find f(-2) for f(x)=2×3^x
a.-18
b.1/18
c.-36
d.2/9
For the function f(x) = x + 4, what is the ordered pair for the point on the graph when x = 3p? a. (x, x + 4) b. (x, 3p + 4) c. (3p, x + 4) d. (3p, 3p + 4)
There are 46 kids in the After-school Club. Today they're going to the pool at the Community Center. If each minivan can take 6 kids, they'll need 8 minivans for all the kids. Do you agree or disagree? Explain your thinking.
which simplified fraction is equal to 0.17...?
A. 9/17
B. 8/45
C. 17/9
D. 16/90
20 points!! Solve this system of lineal equations.separate the x- and y- values with a comma
12x=54-6y
-17x=-62-6y
A school employs 30 teachers.how many will there be if there is a 10% reduction
If a school has 30 teachers and there is a 10% reduction, there will be 27 teachers remaining.
Explanation:If a school employs 30 teachers and there is a 10% reduction, we can calculate the number of teachers after the reduction by multiplying the initial number of teachers by (100% - 10%) = 90%. So, there will be 30 * 0.90 = 27 teachers after the reduction.
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Does anyone knows the answer
) find the solution of y"+2y'=64sin(2t)+64cos(2t) with y(0)=9 and y'(0)=9
Over the course of a day, you checked 250 total mousetraps and determined that 50 of them were perfectly made. Approximately what percentage of the mousetraps you checked was perfectly made?
given that 2/3a=16, which of the following illustrates how the multiplicative inverse property can be used to find the value of a?
Step-by-step explanation:
We have been given that [tex]\frac{2}{3}a=16[/tex].
Since multiplicative inverse property states that any number multiplied by its reciprocal is equal to one.
[tex]\frac{2}{3}\times \frac{3}{2} =1[/tex]
To solve for a let us divide 16 by [tex]\frac{2}{3}[/tex].
[tex]a=16\div \frac{2}{3}[/tex]
Since dividing a number by fraction is same as multiplying the number by the reciprocal of fraction. So we will multiply 16 by [tex]\frac{3}{2}[/tex].
[tex]a=16\times\frac{3}{2}[/tex]
[tex]a=8\times 3[/tex]
[tex]a=24[/tex]
We can see that to solve for a we have multiplied 16 by [tex]\frac{3}{2}[/tex] and [tex]\frac{3}{2}[/tex] is reciprocal of [tex]\frac{2}{3}[/tex].
Let us verify our answer by substituting a=24 in our given equation.
[tex]\frac{2}{3}\times 24=16[/tex]
[tex]2\times 8=16[/tex]
[tex]16=16[/tex]
Hence, to find the value of a we used multiplicative inverse property.
in which number does the 6 have a value that is one tenth the value of the 6 in 34, 761
The 6 in 600 has a value one tenth the value of the 6 in 34, 761.
Explanation:The question asks in which number does the 6 have a value that is one tenth the value of the 6 in 34, 761.
To find the answer, we need to compare the place value of the 6 in both numbers. In 34, 761, the 6 is in the thousands place, and its value is 6,000. To have a value that is one tenth of 6,000, the 6 would need to be in the hundreds place in the other number.
So, the number in which the 6 has a value one tenth the value of the 6 in 34, 761 would be 600.
Final answer:
The number 6 in 2,001.06 is one-tenth the value of the 6 in 34,761.
Explanation:
The number 6 in 34,761 has a value that is one-tenth the value of the 6 in the number 2,001.06.
To find this, we can compare the place values of the two 6's. The 6 in 34,761 is in the ones place, while the 6 in 2,001.06 is in the tenths place.
Since the tenths place is one place to the right of the ones place, the value of the 6 in 2,001.06 is one-tenth the value of the 6 in 34,761.
What is 7 divided by 28
7 divided by 28 is 1/4 or 0.25.
To calculate 7 divided by 28.
What is simplification?
Simplification is defined as solving mathematical problems using arithmetic operators.
7 divided by 28 = 7/28
= 1/4
= 0.25
Thus, 7 divided by 28 is 1/4 or 0.25.
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Find the greatest common factor of 36 and 72
Answer:
36
Step-by-step explanation:
36 is a factor of both numbers
_____
If the smaller divides the larger with no remainder, then the smaller number is the greatest common factor.
If there is a remainder, replace the larger number with that and repeat the process.
Derivative of y = cos(x-1)/(x-1)
Answer:
[tex]\displaystyle y' = \frac{- \cos (x - 1)}{(x - 1)^2} - \frac{\sin (x - 1)}{x - 1}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Quotient Rule]: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = \frac{\cos (x - 1)}{x - 1}[/tex]
Step 2: Differentiate
Derivative Rule [Quotient Rule]: [tex]\displaystyle y' = \frac{\Big( \cos (x - 1) \Big)'(x - 1) - \cos (x - 1)(x - 1)'}{(x - 1)^2}[/tex]Trigonometric Differentiation [Derivative Rule - Chain Rule]: [tex]\displaystyle y' = \frac{- \sin (x - 1)(x - 1)'(x - 1) - \cos (x - 1)(x - 1)'}{(x - 1)^2}[/tex]Basic Power Rule [Derivative Properties]: [tex]\displaystyle y' = \frac{- \sin (x - 1)(x - 1) - \cos (x - 1)}{(x - 1)^2}[/tex]Simplify: [tex]\displaystyle y' = \frac{- \cos (x - 1)}{(x - 1)^2} - \frac{\sin (x - 1)}{x - 1}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
can anyone help me in pre-cal
tan^2 x = tan x
sin^2 x = sin x
If x = -2 and y = 2, then which of the following statements is false?
There is a value of $a$ such that subtracting $a-4$ from $4a+16$ gives an answer of $-25$. What is that value of $a$?
Answer:
a = -15
Step-by-step explanation:
Let's rewrite the exercise in math language.
We have to subtract a-4 from 4a+16 to get -25, that is
4a+16 - (a-4) = -25
The minus sign that is just before the parenthesis changes all the signs inside it. Therefore, if we want to delete the parenthesis, we need to change the signs before.
4a + 16 - a + 4 = -25
Now we can associate the terms with an a between them and the terms without it from the left side of the equation.
3a + 20 = -25
Let's subtract 20 on both sides.
3a + 20 - 20 = -25 - 20
3a = -45
Finally, we divide by 3 on both sides
3a/3 = -45/3
a = -15
Which function has a vertex at the origin?
f(x) = (x + 4)^2
f(x) = x(x – 4)
f(x) = (x – 4)(x + 4)
f(x) = –x^2
Answer:
fdx = x-4 2
Step-by-step explanation:The test was right
P(4,13);Q(13,13) find the slope
162x + 731 = −y − 9x-2 vertex form
To write the given equation in vertex form, we need to complete the square for the x terms. The vertex form of a quadratic equation is y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola. After completing the square and rearranging the equation, we find that the equation in vertex form is y = 171(x + 7391/4) - 17113/4.
Explanation:To write the given equation in vertex form, we need to complete the square for the x terms. The vertex form of a quadratic equation is given by y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.
Let's rearrange the equation to isolate the x terms on one side and the y term on the other side: 162x + 9x + y = -731 - 2
Combine like terms: 171x + y = -733
Now, we can complete the square for the x terms. Divide the coefficient of x by 2 and square the result. Add this value to both sides of the equation: 171x + y + (171/2)^2 = -733 + (171/2)^2
Simplify: 171x + y + 7391/4 = 17113/4
Finally, we can rewrite the left side as a binomial squared and simplify the right side: 171(x + 7391/4) + y = 17113/4
Therefore, the equation in vertex form is: y = 171(x + 7391/4) - 17113/4
What is the mean of 85,89,95,71,80,85,76
The table shows the heights and weights of a few students in a class.
Height (inches) Weight (pounds)
58 122
59 128
60 126
62 133
63 145
64 136
66 144
68 150
70 152
Complete the following sentences based on your observations.
The data seems to have a correlation coefficient close to .
This indicates that the weight of a student as the height of the student increases.
NextReset
The data on student heights and weights suggests a strong positive correlation, implying that as a student's height increases, their weight tends to increase as well.
Explanation:The data provided on student's heights and weights suggests a linear relationship. To complete the sentences based on the data:
The data seems to have a correlation coefficient close to positive one. This indicates that the weight of a student increases as the height of the student increases.
In statistics, when we observe that as one variable increases, the other also increases, we describe this as a positive correlation. A positive correlation coefficient closer to +1 implies a strong positive correlation, meaning that generally taller students in the given data set tend to weigh more.
Final answer:
The correlation coefficient for the given data is approximately 0.86, indicating a positive correlation between height and weight.
Explanation:
The data seems to have a correlation coefficient close to 0.86. This indicates that the weight of a student increases as the height of the student increases.
Which property is represented by the number sentence shown below?
6+(4+5) = (6+4)+5
A. Commutative property of multiplication
B. Associative property of addition
C. Commutative property of addition
D. Associative property of multiplication
If you can also explain how you got the I’ll appreciate it.
Abe is going to plant 54 oak trees and 27 pine trees. Abe would like to plant the trees in rows that all have the same number of trees and are made up of only one type of tree. What is the greatest number of trees Abe can have in each row?
Answer:
27 trees in each row
Step-by-step explanation:
Abe is going to plant 54 oak trees and 27 pine trees
greatest number of trees Abe can have in each row =?
54 = 2 x 27
27 = 1 x 27
Now 27 is the common in both numbers and also is the greatest number
So, there are 2 rows of oak trees and 1 row of pine trees and all the rows have 27 number of trees.
Samuel order four did from an online music stores. Each dvd cost 9.99$. He has a 20% discount code and sales tax is 6.75%. What is the total cost of the order
multiply 4 by 9.99 for cost of the 4 dvd's
9.99 *4 = 39.96
20% discount is: 39.96 *0.20 = 7.99
39.96 - 7.99 = 31.97
now add the sales tax:
31.97 * 1.0675 = 34.13
total cost is $34.13
Evaluate (1/2^-2) + 1/2
After a power failure, the temperature in a freezer increased an average rate of 2.5 Fahrenheit per hour. The total increase was 7.5 Fahrenheit. Right and solve any Quetion to find the number of hours until the power was restored.
Can the leaves of an ordered rooted tree have the universal address 1.1, 1.2.1, 1.2.2, 1.2.3, 2.1, 2.2.1, 2.3.1, 2.3.2, 2.4.2.1, 2.4.2.2, 3.1, 3.2.1, 3.2.2? if so, identify such an ordered rooted tree.
What is the answer to this question?
2A on 2A + 3B + 3C = 8 pieces
The probability:
[tex]\dfrac{2}{8}=\dfrac{2:2}{8:2}=\dfrac{1}{4}[/tex]
[tex]\dfrac{1}{4}=\dfrac{1}{4}\cdot100\%=25\%[/tex]
Answer: 25%The demand equation for soccer tournament T-shirts is xy − 5,000 = y where y is the number of T-shirts the Enormous State University soccer team can sell at a price of $x per shirt. Find dy dx x = 6 . dy/dx x = 6 = T-shirts per dollar Interpret the result. When the price is set at $6, the demand is by T-shirts per $1 increase in price.
The given equation is:
x y – 5000 = y
Rewrite this to create an explicit equation:
x y – y = 5000
y ( x – 1) = 5000
y = 5000 / (x – 1)
Derive to get dy / dx:
dy = - 5000 dx / (x – 1)^2
dy / dx = - 5000 / (x – 1)^2
So plugging in x = 6,
dy / dx = - 5000 / (6 – 1)^2
dy / dx = - 200
Answer:
[tex]\frac{dy}{dx}|_{x=6}= -200[/tex]
Step-by-step explanation:
Given : Demand equation [tex]xy − 5,000 = y[/tex]
To Find [tex]\frac{dy}{dx}|_{x=6}[/tex]
Solution :
[tex]xy- y= 5000[/tex]
[tex]y(x-1)= 5000[/tex]
[tex]y= \frac{5000}{x-1}[/tex]
Differentiating with respect to x
[tex]\frac{dy}{dx}= \frac{-5000}{(x-1)^2}[/tex]
Now substitute x = 6
[tex]\frac{dy}{dx}|_{x=6}= \frac{-5000}{(6-1)^2}[/tex]
[tex]\frac{dy}{dx}|_{x=6}= \frac{-5000}{5^2}[/tex]
[tex]\frac{dy}{dx}|_{x=6}= \frac{-5000}{25}[/tex]
[tex]\frac{dy}{dx}|_{x=6}= -200[/tex]
Hence [tex]\frac{dy}{dx}|_{x=6}= -200[/tex] =T-shirts per dollar