Since y varies directly as the cube of x, y can be calculated by multiplying a constant value "k" by x³, like this:
y = kx³
We are told that y = 17 when x = 4. By replacing 4 for x and 17 for y into the above expression, we get:
17 = k(4)³
From this expression, we can solve for k to get:
17/(4)³ = k
k = 17/(4)³
k = 17/64
Then, we get the following expression of y as a function of x:
y = (17/64)x³
By replacing 3 for x, we get:
y = (17/64)3³ = 459/64 = 7.17
Then, the y is 7.17 when x = 3
A ribbon is 18in long. Convert the length to feet.
Answer:
1.5 feet
Step-by-step explanation:
1 feet = 12 inches
18 inches --> x feet
18/12 = 1.5 feet
Answer:
1.5 feet
Step-by-step explanation:
12 inches in 1 foot 12/18= 1.6 So 1 foot and 6 inches or 1.5 feet
Whose reasoning is correct?
A) Only Marcy is correct.
B) only Jake is correct.
C) Both Marcy and Jake are correct.
D) Neither Marcy nor Jake is correct
Answer:
B) only Jake is correct
Step-by-step explanation:
Marcy comes to the correct conclusion, but the statement "therefore the measure of each of the angles has to be half of 180°" comes too early and is not supported by the previous logic. Had it been the very last statement in the argument, she would have been correct as well.
Dada la sucesión an = 1700 + 4,1· n2 + 304,9· n
Acerca de la sucesión (an), podemos afirmar como verdadero que:
I. a n es una sucesión aritmética
II. a n es una sucesión monótona creciente
III. a n es una sucesión geométrica
Solo I y II
Solo II
Solo III
Sólo II y III
Solo I
Concluimos que la opción correcta es "Solo II".
Una expresión es una sucesión aritmética si y solo si existe entre dos elementos consecutivos cualesquiera de la serie la misma diferencia. La sucesión aritmética es definida por una expresión de la forma:
\(a_{n} = a + b\cdot n\), \(n\in \mathbb{N}\) (1)
Donde \(a,b\) son coeficientes de la sucesión.
Asimismo, una expresión es una sucesión geométrica si y solo si entre dos elementos consecutivos cualesquiera de la serie existe la misma razón. La sucesión geométrica es definida por una expresión de la forma:
\(a_{n} = a\cdot r^{b\cdot n}\), \(n\in \mathbb{N}\) (2)
Donde \(a, b, r\) son coeficientes de la sucesión.
Por último, una expresión es una sucesión monótona creciente si dados dos elementos consecutivos de una serie, el elemento posterior es siempre mayor que el elemento anterior. Matemáticamente, debe satisfacerse la siguiente condición:
\(\frac{a_{n+1}}{a_{n}} > 1, n\in \mathbb{N}\) (3)
Esta claro por inspección directa que la sucesión dada no es aritmética ni geométrica y cabe comprobar si es monótona creciente. Valiéndonos de (3), realizamos las operaciones algebraicas pertinentes:
\(r = \frac{1700 + 4,1\cdot (n+1)^{2}+304,9\cdot (n+1)}{1700 + 4,1\cdot n^{2}+304,9\cdot n}\)
\(r = \frac{1700+4,1\cdot (n^{2}+2\cdot n +1) +304,9\cdot (n+1)}{1700 + 4.1\cdot n^{2}+304,9\cdot n}\)
\(r = \frac{1700+4,1\cdot n^{2}+304,9\cdot n+4,1\dot (2\cdot n +1) +304.9}{1700+4,1\cdot n^{2}+304,9\cdot n}\)
\(r = 1 + \frac{8,2\cdot n +309}{1700 + 4,1\cdot n^{2}+304,9\cdot n}\)
Como puede apreciarse, \(r > 1\). Por tanto, la sucesión es monótona y creciente.
En consecuencia, concluimos que la opción correcta es "Solo II".
Invitamos cordialmente a leer esta pregunta sobre sucesiones: https://brainly.com/question/21709418
Review the table showing the population of a city.
What are the values of a, b, and c for a logistic
regression model y =c/1+ae^-bx
that represents this population?
a = 27.47, b = 3.26, and c = 0.30
a = 3.26, b=0.30, and c = 27.47
a = -0.09, b = 4.53, and c = 2.81
a= -0.09, b = 2.81, and c = 4.53
Answer:
a = 3.26, b = 0.30, and c = 27.47
Step-by-step explanation:
It's B on Edge. 2021
Answer:
B: a = 3.26, b = 0.30, and c = 27.47
Step-by-step explanation:
Took the review
The quadrant that contains the point (-7,-16) is quadrant PLSS ANWAR NOW NEED HELP NOW
Answer:
hi how may i help
Step-by-step explanation:
how can i help u
plssss ill give anything. 2 x 3[7 + (6/2)]=
Please give Brainliest!
Answer:
60
Step-by-step explanation:
Get that A.
Identify the meaning of the variables in the point-slope form of a line.
Answer:m=the slope of the line
(x1, y1)= a given point on the line (x,y)=any point on the line
Step-by-step explanation:
Answer:
answer in picture
Step-by-step explanation:
Find the numbers with the following property three times the sum of four and a number is less than seven times the same number
Let's represent the number with the variable "x". According to the given property, we can write the following equation:
3(x + 4) < 7x
Now, let's solve this inequality to find the range of numbers that satisfy the property.
3x + 12 < 7x
Subtract 3x from both sides:
12 < 4x
Divide both sides by 4 (since the coefficient of x is 4):
3 < x
So, the range of numbers that satisfy the given property is x > 3.
Therefore, any number greater than 3 will satisfy the condition. For example, 4, 5, 6, 7, 8, etc.Step-by-step explanation:
Two small pitchers and three large pitchers can hold a total of 16 cups of water. The large pitcher holds 2 more cups of water than the small pitcher. Solve the word problem with subsistence or elimination method.
The number of cups for small pitchers = 2
The number of cups for large pitchers = 4.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Two small pitchers and three large pitchers can hold a total of 16 cups of water.
And, The large pitcher holds 2 more cups of water than the small pitcher.
Now,
Let number of cups for small pitchers = x
And, The number of cups for large pitchers = y
Here, Two small pitchers and three large pitchers can hold a total of 16 cups of water.
So, We can formulate;
⇒ 2x + 3y = 16 .. (i)
And, The large pitcher holds 2 more cups of water than the small pitcher.
So, We get;
⇒ y = 2 + x .. (ii)
Substitute the value of y from (ii) in (i), we get;
⇒ 2x + 3 (2 + x) = 16
Solve for x as;
⇒ 2x + 6 + 3x = 16
⇒ 5x = 16 - 6
⇒ 5x = 10
⇒ x = 2
And, From (ii);
⇒ y = 2 + x
⇒ y = 2 + 2
⇒ y = 4
Thus, The number of cups for small pitchers is 2
The number of cups for large pitchers is 4.
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A math class has 7 girls and 5 boys in the seventh grade and 4 girls and 4 boys in the eighth grade. The teacher randomly selects a seventh grader and an eighth grader from the class for a competition. What is the probability that the students she selects are both boys?
Answer:
Answer : 21%
Step-by-step explanation:
To find the probability of picking two boys, we need to first know how many different ways she can pick the 7th and 8th grader.
There are 12 7th-graders and 8 8th-graders. So the total number of ways she can pick is:
12×8=96
To get two boys picked, there are 5 boys in the 7th-grade class and 4 in the 8th-grade class, so there are:
5×4=20 ways
Which gives us the probability of:
2096=524≅21%
Hope this was helpful!❤
please the answer fast i need it very importent
The length of line having mid point B ⇒ 7x - 2.
Given that,
B is the mid point of AC
And also given that
length of segment AB = 2x+5
And length of segment BC = 5x - 7
A straight path established by linking a group of points in a plane is known as a line. It is a one-dimensional form with only a length and no width or height. A line can extend indefinitely in both ends in opposite directions. To indicate a line, we can use upper case characters.
Now since B is the mid point of AC,
So, The line AC is sum of the line segment AB and line segment BC.
Therefore,
AC = AB+BC
= (2x+5)+(5x - 7)
= 7x - 2
Hence,
The length of AC is 7x - 2
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Give the slope between the points. Answer
You sailed 0.055 units to the left and found treasure at 0.085 units find where the ship started
5 1/2 + 3/4 Give your answer in its simplest form.
Answer:
5 1/2 + 3/4
11/2 + 3/4
22+3/4
25/4
=6 1/4
For a spelling bee, each student was given 537 words to stydy. There are 45 students in the spelling bee. How many words will be studied.
Answer: 24165, I think
Step-by-step explanation:
I just multiply the kids that were there by the words they were each given
Answer:
24,165
Step-by-step explanation:
=537*45
=24,165
If a=3i+4j+5k and b=2i+j+7k. Find a.b
In circle O, secants ADB and AEC are drawn from external point A
such that points D, B, E, and C are on circle O. If AD = 8, AE = 6,
and EC is 12 more than BD, the length of BD is
(1) 6
(2) 22
(3) 36
(4) 48
The length of BD is 22.
In the given scenario, let's consider the following information.
AD = 8
AE = 6
EC is 12 more than BD.
To find the length of BD, we can utilize the Intercepted Arcs Theorem, which states that when two secants intersect outside a circle, the measure of an intercepted arc formed by those secants is equal to half the difference of the measures of the intercepted angles.
From the given information, we know that AD = 8 and AE = 6.
Since these are the lengths of the secants, we can use them to calculate the intercepted arcs.
First, let's find the intercepted arc corresponding to AD:
Intercepted Arc ADB = 2 \(\times\) AD = 2 \(\times\) 8 = 16
Similarly, we can find the intercepted arc corresponding to AE:
Intercepted Arc AEC = 2 \(\times\) AE = 2 \(\times\) 6 = 12
Now, we know that EC is 12 more than BD.
Let's assume the length of BD as x.
BD + 12 = EC
Now, let's consider the intercepted arcs theorem:
Intercepted Arc ADB - Intercepted Arc AEC = Intercepted Angle B - Intercepted Angle C
16 - 12 = Angle B - Angle C
4 = Angle B - Angle C.
Since Angle B and Angle C are vertical angles, they are congruent:
Angle B = Angle C.
Therefore, we can say:
4 = Angle B - Angle B
4 = 0
However, we have reached an inconsistency here.
The equation does not hold true, indicating that the given information is not consistent or there may be an error in the problem statement.
As a result, we cannot determine the length of BD based on the given information.
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In angle VWX, VX is extended through point X to point Y,
m/VWX = (x + 14)°, m/XVW = (x +9)°, and
m/WXY = (5x - 10)°. What is the value of x?
Answer:
11
Step-by-step explanation:
This will form triangle VWX. So we have values for ∠VWX and ∠XVW but we don't have value for ∠WXV.
Since ∠WXV and ∠WXY are supplementary angles
=> ∠WXV + ∠WXY = 180
=> ∠WXV = 180 - ∠WXY
So the angles of triangle VXY
∠VWX + ∠XVW + ∠WXV = 180
(x + 14) + (x + 9) + (180 - (5x - 10)) = 180
x + x - 5x + 14 + 9 + 180 + 10 = 180
-3x + 213 = 180
-3x = - 33
x= 11
Solve the equation
2^2x+1 +5(2^x) -3=0
Please help
Answer:
The answer is -1
Step-by-step explanation:
2^(2x+1) = 2^2x × 2^1 = 2^2x × 2
after this we can make appointments
2^x = t
and then solve it :)
Determine the validity of the converse and give a counterexample if the converse is not valid.
If it is sunny, then it is 80° Fahrenheit. The converse is valid.
If it is 80° Fahrenheit, then it is sunny. The converse is valid.
If it is not sunny, then it is not 80° Fahrenheit. The converse is invalid; a counterexample is a day that is not 80° Fahrenheit and not sunny.
If it is 80° Fahrenheit, then it is sunny; The converse is invalid; a counterexample is a day that is 80° and cloudy.
Your analysis is correct. Here's a summary:
If it is sunny, then it is 80° Fahrenheit. (Original statement)
Converse: If it is 80° Fahrenheit, then it is sunny. (Valid)
If it is 80° Fahrenheit, then it is sunny. (Original statement)
Converse: If it is sunny, then it is 80° Fahrenheit. (Valid)
If it is not sunny, then it is not 80° Fahrenheit. (Original statement)
Converse: If it is not 80° Fahrenheit, then it is not sunny. (Invalid)
Counterexample: A day that is not 80° Fahrenheit and not sunny (e.g., 70° and cloudy).
If it is 80° Fahrenheit, then it is sunny. (Original statement)
Converse: If it is sunny, then it is 80° Fahrenheit. (Invalid)
Counterexample: A day that is 80° Fahrenheit and cloudy.
In cases 1 and 2, the original statements and their converses are valid because the relationship between "sunny" and "80° Fahrenheit" holds in both directions. However, in cases 3 and 4, the converses are invalid because there are counterexamples where the second part of the statement (either "not 80° Fahrenheit" or "cloudy") does not necessarily imply the first part ("not sunny" or "80° Fahrenheit").
It costs James $4 to make an order of a dozen cookies. If he sells them for $20, what percentage is each order of cookies marked up?
HELP ASAP THANK YOU SO MUCH
A) 20%
B) 80%
C) 400%
D) 500%
Answer:
Step-by-step explanation:] Answer would be 400%
New value - Original Cost
Original value
= 20 - 4/4
= 16/4
= 4 x 100
= 400%
Which one is a counter example?
cannot be used to prove or disprove a conjecture
shows that a conjecture is always true
is a proof that is not valid
shows that a conjecture is not always true
Answer: Shows that conjectured is always true
Step-by-step explanation:
Help on this too pls
Step-by-step explanation:
Half of 40 is 20 and luckily they already gave us how much she would earn if she worked 20 hours.
So all we have to do is multiply the amount of money she earned when she worked 20 hours by 2 to see how much she earned when she worked 40 hours.
20 hours:165 dollars or 20:165
20 x 2= 40 and 165x2=330
So if Monique worked 40 hours she would earn $330.
Complete the expression so that it is equivalent to 2 (x+6)
The complete expression is (2 × x) + (2 × 6). This is an equivalent expression to the given expression.
What is an expression?
A number, a variable, or a combination of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.
Given expression is
2 (x+6)
Distributive property: The same outcome is obtained by multiplying the sum of two or more addends by a number as it is by multiplying each addend by the number separately and combining the resulting products.
The mathematical representation is a(b+c) = ab + ac.
Apply the Distributive property in the given expression:
(2×x) + (2×6)
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Which of the points below correctly plots the point (−2,−5π/3)?
Select the correct answer below:
A
B
C
D
E
F
Answer: F
Step-by-step explanation:
Answer: correct answer is A
Step-by-step explanation:
Remember that the coordinates (−2,−5π3) tell us the radius r=−2 and the angle θ=−5π3. So the point should be on the circle labeled 2 and form an angle of −5π3 with the negative x-axis. Point A is the correct point.
Find the indicated limit, if it exists. (2 points) limit of f of x as x approaches negative 1 where f of x equals 4 minus x when x is less than negative 1, 5 when x equals negative 1, and x plus 6 when x is greater than negative 1
Answer:
5
Step-by-step explanation:
The limit of f(x) at x=-1 is 5 when approached from the left or right. Since those limits are the same, the limit exists and is ...
\(\boxed{\lim\limits_{x\to-1}f(x)=5}\)
What happens to a consistent slope when the y value starts to decrease and the x value remains the same over time?
A. Y decreases and X decreases
B. Y decreases and X increases
C. Y increases and X increases
D. Y increases and X decreases
When the y-value starts to decrease and the x-value remains constant over time, Y decreases and X increases to a consistent slope.
A consistent slope represents a constant rate of change between two variables, typically represented by the ratio of the change in y to the change in x.
When the y-value starts to decrease and the x-value remains the same over time, the consistent slope represents a negative correlation between y and x.
This means that as the value of y decreases, the value of x remains the same or may increase, depending on the context of the problem.
Therefore, the answer is option B: Y decreases and X increases.
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if x = -5, what is the value of the expression -4x?
Answer:
c; 20
Step-by-step explanation:
-4x
= -4(-5)
=20
The back of a dog house is composed of a square and a triangle . How much wood wood is needed for the back of the dog house to the nearest tenth of square foot. Pls use pi with formula of area and also use a expression
Answer:
68
Step-by-step explanation:
I just know I was in class with my teacher
Help please! Thank you!
Answer:
Step-by-step explanation:
h(x) = 36 - 4.9x^3
Let x be 1.3
The question is not entirely clear. Looks like the iphone moved. Not only that, but the question is not really clear either. I'm taking it to mean that h is the distance from the GROUND to the ROCK after 1.3 seconds.
h(x) = 36 - 4.9(1.3)^2
h(1.3) = 36 - 4.9 * 1.3 * 1.3
h(1.3) = 36 - 27.719
h(1.3) = 8.28 m