h(0)
∴ h(x) = -16x² + vx + h(0) ⇒ proved
* Find the height of the object after x seconds from the ground
∵ h(0) = 144 and v = 128 ft/sec
∴ h(x) = -16x² + 128x + 144
b.
* At the maximum height h'(x) = 0
∵ h'(x) = -32x + 128
∴ -32x + 128 = 0 ⇒ subtract 128 from both sides
∴ -32x = -128 ⇒ ÷ -32
∴ x = 4 seconds
- The time for the maximum height = 4 seconds
- Substitute this value of x in the equation of h(x)
∴ The maximum height = -16(4)² + 128(4) + 144 = 400 feet
c. Attached graph
19)
- The object will reach the maximum height after 4 seconds
20)
- When the rocket hits the ground h(x) = 0
∵ h(x) = -16x² + 128x + 144
∴ 0 = -16x² + 128x + 144 ⇒ divide the two sides by -16
∴ x² - 8x - 9 = 0 ⇒ use the factorization to find the value of x
∵ x² - 8x - 9 = 0
∴ (x - 9)( x + 1) = 0
∴ x - 9 = 0 OR x + 1 = 0
∴ x = 9 OR x = -1
- We will rejected -1 because there is no -ve value for the time
* The time for the object to hit the ground is 9 seconds
Show why, for linear functions, a vertical translation is equivalent to a horizontal translation. For a linear function, what horizontal translation is equivalent to a vertical translation of 3 units up?
Explanation:
A) For the function ...
f(x) = mx + b
the vertical translation by k makes the function ...
g(x) = f(x) + k = mx + b + k
This can be rewritten as ...
g(x) = m(x +k/m) +b = f(x+k/m)
That is, the vertical translation by k is equivalent to a horizontal translation by -k/m, where m is the slope of the linear function.
___
B) For a vertical translation of 3, the equivalent horizontal translation is ...
-k/m for k=3
= -3/m . . . . . where m is the slope of the function
_____
Please note that there is no equivalent for m=0.
PLEASE HELP ME!!!! I need to find m angel 1
Answer:
55 degrees.
Step-by-step explanation:
We can use the postulate if two angles are congruent in both triangles than the triangle is congruent.
That means we can plug in 80 and 45 for triangle QRS.
Then, we can find angle 1 by subtracting the sum of those numbers from 180.
80 + 45 = 125
180 - 125 = 55
What is the solution with steps?
2cosx=-sin^2x
Try this option, the answer is marked with red colour.
Use the graph to determine the domain and range of the piecewise defined function.
Domain:
(the picture is a b c d choices)
Answer:
Domain: -6≤x<0 or 0<x≤2
Range: 1<x≤6
Step-by-step explanation:
Domain = The set of starting numbers - the x values.
Range = The set of numbers it becomes - the y values.
For the domain, it starts at -6, on the left and ends at 0; however, it doesn't include 0. Then is starts at 0, exclusive, and ends at 2.
For the range, it starts at 1, but doesn't include 1, and ends at 6, inclusive.
The domain of the given piecewise-defined function is -6≤x≤0 or 0. The domain of a function refers to the set of all possible input values or x-values of the function, while the range refers to the set of all possible output values or y-values of the function. In a piecewise-defined function, each piece has its own domain and range.
The domain of a function refers to the set of all possible input values or x-values of the function, while the range refers to the set of all possible output values or y-values of the function. In a piecewise-defined function, each piece has its own domain and range.
To determine the domain of the given piecewise-defined function, we need to identify the intervals on the x-axis where each piece of the function is defined. From the graph, we can see that the function is defined from -6 to 0, and also from 0 to 2. So the domain is -6≤x≤0 or 0
The range of the function is the set of all y-values that correspond to the x-values in the domain. Looking at the graph, we see that the function takes on values between 1 and 6, inclusive. So the range is 1≤y≤6.
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the researchers have also determined that the current rate of the rise in water level is twice the 1880 to 2009 rate. assuming that this new rate began in 2009, you can use the function g(x) = 3.2(x - 2009) + 206, which models the total rise in water level in mm since 1880 for any year x, beginning in 2009.
1. what is the domain of g(x)?
2. write a simplified function, g(x)
3. according to the model, what will be the total rise in water level by 2025?
4. when will the total rise in water level be equal to about half a meter?
please help and thank you!!
Answer:
x ≥ 20093.2x -6222.8257.2 mmyear 2100Step-by-step explanation:
1. The problem statement tells you the function applies for year values (x) 2009 and later. The domain is real numbers greater than or equal to 2009.
__
2. We can use the distributive property to eliminate parentheses:
3.2(x -2009) +206 = 3.2x -6428.8 +206
= 3.2x -6222.8
__
3. Put 2025 in the equation and do the arithmetic
g(2025) = 3.2·2025 -6222.8 = 257.2 . . . . mm
__
4. Put this value of level rise in the equation and solve for x.
g(x) = 3.2x -6222.8
500 = 3.2x -6222.8 . . put 500 mm where g(x) is in the equation
6722.8 = 3.2x . . . . . . . add 6222.8
x = 6722.8/3.2 = 2100.875
The water rise will be equal to about half a meter late in the year 2100.
Solve the equation on the interval
Answer:
The solutions of the equations are π/3 , 2π/3 , 4π/3 , 5π/3
Step-by-step explanation:
* Lets revise the four quadrant before solving the equation
# First quadrant the measure of all angles is between 0 and π/2
the measure of any angle is α
∴ All the angles are acute
∴ All the trigonometry functions of α are positive
# Second quadrant the measure of all angles is between π/2 and π
the measure of any angle is π - α
∴ All the angles are obtuse
∴ The value of sin(π - α) only is positive ⇒ sin(π - α) = sinα
# Third quadrant the measure of all angles is between π and 3π/2
the measure of any angle is π + α
∴ All the angles are reflex
∴ The value of tan(π + α) only is positive ⇒ tan(π + α) = tanα
# Fourth quadrant the measure of all angles is between 3π/2 and 2π
the measure of any angle is 2π - α
∴ All the angles are reflex
∴ The value of cos(2π - α) only is positive ⇒ cos(2π - α) = cosα
* Now lets solve the equation
∵ 4 sin²Ф - 3 = 0 ⇒ the domain is 0 ≤ Ф ≤ 2π
- Add 3 for both sides
∴ 4 sin²Ф = 3 ⇒ divide the both sides by 4
∴ sin²Ф = 3/4 ⇒ take square root for both sides
∴ √(sin²Ф) = √(3/4)
∴ sinФ = √3/2 OR sinФ = -√3/2
- When the value of sinФ is positive
∴ The angle Ф is on the first or second quadrant
- When the value of sinФ is negative
∴ The angle Ф is on the third or fourth quadrant
- We have four values of Ф because 0 ≤ Ф ≤ 2π
- Lets find the measure of the acute angle α
∵ sinα = √3/2
∴ α = sin^-1(√3/2) = π/3
- If Ф is on the first quadrant
∴ Ф = α = π/3
- If Ф is on the second quadrant
∴ Ф = π - α = π - π/3 = 2π/3
- If Ф is on the third quadrant
∴ Ф = π + α = π + π/3 = 4π/3
- If Ф is on the fourth quadrant
∴ Ф = 2π - α = 2π - π/3 = 5π/3
* The solutions of the equations are π/3 , 2π/3 , 4π/3 , 5π/3
Find the circumference of a circle:
Whose radius is 3 ½ in. (22/7)
Whose diameter is 3.6 (3.14)
Answer:
1. 22 in
2. 11.304 units
Step-by-step explanation:
Formulas for the circumference are
C = 2πr
C = πd
___
1. Put the given numbers in the appropriate formula:
C = 2·(22/7)·(7/2 in) = 22 in
__
2. Put the given numbers in the appropriate formula:
C = 3.14·3.6 = 11.304 . . . units
Given: m KP =2m IP , m IVK =120° Find: m∠KJL.
Will give 99 points!!!
Answer:
KJL = 40 degrees
Step-by-step explanation:
KJL = 1/2*( arc KP - arc IP)
arc IPK=360-120=240
KP=2(IP)
Kp=2x, IP = x
3x=240, x=80
KP=160
IP=80
KJL=(160-80) / 2 = 40 degrees
Answer:
40°
Step-by-step explanation:
If you vertically stretch the cubic function, F(x)=x^3, what is the equation of the new function?
A. J(x)=(1/3x)^3
B. G(x)=3x^3
C. H(x)=(3x)^3
D. K(x)=1/3x^3
Answer:
B. g(x) = 3x^3.
Step-by-step explanation:
In general a f(x) stretches vertically the graph of f(x) by a factor a.
The new function after a vertical stretch of the cubic function F(x) = x^3 is G(x) = 3x³, which multiplies the output of the original function by 3.
Explanation:When you apply a vertical stretch to the cubic function F(x) = x³, you multiply the output of the function, not the input. A vertical stretch by a factor of 3 would mean that each output value is tripled. Therefore, the correct equation for the new function would be G(x) = 3x³.
Option A is incorrect because (1/3x)³ represents a horizontal stretch by a factor of 3. Option C, (3x)³, represents a horizontal shrink by a factor of 1/3, and results in steeper slopes than the original function, which is the opposite effect of a vertical stretch. Option D, 1/3x³, would be a vertical compression by a factor of 1/3, not a stretch.
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Which is most likely to have a mass of 3 grams? A. an apple B. a backpack C. a paper clip D. a cat
Answer:
C. a paper clip
Step-by-step explanation:
An apple generally weighs more than 3 grams, and can go even into oz.
Depending on the type of material the backpack is made of, and also how big it is, the mass can vary, however, it is safe to say the backpack will be more than 3 grams.
A cat definitely weighs more than 3 grams. Any born cat that weighs only 3 grams will not survive.
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For this case we have the following options:
An apple, it is known that the apple will never weigh 3 grams.
A backpack will not have that weight either.
A cat would never weigh 3 grams or be newborn.
To have an object of 3 grams, the object must be very light.
A paperclip is very likely to weigh 3 grams because it is a very small and extremely light object.
Answer:
Option C
Zach and Roger spent a total of 69 hours building a treehouse. Roger worked 9 hours less than twice the number of hours Zach worked. Which system of equations can be used to determine the number of hours Zach worked, x, and the number of hours Roger worked, y?
A.
x + y = 69
2x + y = 9
B.
x - y = 69
y = 2x + 9
C.
x + y = 69
y = 9x - 2
D.
x + y = 69
y = 2x - 9
Answer:
It is D
Step-by-step explanation:
A box contains 8 red balls, 5 brown balls, 4 purple balls, and 3 green balls. What is the probability that a purple ball will be selected from the box after a red ball is taken out and not replaced?
Write the probability as a percent. Round to nearest tenth of a percent as needed.
Answer:
21.1 percent
Step-by-step explanation:
Total balls after -1 red ball=7+5+4+3=19
Prob of purple ball= purple ball/total balls
= 4/19
=0.2105...
percentage:21.1%
The probability of selecting a red ball and then a purple one without replacement from a box containing 8 red, 5 brown, 4 purple, and 3 green balls is approximately 8.4%.
Explanation:In probability, there are two events of interest here: selecting a red ball and then selecting a purple ball. Since the total number of balls changes after picking the red ball, these are dependent events. The probability of the first event (selecting a red ball) is 8 out of 20 (total balls). Then, with a red ball removed and not replaced, the probability of the second event (selecting a purple ball) is 4 out of 19. To find the overall probability, we multiply the probabilities of these two events.
To convert the probability to a percentage, multiply the result by 100. By doing this, the probability rounds to approximately 8.4%.
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Melinda walked 9/12 mile each day for 5 days. What was the total distance , in miles, she walked in the 5 days?
3.75 miles or 3 3/4 would be your answer
which fraction is closer to 0 than 1
Answer:
5/12
Step-by-step explanation:
Since 1/2 is the same distance from zero and one, we can use it to judge whether a fraction is closer to 0 or 1.
Since 5/8 is greater than 4/8 which is 1/2, it is closer to 1.
Since 8/10 is greater than 5/10 which is 1/2, it is closer to 1.
Since 5/12 is less than 6/12 which is 1/2, it is closer to 0.
So our answer is C. 5/12
The value close 0 than 1 is 0.41667.
FractionA fraction is a part of a whole number. for example, [tex]\bold{\dfrac{1}{4}}[/tex] represent a quarter of a number. Similarly, when we solve the fraction meaning [tex]\bold{\dfrac{1}{4}}[/tex] in the decimal form we divide the numerator, therefore, 1 in this case with the denominator as 4 in this case. the value thereafter we get is known as the decimal form of a fraction.
for example, = 0.25.
DecimalAlso, to convert a decimal to a fraction we simply divide the number by a multiple of 10. the number will be depending upon the number of numbers are after the decimal.
for example, 0.25 will be written as [tex]\bold{\dfrac{25}{100}}[/tex] while 0.5 will be written as [tex]\bold{\dfrac{5}{10}}[/tex].
Now, solving the question,
Bring every fraction to decimal form,
[tex]\bold{\dfrac{5}{8}= 0.625}[/tex]
[tex]\bold{\dfrac{8}{10} = 0.8}[/tex]
[tex]\bold{\dfrac{5}{12} = 0.41\overline6}[/tex]
[tex]\bold{\dfrac{7}{14} = 0.5}[/tex]
Hence, the value close 0 than 1 is 0.41667.
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If 4a+8b+4c=1
What is 16a+16c+32b?
Answer:
4
Step-by-step explanation:
[tex] 16a+32b+16c= 4*(4a+8b+4c)[/tex]
Answer:
If 4a+8b+4c=1, then 16a+16c+32b = 4
Step-by-step explanation:
To answer the question, a rule of three can be raised:
4a + 8b + 4c --------------- 1
16a + 16c + 32b --------- X
X = (16a + 16c + 32b) ÷ (4a + 8b + 4c)
This is equivalent to the division of the two polynomials, 16a + 16c + 32b by 4a + 8b + 4c.
Before dividing we organize the first polynomial,
16a + 16c + 32b = 16a + 32b + 16c
Dividing the two polynimials, we have
16a + 32b + 16c | 4a + 8b + 4c
-16a - 32b - 16c 4
= 0 =
The exact quotient is 4, since the residue is 0
Hope this hepls!