Answer:
B. All real numbers
Step-by-step explanation:
I assume the function is f(x) = 3^x, where x is an exponent.
Since an exponent can be a positive number, a negative number, and zero, x can be any real number. The domain of a function is the set of values that can be used for x.
Answer: B. All real numbers
For f(x) = 3*x
Domain of given function is B. All real numbers
What is domain?It is a set of all values that gives a valid value if we put it in a function.
Any value which can be substituted in function and doesn't return infinity or complex form is part of domain.
How to solve?Check for which value f(x) can return infinite?
Answer is none.
for which value f(x) can give complex number?
Answer is none.
since there exists no such value for which f(x) return infinity or complex number, Domain of f(x) is all real numbers.
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If z is a standard normal variable, find the probability.
The probability that z lies between –1.10 and –0.36
0.4951
–0.2237
0.2237
0.2239
Answer:
0.2237
Step-by-step explanation:
Use the Table of Standard Normal Probabilities for Negative z-scores.
For z= -0.36 NORMSDIST(-0.36)=0.3594 (read value from the table)
For z= -1.10 NORMSDIST(-1.10)=0.1357 (value from the table)
You know P(-1.10<z<-0.36) = 0.3594-0.1357=0.2237
what is the simplest form of 3√27a3b7
Answer:
[tex]3ab^2\sqrt[3]{b}[/tex]
if the problem was [tex]\sqrt[3]{27a^3b^7}[/tex].
Step-by-step explanation:
Correct me if I'm wrong by I think you are writing [tex]\sqrt[3]{27a^3b^7}[/tex].
[tex]\sqrt[3]{27a^3b^7}[/tex]
I'm first going to look at this as 3 separate problems and then put it altogether in the end.
Problem 1: [tex]\sqrt[3]{27}=(3)[/tex] since [tex](3)^3=27[/tex].
Problem 2:[tex]\sqrt[3]{a^3}=(a)[/tex] since [tex](a)^3=a^3[/tex]
Problem 3: [tex]\sqrt[3]{b^7}[/tex]. This problem is a little harder because [tex]b^7[/tex]is not a perfect cubes like the others were. But [tex]b^7[/tex] does contain a factor that is a perfect cube. That perfect cube is [tex]b^6[/tex] so rewrite [tex]b^7[/tex] as [tex]b^6 \cdot b^1[/tex] or [tex]b^6 \cdot b[/tex].
So problem 3 becomes [tex]\sqrt[3]{b^6 \cdot b}=\sqrt[3]{b^6}\cdot \sqrt[3]{b}=b^2 \cdot \sqrt[3]{b}[/tex]. The [tex]b^2[/tex] came from this [tex](b^2)^3=b^6[/tex].
Anyways let's put it altogether:
[tex]3ab^2\sqrt[3]{b}[/tex]
What is the value of 2 over 3 to the power of 0 to the power of -3
Answer:
[tex]((\frac{2}{3})^0)^{-3}=1[/tex]
Step-by-step explanation:
We need to find the value of [tex]((\frac{2}{3})^0)^{-3}[/tex]
Solving:
We know, [tex](a^b)^n = a^{b*n}[/tex]
[tex]((\frac{2}{3})^{0*-3})[/tex]
[tex](\frac{2}{3})^0[/tex]
a^0 = 1
so,
[tex](\frac{2}{3})^0=1[/tex]
So, the value of [tex]((\frac{2}{3})^0)^{-3}=1[/tex]
A parallelogram has vertices at (-5, -1), (-2, -1), (-3, -4), and (-6, -4). What is the approximate perimeter of the parallelogram? Round your answers to the nearest hundredth.
a. 9.16
b. 12 units
c. 12.32 units
d. 14
e. 14.32
I NEED THE ANSWER ASAP!!
Answer:
option C
Step-by-step explanation:
We will call :
A=(-5, -1) B=(-2, -1) C=(-3, -4) D= (-3, -4)
Perimeter= 2*AB+2BC
Where AB= [tex]\sqrt{(-5+2)^{2} +(-1+1)^{2} } = \sqrt{9} =3\\[/tex]
BC =[tex]\sqrt{(-2+3)^{2} +(-1+4)^{2} } = \sqrt{10} =3.16\\[/tex]
So We have:
Perimeter=2*3+2*3.16= 12.32
Answer:
C.
Step-by-step explanation:
Which factor do 9x2 – 12x + 4 and 9x^2 – 4 have in common?
Answer:
3x-2
Step-by-step explanation:
[tex]9x^{2} -12x+4[/tex] can be factored using the perfect square rule into [tex](3x-2)^{2}[/tex]
and
[tex]9x^{2}-4[/tex] can be factored by using the difference of squares formula into [tex](3x+2)(3x-2)[/tex]
Both can be factored by (3x-2) so it is a common factor.
Hence, there are no common factors between the two equations.
What is a factor?factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder.
How to solve?given equation is [tex]9x^2-4[/tex]
solving for x,
[tex]9x^2=4\\x^2=\frac{9}{4} \\x=\frac{3}{2}, -\frac{3}{2}[/tex]
putting values of x in equation 1,
x = [tex]\frac{3}{2}[/tex],
[tex]\frac{81}{4}-12.\frac{3}{2}+4\\ \frac{25}{4}[/tex]Therefore, 3/2 is not a common factor
x=[tex]-\frac{3}{2}[/tex],
[tex]\frac{81}{4}+12.\frac{3}{2}+4\\ \frac{169}{4}[/tex]Therefore, -3/2 is not a common factor
Hence, there are no common factors between the two equations.
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The data shown on the scatter plot below demonstrates the relationship between the time of day and the total number
of calories that a teenager consumes throughout the day.
That as time ___________,
the total number of calories that a teenager consumes throughout the day
___________.
Blank A options:
Stays the same
Increases
Decreases
Blank B options:
Stays the same
Decreases
Increases
Answer:
Good question! The correct answer is a) increases and b) increases.
While the pair of answers a) decreases and b) decreases or the pair a) stays the same and b) stays the same would be technically correct answers, this is the best way of describing the trend of the scatter plot; typically, trends are described by how the dependent or y-variable responds to the independent or x-variable increasing.
Answer:
a) increases and b) increases.
Step-by-step explanation:
What is most likely the correlation coefficient for the set of data shown
Answer:
0.19
Step-by-step explanation:
A correlation coefficient is a measure of how well the line of best fit fits the data. The higher the correlation coefficient, up to 1.0 or -1.0, the better the fit. A positive correlation coefficient means an increasing data set, while a negative correlation coefficient means a decreasing data set.
We can see that this line of best fit is increasing, so our correlation coefficient will be positive.
However we can also see that the points are fairly scattered; this means this is not a very good fit. This means that 0.19 is the better fit.
A ball is released at a height of 27 inches to roll inside a half-cylinder. It rolls
to a height of 9 inches on the other side of the cylinder on roll 1. Each time it
rolls up a side of the cylinder, the ball reaches a point th
high as it
had reached on the other side.
This explicit formula models the height of the ball, in inches, the nth time it
rolls up a side of the cylinder.
How high does the ball roll on its 4th time up the cylinder's side?
Answer:
[tex]\frac{1}{3}\ in[/tex]
Step-by-step explanation:
we have
[tex]a(n)=9(\frac{1}{3})^{n-1}[/tex]
For n=4
substitute
[tex]a(4)=9(\frac{1}{3})^{4-1}[/tex]
[tex]a(4)=9(\frac{1}{3})^{3}[/tex]
[tex]a(4)=9(\frac{1}{27})[/tex]
[tex]a(4)=\frac{1}{3}\ in[/tex]
Answer:
1/3
Step-by-step explanation:
I need some help guys
Answer:
Q1: D
Q2: D
Step-by-step explanation:
Question No 1:
The given sequence is:
-2, 0, 3, 7, ...
We can easily determine that this is not an arithmetic sequence because the common difference between terms is not same.
i.e.
0-(-2) = 0+2 = 2
3-0 = 3
7-3 = 4
As the common difference is not same so the sequqnce is not an arithmetic sequence.
Question no 2:
Given sequence is:
28, 18, 8, -2, ..
We can see that the common difference is -10 i.e 18-28 = -10
And it is same for all numbers.
The standard formula for arithmetic sequence is:
[tex]a_n=a+(n-1)d\\Here\\a = 28\\d=-10\\So,\\a_n=28+(-10)(n-1)\\a_n=28-10n+10\\a_n=38-10n[/tex]
Now for the 52nd term:
[tex]a_{52} = 38-10(52)\\= 38-520\\=-482[/tex] ..
Please Help.
Tracey built a small boat and recorded the distance it traveled. The table below shows the distance traveled (f) during the first 4 seconds after starting (p).
Elapsed Time
(seconds) Distance Traveled
(feet)
1 4.2
2 8.4
3 12.6
4 16.8
Which of the following equations represents the relationship between the distance traveled and the elapsed time?
p = 4.2f
f = 4.2p
p = 4.2 + f
f = 4.2 + p
Answer:
Expressing the distance from the shore by the time needed to reach that distance at an invariable speed of 4.2f/s then f=4.2 p
Answer:
f=4.2p
Step-by-step explanation:
If a graph of y=-4x +2 were changed to a graph of y=-4x+5, how would the y- intercept change?
Answer:
So if y=-4x+2 was changed to y=-4x+5, then the y-intercept would increase by 3.
The y-intercept was (0,2) then it becomes (0,5) in the new line.
Step-by-step explanation:
The slope-intercept form a line is y=mx+b where m is the slope and the y-intercept is b.
Both of these equations given are in this form.
y=-4x+2 when compared to y=mx+b you see that m=-4 and b=2.
Since b=2 then the y-intercept is 2.
y=-4x+5 when compared to y=mx+b you see that m=-4 and b=5.
Since b=5 then the y-intercept is 5.
So if y=-4x+2 was changed to y=-4x+5, then the y-intercept would increase by 3.
Solve the inequality. 1/3+x+2/9>5/6
Answer:
5⁄18 < x
Step-by-step explanation:
Start by adding like-terms [⅓ and 2⁄9] with 9 being the Least Common Denominator [LCD]. Since 2⁄9 already has a 9 in the denominator, it does not get touched, so in order to make ⅓ a denominator of 9, we simply multiply both terms by 3, to get 3⁄9. So, adding that to 2⁄9 gives you 5⁄9, also giving you 5⁄9 + x > ⅚. Now, we have to find the LCD again because we have two unlike fractions. Now, our Least Common Denominator is 18, so multiply both terms in ⅚ by 3 [15⁄18] and multiply both terms in 5⁄9 by 2 [10⁄18]. Now you have two like fractions to work with, and you can clearly see that your answer is x > 5⁄18. Although the answer is written in reverse, it is still the same concept.
I am joyous to assist you anytime.
A cube has side length 0.7 metres.
Work out the total surface area of the cube.
Give your answer in square centimetres
Answer:
2.94cm^2
Step-by-step explanation:
If you're referring to the mathswatch question, this gets you 2/3 :)
Ben has 9 pizza’s with 8 slices each. 59 were eaten. How many slices are left?
Answer:
13 slices.
Step-by-step explanation:
To find your total amount of slices at the start, multiply your pizzas by your slices.
[tex]9*8=72[/tex]
Next, find the difference between your total amount of slices and the amount of slices which have been eaten.
[tex]72-59=13[/tex]
13 slices are left.
-3(6f - 12) = 36 - 18f
Answer:
Step-by-step explanation:
The given expression is:
-3(6f - 12) = 36 - 18f
To prove that L.H.S=R.H.S:
Multiply -3 (6f-12)
-3(6f)-3(-12)
=-18f+36
=36-18f
Hence it is proved that L.H.S = R.H.S....
which equation represents a circle?
Answer:
C
Step-by-step explanation:
The equation of a circle centred at the origin is
x² + y² = r² ← r is the radius
Consider
[tex]\frac{x^2}{2^2}[/tex] + [tex]\frac{y^2}{2^2}[/tex] = 1, that is
[tex]\frac{x^2}{4}[/tex] + [tex]\frac{y^2}{4}[/tex] = 1
Multiply through by 4
x² + y² = 4 ← equation of circle
This is the equation of a circle centred at the origin with radius 2
help pleaseeeee solve 3-x/2=>12
Answer:
x ≤-18
Step-by-step explanation:
3-x/2≥12
Subtract 3 from each side
3-3-x/2≥12-3
-x/2≥9
Multiply each side by -2 to clear the fraction. Remember to flip the inequality since we are multiplying by a negative
-3 * -x/2 ≤ -2 *9
x ≤-18
Answer:
x ≤ - 18
Step-by-step explanation:
Given
3 - [tex]\frac{x}{2}[/tex] ≥ 12
Multiply all terms by 2
6 - x ≥ 24 ( subtract 6 from both sides )
- x ≥ 18
Multiply both sides by - 1, remembering to reverse the sign as a consequence of multiply by a negative quantity.
x ≤ - 18
In which pair of triangles is Triangle EFG=Triangle RTS?
Answer:
The last picture or
The picture with 3 lines on EF and TR, 1 line one EG, 1 line on SR, 2 lines on ST and 2 lines on GF
Step-by-step explanation:
Since EF and RT have 3 lines and FG and TS have 2 lines, they are similar
Answer:
Last pair of triangles represent congruence.Step-by-step explanation:
If [tex]\triangle EFG \cong \triangle RTS[/tex], it can be deducted the following:
[tex]\angle E \cong \angle R\\\angle F \cong \angle T\\\angle G \cong \angle S[/tex]
Also,
[tex]EF \cong RT\\FG \cong TS\\EG \cong RS[/tex]
Notice that the last imag shows the correct congruence, because it shows the congruence between sides as we said before.
18-r=12
[tex]18 - r = 12[/tex]
Answer:
r = 6Step-by-step explanation:
18 - r = 12 subtract 18 from both sides
18 - 18 - r = 12 - 18
-r = -6 change the signs
r = 6
Check
18 - 6 = 12 CORRECT
Leila bought 3 bananas, which weighed a total of 3/4 of a pound . if each banana weighed the same amount , what is the weight of each banana ?
Answer:
I think the answer is A
Step-by-step explanation:
Answer:
C.
Step-by-step explanation: The other answer was not right on edge* but i belive that it is C.
What is the following quotient? sqrt 6 + sqrt 11 / sqrt 5 +sqrt 3
The answer is B) Link below
Answer:
B
Step-by-step explanation:
I just did it
Find the value of x in the picture please
Answer:
Option D 74°
Step-by-step explanation:
we know that
The measurement of the outer angle is the semi-difference of the arcs it encompasses.
so
The arcs that the outer angle encompasses are
254° and (360-254)=106°
therefore
∠x=(1/2)[254°-106°]
∠x=(1/2)[148°]
∠x=74°
Determine the theoretical probability of rolling a number larger than two and a standard 66 sided cube
Answer:
Required probability = 2/3
Step-by-step explanation:
When rolling a 6 sided die, the out comes are
1, 2, 3, 4, 5 and 6
Total number of outcomes = 6
To find the probability
The required outcome is a number greater than 2, therefore possible outcomes are,
3, 4, 5, and 6
Number of possible outcomes = 4
Required probability = 4/6 = 2/3
Answer:
Determine the theoretical probability of rolling a number larger than 2 on a standard 6-sided cube.
2/3
Step-by-step explanation:
Use the distributive property to evaluate 4(2x-1) when x=6 .
Answer:
44Step-by-step explanation:
The distributive property: a(b + c) = ab + ac
4(2x - 1) = (4)(2x) + (4)(-1) = 8x - 4
Put x = 6 to the expression:
8(6) - 4 = 48 - 4 = 44
The solution to the given expression is 44.
What is the distribution property of multiplication?The distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a given numerical value or factor, the same output would be produced as when each addend is multiplied respectively by the numerical value or factor, and the products are added together.
By applying the distributive property of multiplication to the given expression, we have:
4(2x - 1) = 4(2x) - 4(1)
4(2x - 1) = 8x - 4
when x = 6, we have;
8x - 4
8(6) - 4
48 - 4 = 44.
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What is solution to equation X-5/7=-3/7
The isosceles triangle has a perimeter of 7.5 m which equation can be used to find the value of x if the shortest side, y measures 2.1 m ?
Answer:
7.5 = 2x + 2.1
Step-by-step explanation:
The perimeter of a triangle is the sum of the sides. In an isosceles triangle, two sides are the same length. If x is the length of the two sides and y is the length of the third side, then:
P = 2x + y
Given that P = 7.5 and y = 2.1:
7.5 = 2x + 2.1
Answer: The equation that can be used to find the value of x is
2x + 2.1 = 7.5
Step-by-step explanation: An isosceles triangle is a type of triangle which has two of its sides equal to each other. It also has two it's angles (the base angles) equal to each other.
From the question, the given triangle has the shortest side, y to be 2.1 m. This means side y is shorter than the other two sides. Hence, the other two sides must be the sides that are equal to each other. These other two sides are denoted by x ( see the attachment for an illustrative diagram).
The perimeter of a triangle is the sum of all its sides. Therefore, the perimeter (P) of the given triangle is
P = x + x + y
P = 2x + y
From the question, P = 7.5 m
and y = 2.1 m
Hence,
7.5 m = 2x + 2.1 m
2x + 2.1 m = 7.5 m
This equation can be used to find the value of x. The equation can also be written as:
2x = 7.5 m - 2.1m OR
x = (7.5 m - 2.1m) / 2
The given line passes through the points (0, -3) and (2, 3).
What is the equation, in point-slope form of the line that is
parallel to the given line and passes through the point
-1, - 1)?
y+1=3(x+1)
y+1=-=(x + 1)
-
532
v+1={(x+1)
y+1 =3(x+1)
Mark this and return
Save and Exit
S
Answer:
[tex]y+1=3(x+1)[/tex]
Step-by-step explanation:
Ok so we are looking for line parallel to the line containing points (0,-3) and (2,3).
Parallel lines have the same slope.
So let's find the slope of the line containing the points (0,-3) and (2,3).
You can use the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].
However, I just like to line up the points vertically and subtract them vertically, then put 2nd difference over 1st difference. Like this:
(0 , -3)
-(2 , 3)
-----------
-2 -6
So the slope is -6/-2 or just 3.
So the slope of the line we are looking for has slope 3 (or m=3) and your line should contain the point (-1,-1).
The point slope form of a line is:
[tex]y-y_1=m(x-x_1)[/tex] where [tex]m[/tex] is the slope and [tex](x_1,y_1)[/tex] is a point you know on the line.
So we just plug into that equation now. That gives us:
[tex]y-(-1)=3(x-(-1))[/tex]
Simplify a bit:
[tex]y+1=3(x+1)[/tex]
Answer:
The answer is: y+1=(3x+1)
Step-by-step explanation:
Mixed 3 liters 20% solutions with 2 liters 70% solution. What’s the final concentration,
Answer:
(3×20%+2×70%)/3+2=40%
Step-by-step explanation:
Assuming the potions are the same type or do mix then probably the concentration of the potion depends on the type of reaction they have to each other.
Yet we can average the percentage of the active ingredient by the principle mentioned above
Answer:
The final concentration is 40%.
Step-by-step explanation:
Let x the concentration of final solution.
3 liters of solution (1) with 20% concentration is mixed with 2 liters of 70% solution producing (3 + 2) = 5 liters of x% mixture.
Now 3 × (20%) + 2 × (70% = 5 (x%)
3 × 0.2 + 2 × 0.7 = 5 (0.1x)
0.6 + 1.4 = 0.05x
2 = 0.5x
x = 2/0.05
= 40%
The final concentration is 40%.
Given that the first term and the common difference of an arithmetic progression are 6 and 3 respectively. Calculate the sum of all terms from 4th term to the 14th term.
Answer:
330
Step-by-step explanation:
Evaluate the sum of 14 terms and subtract the sum of the first 3 terms
The sum to n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ], so
[tex]S_{14}[/tex] = 7 [ (2 × 6) + (13 × 3)]
= 7(12 + 39) = 7 × 51 = 357
[tex]S_{3}[/tex] = 6 + 9 + 12 = 27
Sum of terms from 4 th to 14 th = 357 - 27 = 330
A set of equations is given below: equation C:y=5x+10 equation D:y=5x+2 which of the following best describes the solution to the given set of equations? One solution no solution two solutions infinitely many solutions
Answer:
The system has no solution
Step-by-step explanation:
we have
y=5x+10 -----> equation C
The slope of the equation C is m=5 and the y-intercept is b=10
y=5x+2 -----> equation D
The slope of the equation C is m=5 and the y-intercept is b=2
Remember that
If two lines are parallel, then their slopes are the same
Equation C and equation D are parallel lines with different y-intercept
therefore
The system has no solution (the lines do not intersect)