The union consists of all of the elements that are contained in each interval.
Inequality Form:
x<6
Interval Notation:
(−∞,6)
The triangles in the diagram below are similar. Find the distance across Clarence Lake. ( Figure may not be drawn to scale)
Answer: 40 km
Step-by-step explanation:
As corresponding sides of similar triangles are proportional, if we let the distance across Clarence lake be x,
[tex]\frac{x}{8}=\frac{15}{3}\\\\\frac{x}{8}=5\\\\x=\boxed{40 \text{ km}}[/tex]
The stock of Company A gained 6% today to $87.45. What was the opening price of the stock in the beginning of the day?
The opening price of the stock at the beginning of the day was $82.5 and the stock of Company A gained 6% today to $87.45.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
We have:
The stock of Company A gained 6% today to $87.45.
Let x be the opening price of the stock in the beginning of the day.
(x + 0.06x) = 87.45
Because gained 6% today to $87.45
1.06x = 87.45
x = $82.5
Thus, the opening price of the stock at the beginning of the day was $82.5 and the stock of Company A gained 6% today to $87.45.
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The account balance of each of three children at the end of a month is shown below:
Daniel has −$1.25
Libby has −$2.00
Sandra has as much savings in her account as the amount Daniel owes the bank.
Part A: On a blank paper, draw a number line from −4 to +4. Plot points on the number line to show the account balances of the three children. Label the points using the name of each child. Describe in detail how you created and labeled this number line, and what it looks like in detail. (5 points)
Part B: Determine whether Daniel or Libby owes the bank more. Use absolute values and inequalities to write statements that justify your conclusion. (5 points)
Answer:
Using the concept of number line, we find that Libby owes more than Daniel.
Step-by-step explanation:
Given that the account balance of Daniel is -$1.25 and of Libby is -$2.00. Sandra has as much savings in her account as the amount Daniel owes the bank. So, her account balance is +$1.25.
The numbers to be plotted on the number line are -2.00, -1.25 and 1.25.
The number line is in the attachment.
These numbers are related as: -2 < -1.25 < 1.25.
From the number line, all the names that come left to the origin owe some amount to the bank while all the names that come right to the origin have some money as savings in their account.
Clearly, Daniel and Libby owe the bank.
But since Libby comes before Daniel, Libby owes more than Daniel.
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find the highest number of student of whom 125 apples, 150 oranges and 225 mangoes can be divided equally
Answer:
25
Step-by-step explanation:
find the greatest common factor (GCF) of the 3 quantities using prime factorisation.
125 = 5 × 5 × 5
150 = 2 × 3 × 5 × 5
225 = 3 × 3 × 5 × 5
Next, identify those prime factors that the 3 numbers have in common and multiply them.
the common factors are 5 × 5 = 25
then
125 ÷ 25 = 5
150 ÷ 25 = 6
225 ÷ 25 = 9
the 25 students each get 5 apples, 6 oranges and 9 mangoes
A country's population in 1991 was 103 million, in 1999 it was 108 million. estimate the total population in 2013
Answer:
117
Step-by-step explanation:
The total population is 117 million
12x² + 9x² =
A. 21x²²
B. 21x
C. 22x²
D. 22xA
Answer:
21x²
Step-by-step explanation:
hopefully A is a typo
Answer: A (if it's just a typo) or [tex]21x^{2}[/tex]
Step-by-step explanation:
Since it's the same variable and same exponent, you just need to add the whole numbers and put the same variable and exponent.
12 + 9 = 21
[tex]21x^{2}[/tex]
Indicate the equation of the given line in standard form. Show all of your work for full credit.
The line containing the altitude to the hypotenuse of a right triangle whose vertices are P(-1, 1), Q(3, 5), and R(5, -5).
Answer: 24 sq units is the area of triangle.
Step-by-step explanation:
Given , (x1 , y1) = (-1, 1), (x2 , y2) = (3, 5) , (x3, y3) = (5, -5)
Using the Formula :
Area of triangle = [tex]\[\frac{1}{2}(x1(y2-y3) + x2(y3-y1) + x3(y1 -y2))\][/tex]
[tex]\[=\frac{1}{2}(-1(5-(-5)) + 3(-5-1) + 5(1-5)) \\=\frac{1}{2}(-10 -1 8 -20) \\=\frac{1}{2}(-48) = -24\][/tex]
Area cannot be negative. We only consider the numerical value of answer. Therefore, area of triangle = 24 sq units.
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(-4, 150) find two pair of polar coordinates
The polar coordinates of (-4, 150°) will be [tex]\sqrt[2]{5629}\\[/tex] and 5069.09939523°
What is the coordinate about?The formula for this conversion will be:
r = [tex]\sqrt{x^2 + y^2}[/tex]
θ = [tex]tan ^-1 (\frac{y}{x} )[/tex]
[tex]r = \sqrt{(4^2) + (150^0)^2} \\\\θ = tan ^-1 (\frac{y}{x} )\\\\\\r = \sqrt[2]{5629} \\\\ = tan ^-1 (\frac{150}{4} )\\[/tex]
= [tex]\frac{75}{2}[/tex]
the inverse of: [tex]\frac{75}{2}[/tex] is θ = 5069.09939523°
Therefore:
[tex]r = \sqrt[2]{5629}\\[/tex]
θ = 5069.09939523°
So the polar coordinates of (-4, 150°) will be [tex]\sqrt[2]{5629}\\[/tex] and 5069.09939523°
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can you please help me
The basic parabola is stretched in the y-direction by a factor of 2 (and hence made steeper) and translated.
To create a new parabola that resembles the fundamental parabola, we can translate the parabola vertically. The graph of the function y=x2+b simply resembles a regular parabola with the vertex moved b units down the y-axis. The vertex is so situated at (0,b). The parabola shifts upward if b is positive and downward if b is negative.
The parabola can also be translated horizontally. The graph of the function y=(x-a)^2 resembles a conventional parabola with the vertex moved one unit down the x-axis. then, the vertex is found at (a,0). Observe how we go to the right if an is positive and to the left if an is negative.
All parabolas can be obtained from the basic parabola by a combination of:
translationreflectionstretchingrotation.Thus, all parabolas are similar.
Hence the basic parabola is stretched in the y-direction by a factor of 2 (and hence made steeper) and translated.
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Let f(x)=7x^5 ln(x) + 1/3 x^3
f’(x)=
I’m stuck on this calculus problem. If anyone could help me work this out. I would appreciate if you showed all your steps.
Answer:
f'(x) = 7x^4 (5 ln(x) + 1) + x^2
Explanation:
[tex]\sf Let \ f(x)=7x^5 ln(x) + \dfrac{1}{3} x^3[/tex]
Properties used while differentiating:
[tex]i) \quad \sf \dfrac{d}{dx} (ln(x)) = \dfrac{1}{x}[/tex]
[tex]ii) \quad \sf \dfrac{d}{dx} (x^n) = n(x)^{n-1}[/tex]
[tex]iii) \quad \sf \dfrac{d}{dx}(uv)=u \dfrac{dv}{dx}+v \dfrac{du}{dx}[/tex]
Begin solving:
f'(x) =
[tex]\Longrightarrow \sf \dfrac{d}{dx}\:\left(7x^5\:ln\left(x\right)\:+\:\dfrac{1}{3}\:\:x^3\right)[/tex]
[tex]\Longrightarrow \sf \dfrac{d}{dx}\:\left(7x^5\:ln\left(x\right)\right) + \dfrac{d}{dx}\left(\dfrac{1}{3}x^3\right)[/tex]
[tex]\Longrightarrow \sf \dfrac{d}{dx}(7x^5)\:\ \times ln\left(x\right) + \dfrac{d}{dx}(ln(x)) \times \ 7x^5 + \left(3\:\times \dfrac{1}{3}x^{3-1}\right)[/tex]
[tex]\Longrightarrow \sf 5(7x^{5-1})\:\times\ ln(x) + \dfrac{1}{x} \:\times\ 7x^5 \ + x^2[/tex]
[tex]\Longrightarrow \sf 35x^{4} ln(x) + \ 7x^4 \ + x^2[/tex]
[tex]\Longrightarrow \sf 7x^4(5 ln(x) + 1) \ + x^2[/tex]
Use the graph to Write an equation of the line(3,165)(1,55)
Answer:
y=55x
Step-by-step explanation:
(y1-y2)/(x1-x2)=(165-55)/(3-1)=55
55 is the slope
To find y-intercept:
y=55x+b
substitute 1 for x and 55 for y
55=55(1)+b
b=0
So y= 55x
the equation of the line passing through the points (3, 165) and (1, 55) is y = 55x. To write the equation of the line that passes through the points (3, 165) and (1, 55), you can use the point-slope form of a linear equation, which is: y - y₁ = m(x - x₁)
where (x₁, y₁) is one of the points on the line, m is the slope of the line.
First, calculate the slope (m) using the given points (3, 165) and (1, 55):
m = (y₂ - y₁) / (x₂ - x₁) = (55 - 165) / (1 - 3) = (-110) / (-2) = 55
Now that you have the slope (m = 55) and one of the points (let's use (3, 165)), you can plug them into the point-slope form:
y - 165 = 55(x - 3)
Now, you can simplify and rewrite this equation in slope-intercept form (y = mx + b):
y - 165 = 55x - 165
To isolate y, add 165 to both sides:
y = 55x
So, the equation of the line passing through the points (3, 165) and (1, 55) is y = 55x.
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.Let S =(5, 10, 15, 20, 25, 30} be the sample space of an experiment and let T = {5,10}, V = {5, 20, 30} and W = {10, 15, 25} be the events of the experimen.
I meed the true answer. tnx!
A set is a mathematical model for a collection of items. The set of W' is {5, 20, 30}.
What is a set?A set is a mathematical model for a collection of items; it comprises elements or members, which may be any mathematical object: numbers, symbols, points in space, lines, other geometrical structures, variables, or even other sets.
The complete question is given below.
Q13.
T ∪ V = Data points that are in T or V or both.
T ∪ V = {5, 10, 20, 30}
Q14.
T ∩ W = Data points that are in T and W both.
T ∩ W = {10}
Q15.
W' = Data points that are not in W.
W' = {5, 20, 30}
Hence, the set of W' is {5, 20, 30}.
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4. At what coordinates does the terminal side of a -420° angle intersect the unit circle?
Answer:
[tex]\left(\dfrac{1}{2},-\dfrac{\sqrt{3}}{2}\right)[/tex]
Step-by-step explanation:
An angle is co-terminal with the same angle that has any multiple of 360° added to it.
__
The angle -420° is co-terminal with (-420° +720°) = 300°. The attached unit circle chart shows the coordinates of the terminal side of that angle.
These coordinates are ...
(x, y) = (cos(300°), sin(300°))
(x, y) = (1/2, -√3/2)
in quadlateral wxyz wc equals 2X +5 and CY equals 3X +2 what must x equal
The value of x in the given quadrilateral is; x = 3
How to find the angle in a quadrilateral?
The diagonals of a parallelogram bisect each other.
Thus, from the image attached, we can say that;
WC = CY.
Thus;
2x + 5 = 3x + 2
Subtract 2x from each side to get;
5 = x + 2
Subtract 2 from each side to get;
5 - 2 = x + 2 - 2
x = 3
The complete question is;
In quadrilateral WXYZ, WC = 2x + 5 and CY = 3x + 2. What must x equal for quadrilateral WXYZ to be a parallelogram?
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What is the value of x for the regular polygon shown below?
2x + 4
36
Determin d/dx (x²+1) (7x-3) and d/dt(3t-2/5t+1)
Answer:
2x(7x-3) + (x²+1)(7)
Step-by-step explanation: use product rule
in case of severe pathologic hypersecretory conditions a physician may order ZantacR up to 6 g/day if the patient is to be given 1.5 g/day divided into four doses what is the amount to administer per dose?
Step-by-step explanation:
sorry sorry ^$£%£$¥#^÷£=₩€%¥=£=;÷¥÷¥9=
Two dice are rolled. What is the probability that the sum of the numbers rolled is either 10 or 11? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answer:
P(Event) = N(Favorable Outcomes) / N (Total Outcomes)
P(sum of 10 or 11) = 5/36
Step-by-step explanation:
Probability states how likely an event is about to happen. The probability of an event can exist only between 0 and 1 where 0 indicates that event is not going to happen i.e. Impossibility and 1 indicates that it is going to happen for sure i.e. Certainty.
The higher or lessen the probability of an event, the more likely it is that the event will occur or not respectively. For example – An unbiased coin is tossed once. So the total number of outcomes can be 2 only i.e. either “heads” or “tails”. The probability of both outcomes is equal i.e. 50% or 1/2.
So,
P(Event) = N(Favorable Outcomes) / N (Total Outcomes)
Sample Space:
All the possible outcomes of an event are called Sample spaces.
Examples-
• If two dice are rolled together then total outcomes will be 36 and
Sample space will be
[ (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) ]
Probability of rolling a sum of 10 or 11 with two dice:
When two dice are rolled together then total outcomes are 36 and
Sample space is
[ (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) ]
So, pairs with sum 10 or 11 are (4, 6) (5, 5) (6, 4) (5,6) (6,5) i.e. total 5 pairs
Total outcomes = 36
Favorable outcomes = 5
Probability of getting the sum of 10 or 11 = Favorable outcomes / Total outcomes
= 5 / 36
So, P(sum of 10 or 11) = 5/36
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2. Find the LCM of the following numbers by division method. (a) 16 and 28 (b) 36 and 44 (c) 45 and 120 (d) 10, 15 and 30 (e) 52 and 128 (f) 20, 60 and 80
(a):112
(b):396
(c):360
(d):30
(e):1664
(f):240
Please please help asap I’ll make I brainliest
Answer: [tex]x=5\sqrt{3}[/tex]
Step-by-step explanation:
As the triangle is equilateral, we know that all sides have a length of 10. Thus, if we consider either of the right triangles, we know they have legs of lengths 5 and x (since an altitude of an equilateral triangle bisects the side it is drawn to), and a hypotenuse of 10.
Thus, by the Pythagorean theorem,
[tex]5^{2}+x^{2}=10^{2}\\\\25+x^{2}=100\\\\x^{2}=75\\\\\boxed{x=5\sqrt{3}}[/tex]
On Sunday, there were 22 inches of snow. The weather finally began to warm up and by Monday afternoon there were 19 inches. Then on Tuesday, there were 16 inches. If the snow continues to melt the same number of inches every day complete the equation to model the snowmelt if d represents the number of days after Sunday.
Answer:
22-3d=x
Step-by-step explanation:
where d is the days that it melts and the amount of snow x is the snow that is left.
Find the x-intercept of the line whose equation is 8x + 2y = 4.
Answer: (I am copying and pasting my answer from the same question you did before in case you are waiting for an answer on this instead.)
1/2
Step-by-step explanation:
To find the x-int of any equation, you will need to replace the y with a 0 since when the x-int is when y is 0.
8x+2y = 4 ➨ 8x+2*0 = 4
Now I will do 2*0 which anything times 0 is equal to 0. And we are left with the equation of:
8x = 4
Now I will divide both sides by 8, which isolates our x.
x = 1/2
The x-int is 1/2.
Answer:
(0.5 , 0) or (1/2 , 0)
Step-by-step explanation:
Any x-intercept must be at (x,0), so we substitute y=0 into the equation.
8x + 2(0) = 4
8x = 4
x = 1/2 = 0.5
Therefore, the x-intercept is at (0.5 , 0) or (1/2 , 0)
Para administrar 500 ml de suero fisiológico (SF) al 0,9% en el período de 8 horas a las 20 horas, se debe planear un goteo, en gotas/min. Igual a:
Si administran 500 ml. La tasa de goteo requerida en gotas por minuto es de 21 gtt/min.
Tasa de goteo requeridaUsando esta fórmula
Tasa de goteo requerida=(ml administrado×gotas/mL)÷ (Número de horas×Número de minutos por hora)
Vamos a conectar la fórmula
Tasa de goteo requerida =(500 mL x 20 gtt/mL) ÷ (8 hrs. x 60 min)
Tasa de goteo requerida =10,000÷480
Tasa de goteo requerida = 20.8
Tasa de goteo requerida =21 gtt/min (Aproximadamente)
Por lo tanto, la tasa de goteo requerida en gotas por minuto es de 21 gtt/min.
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To prove triangles similar, we only need to prove corresponding angles congruent OR corresponding sides are proportional. However, with a quadrilateral we need to prove corresponding angles congruent AND corresponding sides are proportional. Explain in your own words why it takes more to prove that quadrilaterals are similar. Include examples demonstrating how “just angles” or “just sides” is not enough.
It takes more to prove that quadrilaterals are similar because there are several quadrilaterals such as rectangle, square, etc.
What is a quadrilateral?It should be noted that a quadrilateral simply means a shape that has four sides and four angles.
In orde to prove that triangles are similar, we only need to prove corresponding angles congruency.
On the other hand, it takes more to prove that quadrilaterals are similar because there are several quadrilaterals such as rectangle, square, etc. This makes them more elaborate.
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Which statements about the location of the point are
true? Select three options.
The point is in the first octant.
The point lies behind the yz-plane.
The x-coordinate is -3.
The y-coordinate is positive.
The point lies to the left of the xz-plane.
Answer:
Step-by-step explanation:
Solve the problem.
Determine dy/dt for x^3 + y^3 = 9 given x = 1, y = 2, and dx/dt= -3
Differentiate both sides with respect to [tex]t[/tex], treating both [tex]x[/tex] and [tex]y[/tex] as functions of [tex]t[/tex].
[tex]x^3 + y^3 = 9 \implies 3x^2 \dfrac{dx}{dt} + 3y^2 \dfrac{dy}{dt} = 0[/tex]
Then when [tex]x=1[/tex], [tex]y=2[/tex] and [tex]\frac{dx}{dt}=-3[/tex], we get
[tex]3\times1^2\times(-3) + 3\times2^2\dfrac{dy}{dt} = 0 \implies \dfrac{dy}{dt} = \dfrac9{12} = \boxed{\frac34}[/tex]
Find the length of AB.
OA. 89 units
OB. About 3.6 units
OC. 13 units
O D. About 9.4 units
Applying the distance formula, the length of AB is: D. About 9.4 units.
What is the Distance Formula?Distance formula is given as: [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].
Given the following:
A(4, 2) = (x1, y1)
B(9, 10) = (x2, y2)
Apply the distance formula
AB = √[(9−4)² + (10−2)²]
AB = √[(5)² + (8)²]
AB = √89
AB ≈ 9.4 units
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aron bought an almirah for $1520 and sold it at a profit of 12 1/2% what is the selling price
Answer:
$1710
Step-by-step explanation:
let me know if you want an explanation :))
Factor the polynomial function.
G(v) - 196v² + 100
Answer:
4(49v²+25)
Step-by-step explanation:
[tex]196 {v}^{2} + 100[/tex]
[tex]4(49 {v}^{2} + 25)[/tex]
simplify completely 12x^2 -4x^2+8x over -2x
Answer:
-4*(x+1)
Step-by-step explanation:
Simplify
⇒ 8x2 + 8x/-2x
2: Pulling out like terms
4.1 Pull out like factors :
8x2 + 8x = 8x • (x + 1)
Canceling Out :
4.2 Canceling out x as it appears on both sides of the fraction line
Final result :
-4 • (x + 1)
Answer:
-4(x+1)
Step-by-step explanation:
factor out -2x
-2x(-6x + 2x - 4) / -2x
the -2x in numerator and denominator cancel out
-6x + 2x - 4
-4x - 1
-4(x+1)
