A function f : X → Y assigns only one value of y ∈ Y to any given x ∈ X.
For each of the three elements in {a, b, c}, there are 5 choices of values to assign from {1, 2, 3, 4, 5}, so there are 5³ = 125 possible functions.
simplify
log(125) + log(625) / log(25) - log(5)
Answer:
3.39794000867
Step-by-step explanation:
first add log 125 and 625 and divide the answer by log 25 and minus the answer by 5
Answer:
The answer is 7.
Which equation models the same quadratic relationship as function f? f(x) = 2x^2 - 12x + 11
A) y = 2(x + 6)^2 + 2
B) y = 2(x - 3)^2 -7
C) y = 2(x - 6)^2 + 5
D) y = 2(x + 3)^2 - 7
Answer:
im not sure but i think the answer is C) y = 2(x - 6)^2 + 5
The equation models the same quadratic relationship as function f(x) = 2x^2 - 12x + 11 will be 2(x-3)²-7.Option B is correct.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, the function is,
f(x) = 2x^2 - 12x + 11
We have to find the equation models the same quadratic relationship as the given function,
⇒2x²-12x+11
Take common 2 in the complete equation,
⇒2(x²-6x+11/2)
Add and subtract 9 from the complete equation,
⇒2(x²-6x+9-9+11/2)
Rearrange the equation as,
⇒2[(x-3)²-(7/2)]
⇒2(x-3)²-7
Thus, the equation models the same quadratic relationship as function f(x) = 2x^2 - 12x + 11 will be 2(x-3)²-7.Option B is correct.
Learn more about the equation here,
https://brainly.com/question/10413253
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The volume of a boys' basketball is 434 cubic inches. Dan would like to get a ball
with half the volume for his son. What is be the diameter of the ball that Dan will buy
for his son?
A 9.4 inches
B 4.7 inches
C 3.7 inches
D 7.4 inches
Answer:
The correct answer is A. 9.4 inches.
Step-by-step explanation:
Given that the volume of a boys' basketball is 434 cubic inches, and Dan would like to get a ball with half the volume for his son, to determine what is the diameter of the ball that Dan will buy for his son, the following calculation has to be done, knowing that the volume of a sphere is four thirds multiplied by pi multiplied by the radius cubed:
4/3 x 3.14 x X ^ 3 = 434
4.186 x X ^ 3 = 434
X ^ 3 = 434 / 4.186
X = 3√ 103.662
X = 4.7
In turn, since the radius of a sphere is equal to half its diameter, the diameter of the basketball is 9.4 inches (4.7 x 2).
At the city museum, child admission is S5.80 and adult admission is $9.20. On Monday, twice as many adult tickets as child tickets
were sold, for a total sales of $895.40. How many child tickets were sold that day?
[tex]You can call c the number of children and a for adults; you get:5.20c+8.50a=1097.60anda=4c meaning that the number of adults was four times the children.Substituting this value of a into the first equation we get:5.2c+8.5(4c)=1097.65.2c+34c=1097.6rearranging:c=1097.639.2=28and so:a=4c=4⋅28=112[/tex]
I got: 28 children and 112 adults.
I need help ASAP!!!!
What is 4 log Subscript one-half Baseline w + (2 log Subscript one-half Baseline u minus 3 log Subscript one-half Baseline v) written as a single logarithm?
4 log Subscript one-half Baseline 2 Superscript 4 Baseline u squared minus v cubed
log Subscript one-half Baseline w Superscript 4 Baseline (StartFraction u squared Over v cubed EndFraction)
log Subscript one-half Baseline (StartFraction w Superscript 4 Baseline Over u squared v cubed EndFraction)
log Subscript one-half Baseline (w (StartFraction u squared Over v cubed EndFraction)) Superscript 4
Given:
The expression is:
[tex]4\log_{\frac{1}{2}}w+(2\log_{\frac{1}{2}}u-3\log_{\frac{1}{2}}v)[/tex]
To find:
The single logarithm for the given expression.
Solution:
We have,
[tex]4\log_{\frac{1}{2}}w+(2\log_{\frac{1}{2}}u-3\log_{\frac{1}{2}}v)[/tex]
It can be written as:
[tex]=\log_{\frac{1}{2}}w^4+(\log_{\frac{1}{2}}u^2-\log_{\frac{1}{2}}v^3)[/tex] [tex][\because \log a^b=b\log a][/tex]
[tex]=\log_{\frac{1}{2}}w^4+\log_{\frac{1}{2}}\dfrac{u^2}{v^3}[/tex] [tex][\because \log \dfrac{a}{b}=\log a-\log b][/tex]
[tex]=\log_{\frac{1}{2}}\left(w^4\times \dfrac{u^2}{v^3}\right)[/tex] [tex][\because \log ab=\log a+\log b][/tex]
[tex]=\log_{\frac{1}{2}}\dfrac{w^4u^2}{v^3}[/tex]
Therefore, the correct option is B.
Answer:
The answer is B :))
Step-by-step explanation:
If the surface area of an orange is 616 cm2 what is its radius?
9514 1404 393
Answer:
7.0 cm
Step-by-step explanation:
The relationship between radius and area of a sphere is ...
A = 4πr²
Then the radius as a function of area is ...
r = √(A/(4π)) = (√(A/π))/2
For an area of 616 cm², the corresponding radius is ...
r = (√(616/π))/2 ≈ 7.0 cm . . . . radius of the orange
Hope you could understand.
If you have any query, feel free to ask.
(2/5-1/2)+3/5 . [7/2-3/5÷(1/4-1/5)]
Answer: -8
Step-by-step explanation: So we after simplification we get
[(2/5) - (1/2) + (3/5)+ (7/2)] - [(3/5)/(1/4) - (1/5)]
After this I suppose it's just addition & subtraction, and can be easily done to get -8.
Economists have found that the amount of corruption in a country's government is correlated to the gross domestic product (GDP) per capita of that country. This can be modeled by y=507x−8030 where x is the corruption score and y is GDP per capita in dollars. Corruption scores range from 0 to 100 with 0 being highly corrupt and 100 being least corrupt.
Using this model, a country with a corruption score of 99 would have what GDP per capita? Round your answer to the nearest dollar.
A. $46,853
B. $36,444
C. $42,163
D. $50,546
Answer:
B i think
Step-by-step explanation:
Please help me answer this question if you have time
Answer:
C: [tex]\frac{7x}{4} + 5y[/tex]
Step-by-step explanation:
1. Realize that 12 inches is 1 feet and 36 inches is 1 yard.
2. Multiply it so that both are inches.
[tex]\frac{5y}{12} * 12 = 5y[/tex]
[tex]\frac{7x}{144} * 36 = \frac{7x}{4}[/tex]
3. Add together [tex]\frac{7x}{4} + 5y[/tex]
Answer:
C.
Step-by-step explanation:
I also recommend to just search these things on the internet. it would be much faster.
1 ft = 12 in
1 yd = 3 ft = 3×12 = 36 in
so, we need to multiply a given number of ft by 12, and a given number of yards by 36 to get the inches.
5y/12 × 12 = 5y
7x/144 × 36 = 7x/4
that is all there is to it.
Subtract the following polynomials.
(3.1x+2.8z)−(4.3x−1.2z)
Answer:
-2/5 (3x-10z)
Step-by-step explanation:
Find the x- and y-intercepts of the following line: 4x − 3y = 12
Answer:
x-intercept: (3,0)
y-intercept: (0,-4)
Step-by-step explanation:
To find the x and y-intercepts, we first need to understand what they are. X and y-intercepts are points on the line that passes through the x-axis and y-axis. When a point is an x-intercept, it passes through the x-axis. This means the x-coordinate is an integer, while the y-coordinate is always 0. This can be denoted by (x,0). When a point is a y-intercept, it passes through the y-axis. This means the y-coordinate is an integer, while the x-coordinate is always 0. This can be denoted by (0,y).
Now that we know what x and y-intercepts are, we can plug in x=0 and y=0 to find the intercepts.
x-intercept
4x-3y=12 [plug in y=0]
4x-3(0)=12 [multiply]
4x-0=12 [add both sides by 0]
4x=12 [divide both sides by 4]
x=3
---------------------------------------------------------------------------------------------------------
y-intercept
4x-3y=12 [plug in x=0]
4(0)-3y=12 [multiply]
0-3y=12 [subtract both sides by 0]
-3y=12 [divide both sides by -3]
y=-4
Therefore, the x-intercept is (3,0) and y-intercept is (0,-4).
Which diagram best shows how fraction bars can be used to evaluate One-half divided by one-fourth? A fraction bar labeled 1. Under the 1 are 2 boxes containing one-half. Under the 2 boxes are 4 boxes containing one-fourth. 2 one-fourths are circled. A fraction bar labeled one-fourth. Under the one-fourth are 2 boxes containing one-half. Under the 2 boxes are 4 boxes containing 1. 2 boxes containing 1 are circled. A fraction bar labeled 1. Under the 1 are 4 boxes containing one-fourth. Under the 4 boxes are 8 boxes containing one-half. One box containing one-half is circled. A fraction bar labeled 1. Under the 1 are 4 boxes containing one-fourth. Under the 4 boxes are 2 boxes containing one-half. One box containing one-half is circled.
Answer:
Step-by-step explanation:
The description is too ambiguous to reconstruct the diagram. You need to post the actual diagram.
That diagram is just one way to view division by a fraction. An easier way: DIVIDING by a fraction is the same as MULTIPLYING by the upside-down fraction. For example,
(1/2) ÷ (1/4) = (1/2) × (4/1) = 2
That doesn’t help you answer this particular question, though.
Answer:
C
Step-by-step explanation:
Work out 45% of $200.00
Answer:
If you are using a calculator, simply enter 45÷100×200 which will give you 90 as the answer.
Mark me brainliest plz.
Suppose 5 men and 7 women are on a crowded elevator. At the next floor, four people get off the elevator. Find the probability that three are women.
0.010
0.354
0.424
0.25
Answer:
B. 0.354Step-by-step explanation:
Combination of 4 out of 5 + 7 = 12 is:
12C4 = 12!/8!4! = 495Combination of 1 man and 3 women is:
5C1*7C3 = 5*7!/4!3! = 5*35 = 175Required probability:
P(3W) = 175/495 ≈ 0.353Correct choice is B
What is the best interpretation of the y-intercept of the line
Answer:
vertical line
Step-by-step explanation:
because horizontal means horizon which goes left to right across a board
Hi there!
The y-intercept of a line represents its initial value. On a graph, the y-intercept would represent the value of y when the line crosses the y-axis.
For example, if an equation were to model the amount of money someone had in their bank account overtime starting from the day they opened their account, the y-intercept would represent the original amount of money they had.
I hope this helps!
Which expression is equivalent to -6(-2/3 + 2x)?
Answer:
4-12x
Step-by-step explanation:
-6 ×(-2/3 + 2x)
2 × 2-12x=
4-12x
The thicknesses of 81 randomly selected aluminum sheets were found to have a variance of 3.23. Construct the 98% confidence interval for the population variance of the thicknesses of all aluminum sheets in this factory. Round your answers to two decimal places
Answer:
The confidence interval for the population variance of the thicknesses of all aluminum sheets in this factory is Lower limit = 2.30, Upper limit = 4.83.
Step-by-step explanation:
The confidence interval for population variance is given as below:
[tex][(n - 1)\times S^{2} / X^{2} \alpha/2, n-1 ] < \alpha < [(n- 1)\times S^{2} / X^{2} 1- \alpha/2, n- 1 ][/tex]
We are given
Confidence level = 98%
Sample size = n = 81
Degrees of freedom = n – 1 = 80
Sample Variance = S^2 = 3.23
[tex]X^{2}_{[\alpha/2, n - 1]} = 112.3288\\\X^{2} _{1 -\alpha/2,n- 1} = 53.5401[/tex]
(By using chi-square table)
[(n – 1)*S^2 / X^2 α/2, n– 1 ] < σ^2 < [(n – 1)*S^2 / X^2 1 -α/2, n– 1 ]
[(81 – 1)* 3.23 / 112.3288] < σ^2 < [(81 – 1)* 3.23/ 53.5401]
2.3004 < σ^2 < 4.8263
Lower limit = 2.30
Upper limit = 4.83.
the coefficients corresponding to k=0,1,2,5 in the expression (x+y)^5 are
Answer:
Step-by-step explanation: you got trolded
6
1
10 points
Find the probability that a randomly selected person's birthday is not in May. Ignore leap years.
31
334
31
365
334
365
11
2
3
12
Previous
Answer:
c. [tex]\frac{334}{365}[/tex]
Step-by-step explanation:
May has 31 days and a normal year is 365 days, so the probability is [tex]\frac{31}{365}[/tex]
The probability that isn't in May is: 1 - [tex]\frac{31}{365}[/tex] = [tex]\frac{334}{365}[/tex]
Let P(1,2,1), Q(1,0,-1), R(2,2,0) be the vertices of a parallelogram with adjacent sides PQ and PR. Find the other vertex S.
Given:
The vertices of a parallelogram are P(1,2,1), Q(1,0,-1), R(2,2,0).
PQ and PR are the adjacent sides of the parallelogram.
To find:
The coordinates of vertex S.
Solution:
We know that, the diagonals of a parallelogram bisect each other.
Let the coordinates of the vertex S are (a,b,c).
In the given parallelogram PS and QR are the diagonals. It means their midpoints are same.
[tex]\left(\dfrac{1+a}{2},\dfrac{2+b}{2},\dfrac{1+c}{2}\right)=\left(\dfrac{1+2}{2},\dfrac{0+2}{2},\dfrac{-1+0}{2}\right)[/tex]
[tex]\left(\dfrac{1+a}{2},\dfrac{2+b}{2},\dfrac{1+c}{2}\right)=\left(\dfrac{3}{2},\dfrac{2}{2},\dfrac{-1}{2}\right)[/tex]
On comparing both sides, we get
[tex]\dfrac{1+a}{2}=\dfrac{3}{2}[/tex]
[tex]1+a=3[/tex]
[tex]a=3-1[/tex]
[tex]a=2[/tex]
Similarly,
[tex]\dfrac{2+b}{2}=\dfrac{2}{2}[/tex]
[tex]2+b=2[/tex]
[tex]b=2-2[/tex]
[tex]b=0[/tex]
And,
[tex]\dfrac{1+c}{2}=\dfrac{-1}{2}[/tex]
[tex]1+c=-1[/tex]
[tex]c=-1-1[/tex]
[tex]c=-2[/tex]
Therefore, the coordinates of vertex S are (2,0,-2).
Foot Locker is having a 60% off sale on shorts. John paid $18 for a pair of shorts that were on sale. What was the original price of the shorts?
Answer:
=$45
Step-by-step explanation:
$18=40%
18÷4=4.5
$4.5=10%
4.5×10=45
$45=100%
Question 7 of 13
Find the solution to the system of equations,
5x - 3y - Z= 6
-4x + 5y + z = 6
Х
+ 3z = 10
Answer:
D. x = 4, y = 4, z = 2
Step-by-step explanation
Plugged in given answers as trying to substitute is impossible, already tried all combinations
URGENT HELP
The gradient of the tangent to the curve y = ax + bx^3 at the point (2, -4) is 6.
Determine the unknowns a and b.
a=?
b=?
Answer:
a = -6
b = 1
Step-by-step explanation:
The gradient of the tangent to the curve y = ax + bx^3, will be:
dy/dx = a + 3bx²
at (2, -4)
dy/dx = a+3b(2)²
dy/dx = a+12b
Since the gradient at the point is 6, then;
a+12b = 6 ....1
Substitute x = 2 and y = -4 into the original expression
-4 = 2a + 8b
a + 4b = -2 ...2
a+12b = 6 ....1
Subtract
4b - 12b = -2-6
-8b = -8
b = -8/-8
b = 1
Substitute b = 1 into equation 1
Recall from 1 that a+12b = 6
a+12(1) = 6
a = 6 - 12
a = -6
Hence a = -6, b = 1
a gym class has 10 boys and 12 girls. how many ways can a team of 6 be selected if the team must have the same number of boys and girls
Answer:
The number of ways of selecting the team is 26,400 ways.
Step-by-step explanation:
Given;
total number boys in the gym, b = 10 boys
total number of girls in the gym, g = 12 girls
number of team to be selected, n = 6
If there must equal number of boys and girls in the team, then the team must consist of 3 boys and 3 girls.
Number of ways of choosing 3 boys from the total of 10 = [tex]10_C_3[/tex]
Number of ways of choosing 3 girls from a total of 12 = [tex]12_C_3[/tex]
The number of ways of combining the two possibilities;
[tex]n = 10_C_3 \times 12_C_3\\\\n = \frac{10!}{7!3!} \ \times \ \frac{12!}{9!3!} \\\\n = \frac{10\times 9 \times 8}{3\times 2} \ \times \ \frac{12\times 11 \times 10}{3\times 2} \\\\n = 120 \times 220\\\\n = 26,400 \ ways[/tex]
Therefore, the number of ways of selecting the team is 26,400 ways.
Look at the figure. Find the value of x.
K
x + 5
J
L
2X-7
M
JK=JM
[tex] \\ \sf \longmapsto \: x + 5 = 2x - 7 \\ \\ \sf \longmapsto \: x - 2x = - 7 - 5 \\ \\ \sf \longmapsto \: - x = - 12 \\ \\ \sf \longmapsto \: x = 12[/tex]
distance between 4, -4 and -7, -4
Step-by-step explanation:
here's the answer to your question
Answer: Distance = 11
Step-by-step explanation:
Concept:
Here, we need to know the idea of the distance formula.
The distance formula is the formula, which is used to find the distance between any two points.
If you are still confused, please refer to the attachment below for a clear version of the formula.
Solve:
Find the distance between A and B, where:
A (4, -4)B (-7, -4)[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]Distance=\sqrt{(4+7)^2+(-4+4)^2}[/tex]
[tex]Distance=\sqrt{(11)^2+(0)^2}[/tex]
[tex]Distance=\sqrt{121+0}[/tex]
[tex]Distance=\sqrt{121}[/tex]
[tex]Distance=11[/tex]
Hope this helps!! :)
Please let me know if you have any questions
If the length is 10 cm and the width of a rectangle is 3cm , what is the area
Answer: 30cm
Step-by-step explanation:
The area of a rectangle is determined by length times width
Equation: A=LW
10cm×3cm = 30cm
3w2 – 21w = 0
Need some help.
Answer:
The solutions are w=0 ,7
Step-by-step explanation:
3w^2 – 21w = 0
Factor out 3w
3w(w-7) =0
Using the zero product property
3w=0 w-7=0
w =0 w=7
The solutions are w=0 ,7
PLEASE HELP ME AND BE CORRECT
Answer:
please someone help me with my latest question
Answer:
41 units
Step-by-step explanation:
Its the reflection the length are same
