Answer:
30%
Step-by-step explanation:
The unemployment rate is 30%
lim(lnx-ln4/x-4) as x approaches 4
Answer:
1/4 = 0.25
Step-by-step explanation:
I assume you mean
lim((ln(x) - ln(4)) / (x - 4))
ln(x) - ln(4) = ln(x/4)
rule of l'hopital
lim f(x)/g(x) = lim f'(x)/g'(x)
if g'(x) <> 0
f(x) = ln(x/4)
g(x) = x - 4
ln(x)' = 1/x
ln(x/4)' = 1/x/4 × 1/4 = 1/x
(x - 4)' = 1
so,
lim f'(x)/g'(x) = 1/x / 1 = 1/x
which is for x approaching 4 : 1/4 = 0.25
Match each equation below with its solution(s).
1. x² =4
2.x² = -4
3.x² +2=0
4.x²-2=0
5.x² = -18
6.x²=18
8.x+2=0
7.x-2=0
+2i +3i√√2 +√√2 2 ±2 -2 ±i√√2 +3√√2
Drag each solution above to the matching equation below.
1.
2.
3.
4.
5.
6.
7.
8.
[tex]1) \pm 2 \\\\2) \pm 2i\\\\3) \pm i\sqrt{2}\\\\4) \pm \sqrt{2}\\\\5) \pm 3i\sqrt{2}\\\\6) \pm 3\sqrt{2}\\\\7) 2\\\\8) -2[/tex]
Which expression is equivalent to this polynomial?
x2+12
OA. (X +2v3i)(c – 2v3i)
OB. (x+6i)(x - 6i)
OC. (x + 2√3)²
OD. (x + 2√3)(x − 2√3)
x² + 12 is equivalent to the polynomial (x + 2[tex]\sqrt{3}[/tex]i) (x + 2[tex]\sqrt{3}[/tex]i).
What are Polynomials?Polynomials are defined as algebraic expressions consisting of constants, variables and exponents combined using operations like addition, multiplication, subtraction and division.
The given expression is x² + 12.
We have the identity (a + b) (a - b) = a² - b²
(x + 2[tex]\sqrt{3}[/tex]i) (x + 2[tex]\sqrt{3}[/tex]i) = x² - (2[tex]\sqrt{3}[/tex]i)²
= x² - (2² × √3² × i²)
We know that i² = -1, where i is the imaginary number in complex numbers
(x + 2[tex]\sqrt{3}[/tex]i) (x + 2[tex]\sqrt{3}[/tex]i) = x² - (4 × 3 × -1)
= x² + 12
Hence we get that (x + 2[tex]\sqrt{3}[/tex]i) (x + 2[tex]\sqrt{3}[/tex]i) is equivalent to x² + 12.
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find the first 4 terms and the 10th term from 3n+4
Answer:
16 and 34
Step-by-step explanation:
The general form = 3n+4
The 4th term = 3(4)+4 = 12+4 = 16
The 10th term = 3(10)+4= 30+4= 34
Select the point that is a solution to the system of inequalities.
y≤2x-2
y≤ x²-3x
Both statements are true. Therefore (4,2) is a solution and option D is correct.
The given inequalities are [tex]y\leq 2x-2[/tex] and [tex]y\leq x^{2} -3x[/tex].
We need to select the point that is a solution to the system of inequalities (-2,-1), (1,3), (2,1) and (4,2).
What is an example of a system of inequalities in real life?Inequalities can be seen in the speed limits on roads, the minimum age for seeing certain movies, and the distance you have to walk to go to the park. Inequalities represent a limit of what is permitted or achievable rather than a precise quantity.
Any point is a solution to this system of inequality if it satisfies both inequalities.
Check the inequalities by each option.
For (-2, -1), [tex]-1\leq 2(-2)-2 \implies -1\leq -6[/tex].
This statement is false because -1 is greater than -6. Therefore (-2,-1) is not a solution and option A is incorrect.
For (1, 3), [tex]3\leq 2(1)-2 \implies 3\leq 0[/tex]
This statement is false because 3 is greater than 0. Therefore (1,3) is not a solution and option B is incorrect.
For (2,1), [tex]1\leq 2(2)-2 \implies 1\leq 2[/tex].
[tex]1\leq 2^{2} -3(2) \implies 1\leq -2[/tex]
This statement is false because 1 is greater than -2. Therefore (2,1) is not a solution and option C is incorrect.
For (4,2), [tex]2\leq 2(4)-2 \implies 2\leq 6[/tex]
[tex]2\leq 4^{2} -3(4) \implies 2\leq 4[/tex]
Both statements are true. Therefore (4,2) is a solution and option D is correct.
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For a population with μ = 60 , X=81, and σ = 12. Find the z-score for 81.
The z-score for 81 is 1.75
How to determine the z-score for 81?The given parameters are:
μ = 60 , X=81, and σ = 12
The z scores is calculated using:
[tex]z = \frac{x - \mu}{\sigma}[/tex]
Substitute the given values
[tex]z = \frac{81 - 60}{12}[/tex]
Evaluate the difference
[tex]z = \frac{21}{12}[/tex]
Simplify
z = 1.75
Hence, the z-score for 81 is 1.75
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Solve this for me please
Answer:
30.5
Step-by-step explanation:
here :
n represents the number of trials
p represents the probability of success
In a binomial distribution, The mean
is equal to the product of those two values.
In other words,
The mean = n × p
= 122 × 0.25
= 30.5
A wagon is being pulled by a handle making a 40° angle with a force of 35 pounds. What amount of force is moving the wagon along level ground? Round to the nearest tenth.
The amount of force is moving the wagon along ground level will be 26.8 pound
A force in physics is an effect that has the power to alter an object's motion. A mass-containing object's velocity can vary, or accelerate, as a result of a force. Intuitively, a push or a pull can also be used to describe force. Being a vector quantity, a force has both magnitude and direction.
Given a wagon is being pulled by a handle making a 40° angle with a force of 35 pounds
We have to find amount of force is moving the wagon along level ground
The angle with force is given 40 degree
So the formula to find amount of force is moving the wagon along level ground will be as follow:
Fₓ = F cosθ
Fₓ = 35 * cos40
Fₓ = 26.8 pound
Hence amount of force is moving the wagon along ground level will be 26.8 pound
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Line AB and line BC form a right angle at point B with points A(2,5) and B(8,3) . What is the equation of line BC ?
Answer: y = 3x - 21
Step-by-step explanation:
If the lines form a right angle, this means that they are perpendicular. Therefore, we can use the fact that perpendicular lines have slopes that are negative reciprocals of each other (in other words, their slopes multiply to -1).
The slope of AB is [tex]\frac{3-5}{8-2}=\frac{-2}{6}=-\frac{1}{3}[/tex]. This means that the slope of BC is 3.
Substituting into point-slope form,
[tex]y-3=3(x-8)\\\\y-3=3x-24\\\\\boxed{y=3x-21}[/tex]
Graph the feasible region for the follow system of inequalities by drawing a polygon around the feasible region. Click to set the corner points. 2 x + 4 y ≤ 36 7 x + 5 y ≤ 63 x ≥ 0 y ≥ 0 { 2x+4y ≤ 36 7x+5y ≤ 63 x ≥ 0 y ≥ 0
Feasible region for the given inequalities is shaded via black color in graph.
What is Inequalities?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Here, given Inequalities are;
2 x + 4 y ≤ 36
7 x + 5 y ≤ 63
x ≥ 0 y ≥ 0
The graph of given inequalities are given below and the feasible region is shaded with the black color.
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Need help with this geometric question
Answer: A
Step-by-step explanation:
[tex]V=\frac{1}{2}(6)(4)(2)=\boxed{24}[/tex]
Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene 97degree
Answer:
Obtuse and the rest of the question is incomplete.
Step-by-step explanation:
&= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} S = square numbers E = even numbers Complete the Venn diagram. E, S 4 2,6 8, 10, 12 E & = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 } S = square numbers E = even numbers Complete the Venn diagram . E , S 4 2,6 8 , 10 , 12 E
The remaining elements if Venn diagram is S= { 4, 9}
What is Venn diagram?A Venn diagram uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items.
Given:
E = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 }
S = square numbers
E = even numbers
Element in set S= { 4, 9}
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14. The probability my daughter will eat her dinner without complaining is 5/7. The probability she will eat
her dinner and do her homework all without complaining is 2/7. What is the probability she will do her
homework without complaining given that she ate her dinner without complaining?
Probability helps us to know the chances of an event occurring. The probability she will do her homework without complaining given that she ate her dinner without complaining is 2/5.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Let eating dinner without complaining be A, and doing homework without complaining be B.
Given the probability my daughter will eat her dinner without complaining is 5/7. So, we can write,
P(A) = 5/7
Also, The probability she will eat her dinner and do her homework all without complaining is 2/7. So, we can write,
P(A∩B) = 2/7
Now, the probability she will do her homework without complaining given that she ate her dinner without complaining is,
[tex]P(B|A)= \dfrac{P(A\cap B)}{P(A)}[/tex]
[tex]= \dfrac{\dfrac{2}{7}}{\dfrac57}\\\\\\= \dfrac25[/tex]
Hence, the probability she will do her homework without complaining given that she ate her dinner without complaining is 2/5.
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Please answer all four of the questions I would really appreciate it <3
Answer:
1)A because 3 < 3.9 < 4
2)C because 8.2<8.23<8.3
3) D because 6.1>5.9
4)B because 3.6<3.625<3.7
Hope it helps!
What is the domain of the function shown on the graph?
The asnwer is C
for finding domain look at just x-axis from left to right , because there are arrows , so domain is all real numbers or from negative infinity to positive infinity
Please give brainliest
a
b
c
or d
question is in picture
A, -9 ≤ -3X -6 ≤ 6
What is inequality?Inequality is an algebraic statement that shows that two quantities are unequal.
Analysis:
From the above, only A, is the correct inequality represented above.
solving for x in A, we have,
-9 ≤ -3x - 6 ≤ 6
splitting,
-9 ≤ -3x -6
-3 ≤ -3x
1 ≥ x
x ≤ 1
-3x-6 ≤ 6
-3x ≤ 12
x ≥ 12/-3 ≥ -4
-4 ≤x ≤1, A
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What is the distance from P to Q?
OA. 1 unit
OB. 7 units
OC. 5 units
D. 25 units
Answer:
C) 5 units
Step-by-step explanation:
In order to find the distance between points P and Q, we will be using the Distance Formula.
[tex]\sf \textsf{\underline{Distance Formula:}}\ \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Given:
P (3, -1) Q (-1, -4)where:
⇒ x₁ = 3, y₁ = -1
⇒ x₂ = -1, y₂ = -4
Substitute these values into the formula:
[tex]\sf\\\implies d=\sqrt{(-1-3)^2+(-4-(-1))^2}\\\\\implies d=\sqrt{(-1-3)^2+(-4+1)^2}\\\\\implies d=\sqrt{(-4)^2+(-3)^2}\\\\\implies d=\sqrt{16+9}\\\\\implies d=\sqrt{25}\\\\\implies d=5[/tex]
The distance from P to Q is 5 units.
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what is the Smallest numbers :
p = x^2 + 2x +2 / x+1 (x>-1)
t= 1/x + 4/1-x (0
Answer:
I exactly don't know the answer
Chad has a rope that is 24 yards long. How many pieces of rope measuring of a yard can he divide his rope into1/4
The pieces of rope measuring a yard can he divide his rope into1/4 would be 96.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Chad has a rope that is 24 yards long. He wants to divide the rope so each piece will be 1/4 yards
= 24÷1/4
= 24× 4
= 96
Hence he can divide the rope into 96 pieces.
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Tacoma's population in 2000 was about 200 thousand, and has been growing by about 9% each year. If this continues, what will Tacoma's population be in 2019?
The population of Tacoma in 2019 would be 1,028,332.
What will be the population in 2019?The population can be represented with an exponential equation that has the form:
FV = P (1 + r)^n
FV = Future populationP = Present population R = rate of growth N = number of years200,000 (1.09)^19 = 1,028,332.
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What is the inequality for this verbal description?
Kyle has d dollars to spend at the garden store. He wants to buy one small
tree for $9.00 and s pounds of soil that cost $5.00 per pound. Which
inequality represents this situation?
OA. d≥ 5s +9
OB. d> 5s +9
OC. d<9s +5
O D. d≥ 9s +5
Answer:
A) d [tex]\geq[/tex] 5s + 9
Answer:
A. d ≥ 5s + 9
Step-by-step explanation:
9.00 is fixed cost5.00 is cost per pound of soilHence, equation will be :
d ≥ 5s + 9 (As d must be greater than/equal to this value for Kyle to afford it)The cost of renting a car is $47 /week plus $0.25 /mile traveled during that week. An equation to represent the cost would be y=47+0.25x , where x is the number of miles traveled.
Answer:
a. 61.25
b. 70
c. 212
Step-by-step explanation:
a. What is your cost if you travel 57 miles?
The cost is $ .
y=47+0.25x
y=47+0.25(57)
y=47+14.25
answer: 61.25
b. If your cost was $64.50, how many miles were you charged for traveling?
You were charged for traveling miles.
64.50-47=0.25x
17.50=1/4x
17.50*4
answer 70=x
c. Suppose you have a maximum of $100 to spend for the car rental. What would be the maximum number of miles you could travel?
The maximum number of miles you could travel is miles.
100-47
53=1/4x
answer : x= 212
1-tan^2(x)/sec^2 = cos(2x)
By applying the formula of trigonometric function the right hand side will
be equal to right hand side which is 1-[tex]tan^{2} x[/tex]/[tex]sec^{2}x[/tex]=cos2x.
Given: 1-[tex]tan^{2} x[/tex]/[tex]sec^{2}x[/tex]=cos2x.
Taking right hand side first which is cos2x.
We know that cos2x=[tex]1-tan^{2}x/1+tan^{2}x[/tex]
Now we will solve the left hand side of the equation give which is
1-[tex]tan^{2} x[/tex]/[tex]sec^{2}x[/tex]
=1-[tex]tan^{2}x[/tex]/1+[tex]tan^{2}x[/tex]
[secant square x minus tangent square x is equal to 1]
By putting both values left hand side and right hand side we will find our solution which is :
1-tan^{2}x/1+tan^{2}x=1-[tex]tan^{2}x[/tex]/1+[tex]tan^{2}x[/tex].
Hence proved
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What is the slope of the line (14,0), (2, -6)
Answer:
1/2 is the answers
Step-by-step explanation:
please mark me as brainlest
The slope of the line is = 0.5
Given that:-one point is =(14,0)
other is =(2,-6)
Solution:-We can easily solve the question by the formula of a straight line.
The slope is = 0-(-6)/(14-2)
= 1/2
114
4. Line p contains point (6,-5) and is perpendicular to line q. The equation for line gis y = 3x + 5.
Write an equation for line p.
Part I: Find the slope of line q. (1 point)
Part II: Find the slope of line p. (Write the negative reciprocal of the slope you found in Part I.) (1 point)
that
Part III: Use the point given for line p and the slope you found in Part II to write an equation for line pin
point-slope form: y - y₁ = m(x-x₁). (1 point)
Line q has slope 3, as you've found.
Any line perpendicular to q will then have slope -1/3, as you've found.
Line p thus has slope -1/3 and we know it passes through (6, -5), so from the point-slope formula we get the equation
[tex]y - (-5) = -\dfrac13 (x - 6) \implies \boxed{y + 5 = -\dfrac13 (x - 6)}[/tex]
How to solve this one
Please step by step
Answer: 1/2
Step-by-step explanation:
Dividing the numerator and denominator by x, we get the limit is equal to:
[tex]\lim_{x \to -\infty} \frac{-\sqrt{1+\frac{5}{x}+\frac{1}{x^2}}+3}{4+\frac{7}{x}}\\\\=\frac{\lim_{x \to -\infty} \left(-\sqrt{1+\frac{5}{x}+\frac{1}{x^2}}+3 \right)}{\lim_{x \to -\infty} \left(4+\frac{7}{x} \right)}\\\\=\frac{2}{4}=\boxed{1/2}[/tex]
What is the greatest common factor of 20 and 36?
2
4
5
6
Answer:
GFC = 4
Step-by-step explanation:
Factors of 20 1 2 4 5 10 20
Factors of 36 1 2 3 4 6 9 12 18 36
Answer:4
Step-by-step explanation:nice and simple
Denise is designing the seating arrangement for a concert at an outdoor theater. To give everyone a good view, each row must have 6 more seats than the row before it, and the 1st row can only have 11 seats. Explain to Denise how to create an equation to predict the number of seats in any row. Then, using your equation, show your work to determine the number of seats in row 18.
As per the question each row must have 6 seats more than the row before it. And there are 11 seats in the first row.
So, the first row has 11 seats
2nd row has 11+6 seats
3rd row has 11+2*6=11+12=23
4th row has 11+3*6=11+18=29
and so on...
We know that the difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. Arithmetic progression can be calculated as
aₙ = a₁ + (n - 1)d,
where aₙ is the nth and a₁ is the first term of this progression respectively and d is the common difference between terms.
So, we can observe the trend and develop the equation for the problem.
There are 11+(n-1)*6 seats in the n-th row.
So, there is 11+(18-1)*6=11+17*6=113 seats in the 18th row.
Therefore, there are 113 seats in the 18th row.
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What is the scale factor from AABC to ADEF?
B
48
AA
6
A4 CE
48
6
O A.
C
B. 8
32
D
Answer: 8
Step-by-step explanation:
We are going from a smaller triangle to a larger triangle, so the scale factor is greater than 1.
Eliminate A and D.We know scale factor = (image)/(preimage), so the scale factor is 32/4 = 8
The scale factor of dilation of the triangle is k = 8
What is Dilation?Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent
The result of dilation is that the shapes and boundaries of objects in the input image are expanded or thickened. It is often used in conjunction with other morphological operations such as erosion, opening, and closing to manipulate and enhance images.
Given data ,
Let the first triangle be represented as ΔABC
Let the second triangle be represented as ΔDEF
where the measures of sides of ΔABC are
AB = 6 , BC = 6 and AC = 4
The measure of sides of triangle ΔDEF are
DE = 48 , EF = 48 and DF = 32
The scale factor of dilation k = measure of side DE / measure of side AB
k = 48 / 6
k = 8
Hence , the dilation factor is k =8
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