Answer:
D. X= ± square root of 8 - 2
Step-by-step explanation:
Given quadratic equation is \[x^{2}+4x=4\]
Rearranging the terms: \[x^{2}+4x-4=0\]
This is the standard format of quadratic equation of the form \[ax^{2}+bx+c=0\]
Here, a=1 , b=4 and c=-4.
Roots of the quadratic equation are given by \[\frac{-b \pm \sqrt{b^{2}-4ac}}{2a}\]
Substituting the values and calculating the roots:
\[\frac{-4 \pm \sqrt{(-4)^{2}-4*1*(-4))}}{2*1}\]
= \[\frac{-4 \pm \sqrt{32}}{2}\]
= \[\frac{-2*2 \pm 2*\sqrt{8}}{2}\]
= \[-2 \pm \sqrt{8}\]
Hence option D is the correct option.
The solution of x² + 4x = 4 is x = ± √8 - 2,
Hence, option D is correct.
The given quadratic equation is,
x² + 4x = 4
Here we have to solve it by completing square method
Now proceed the expression,
⇒ x² + 4x = 4
Adding 4 both sides,
⇒ x² + 4x + 4 = 4 + 4
⇒ x² + 4x + 4 = 8
Since we know that 2² is equal to 4, then
⇒ x² + 4x + 2² = 8
Since we know that, Formula of complete square,
(a+b)² = a² + 2ab + b²
Therefore,
⇒ (x+2)² = 8
Taking square root both sides we get,
⇒ (x+2) = ±√8
Hence,
x = ± √8 - 2
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Choose the slope-intercept equation of the line that passes through the point (-2, 4) and is parallel to y = -3x + 6.
y = 1/3 x + 14/3
y = 3x + 10
y = -3x - 2
y = - 1/3 x + 10/3
Answer:
y = -3x - 2
Step-by-step explanation:
Parallel lines have the same slope. The only answer choice with the same slope (x-coefficient = -3) as the given line is the one shown above.
XYZ company uses "Continuous Review System (Q, ROP)" for an item. Lead-time is currently one week. The average demand during the week is 100 units with a standard deviation of 20 units. If the supplier increases lead-time to 4 weeks, what will be the standard deviation of lead-time demand?
a.40 80
b.17.89
c.44.72
d.120
Answer:
The demand value of time lead is
a) 40
Step-by-step explanation:
X Y Z company Uses "Continuous Review System for an item
Currently demand = 100 units
standard deviation = 20 units
lead time increase = 4 weeks
Apply Z statistic we get the value of standard deviation.
Harry has a small business cleaning kitchens and bathrooms. He usually cleans a bathroom in 1 hour and cleans a kitchen in 45 minutes. He never works more than 15 hours in a week. Harry earns $60 per bathroom and $20 per kitchen job. He does not do more than 8 bathroom jobs per week (the smell gets to him). Find a combination of bathroom and kitchen jobs per week that will maximize his income and state the amount.
Answer:
8 bathroom jobs and 9 kitchen jobs
Step-by-step explanation:
B=60
K=20
8*60=480
9*20=180
that would give harry 660 dollars in a week. HOWEVER- we have to make sure that its equal to or less than 15 hours of work.
8*1h= 8 hours in bathroom
9*45m=6.75hr in kitchen
8 hours+6.75 hours=14.75hr 14.75 hr<15hr so it works.
Consider the given function and the given interval.
f(x) = 3 sqrt x, [0, 16]
(a) Find the average value fave of f on the given interval
(b) Find c such that fave = f
(c). (Round your answer to three decimal places.)
Answer:
(a) fave = 8
(b) c = 64/9
(c) c ≈ 7.111
Step-by-step explanation:
(a) The average value of the function is its integral over the interval, divided by the width of the interval.
[tex]f_{ave}=\displaystyle\frac{1}{16-0}\int_0^{16} {3x^{\frac{1}{2}}} \, dx=\left.\frac{x^{3/2}}{8}\right|_0^{16}=8[/tex]
__
(b) We want ...
f(c) = 8
3√c = 8 . . . . . use f(c)
√c = 8/3 . . . . . divide by 3
c = (8/3)² . . . . square
c = 64/9
__
(c) c ≈ 7.111
To find the average value of a function, evaluate the definite integral over the interval and divide by the length of the interval.
Explanation:To find the average value of a function on a given interval, we need to evaluate the definite integral of the function over the interval and divide it by the length of the interval.
For the given function f(x) = 3√x on the interval [0, 16], the average value fave is given by:
fave = (1/[16-0]) * ∫(0 to 16) 3√x dx
Simplifying this integral, we get:
fave = 3/16 * (2/3) * (16^(3/2) - 0^(3/2)) = 4(16 - 0) = 64
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A man starts walking north at 4 ft/s from a point P. Five minutes later a woman starts walking south at 5 ft/s from a point 500 ft due east of P. At what rate are the people moving apart 15 minutes after the woman starts walking
Answer:
Both are moving apart with the rate of 8.99 feet per sec.
Step-by-step explanation:
From the figure attached,
Man is walking north with the speed = 4 ft per second
[tex]\frac{dx}{dt}=4[/tex] feet per sec.
Woman starts walking due south with the speed = 5ft per second
[tex]\frac{dy}{dt}=5[/tex] ft per sec.
We have to find the rate of change in distance z.
From the right angle triangle given in the figure,
[tex]z^{2}=(x+y)^{2}+(500)^{2}[/tex]
We take the derivative of the given equation with respect to t,
[tex]2z.\frac{dz}{dt}=2(x+y)(\frac{dx}{dt}+\frac{dy}{dt})+0[/tex] -----(1)
Since distance = speed × time
Distance covered by woman in 15 minutes or 900 seconds = 5(900) = 450 ft
y = 4500 ft
As the man has taken 5 minutes more, so distance covered by man in 20 minutes or 1200 sec = 4×1200 = 4800 ft
x = 4800 ft
Since, z² = (500)² + (x + y)²
z² = (500)² + (4500 + 4800)²
z² = 250000 + 86490000
z = √86740000
z = 9313.43 ft
Now we plug in the values in the formula (1)
2(9313.43)[tex]\frac{dz}{dt}[/tex] = 2(4800 + 4500)(4 + 5)
18626.86[tex]\frac{dz}{dt}[/tex] = 18(9300)
[tex]\frac{dz}{dt}=\frac{167400}{18626.86}[/tex]
[tex]\frac{dz}{dt}=8.99[/tex] feet per sec.
Therefore, both the persons are moving apart by 8.99 feet per sec.
Final answer:
To find the rate at which the people are moving apart 15 minutes after the woman starts walking, calculate the displacements of both individuals and then find the total displacement between them. Answer comes to be 611.52 feet.
Explanation:
Rate at which people are moving apart:
The question asks at what rate are two people moving apart 15 minutes after one of them starts walking, given that one walks north and the other south from different points. To solve this, one has to understand relative velocity and the concept of adding vectors graphically.
Calculate the man's northward displacement after 15 minutes: 4 ft/s * 5 minutes = 20 ft
Calculate the woman's southward displacement after 15 minutes: 5 ft/s * 15 minutes = 75 ft
Find the total displacement between them: ([tex]\sqrt{(500^2 + 20^2)[/tex]) + [tex]\sqrt{(500^2 + 75^2))[/tex] = 611.52 ft
What value of x will make parallelogram ABCD a rhombus?
Answer:
x = 34
Step-by-step explanation:
The figure will be a rhombus if the diagonals cross at right angles. That is ...
(3x -12)° = 90°
3x = 102
x = 34
The figure is a rhombus when x=34.
The value of x will make parallelogram ABCD a rhombus when all sides are of equal length, which corresponds to the situation where the diagonals have slopes of +1 and -1 and bisect each other at right angles.
Explanation:To determine the value of x that will make parallelogram ABCD a rhombus, we can consider the geometric properties that define a rhombus. A rhombus is a type of parallelogram with all sides of equal length, which also means its diagonals bisect each other at right angles. Given that the diagonals of the parallelogram must have slopes of +1 and -1 to maintain the properties of bisection, x would be the length making the sides of the parallelogram equilateral.
In the scenario where the original shape is a unit square, changes in frame of reference should preserve the affine property of bisection. Hence, parallelogram ABCD will become a rhombus when all sides are of equal length, which can be determined through equilateral properties of the parallelogram when the diagonals bisect each other at right angles and have slopes of +1 and -1.
Isabelle proves that the triangles are congruent by using the parallel lines to determine a second set of angles are congruent. What statement and reason could she have used? ∠ABC ≅ ∠BAC; corresponding angles of parallel lines are congruent. ∠CAB ≅ ∠DCB; alternate interior angles of parallel lines are congruent ∠ABC ≅ ∠DCB; alternate interior angles of parallel lines are congruent ∠ACD ≅ ∠ABD; corresponding angles of parallel lines are congruent.
Answer:
C
Step-by-step explanation:
The true statement is that proves the congruence of both triangles is:
∠ABC ≅ ∠DCB; alternate interior angles of parallel lines are congruent How to prove that angles are congruentFrom the complete question, we have the following highlights
Angles B and C are alternate interior anglesThe triangles are bounded by parallel linesThe above highlights mean that:
Angles ABC and DCB are congruent, by the theorem of alternate interior angles of parallel lines
Hence, the true statement is (c)
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Suppose that 7 female and 5 male applicants have been successfully screened for 5 positions. If the 5 positions are filled at random from the 12 finalists, what is the probability of selecting
a. 3 females and 2 males?
b. 4 females and 1 male?
c. 5 females?
d. at least 4 females?
a. ~0.442, b. ~0.221, c. 0, d. ~0.221. Calculated using combinations: [tex]\( \frac{C(n, k)}{C(12, 5)} \)[/tex].
To solve this problem, we can use the concept of combinations, which is a way to calculate the number of possible outcomes when order doesn't matter.
Let's define:
- [tex]\( n \)[/tex] as the total number of finalists (12 in this case)
- [tex]\( k \)[/tex] as the number of positions to be filled (5 in this case)
- [tex]\( n_F \)[/tex] as the number of female finalists (7 in this case)
- [tex]\( n_M \)[/tex] as the number of male finalists (5 in this case)
We'll use the formula for combinations:
[tex]\[ C(n, k) = \frac{n!}{k!(n - k)!} \][/tex]
where [tex]\( n! \)[/tex] represents the factorial of [tex]\( n \)[/tex], which is the product of all positive integers up to [tex]\( n \)[/tex].
a. Probability of selecting 3 females and 2 males:
[tex]\[ P(3 \text{ females, } 2 \text{ males}) = \frac{C(7, 3) \times C(5, 2)}{C(12, 5)} \][/tex]
[tex]\[ = \frac{\frac{7!}{3!4!} \times \frac{5!}{2!3!}}{\frac{12!}{5!7!}} \][/tex]
[tex]\[ = \frac{\frac{7 \times 6 \times 5}{3 \times 2 \times 1} \times \frac{5 \times 4}{2 \times 1}}{\frac{12 \times 11 \times 10 \times 9 \times 8}{5 \times 4 \times 3 \times 2 \times 1}} \][/tex]
[tex]\[ = \frac{35 \times 10}{792} \][/tex]
[tex]\[ = \frac{350}{792} \][/tex]
[tex]\[ \approx 0.442\][/tex]
b. Probability of selecting 4 females and 1 male:
[tex]\[ P(4 \text{ females, } 1 \text{ male}) = \frac{C(7, 4) \times C(5, 1)}{C(12, 5)} \][/tex]
[tex]\[ = \frac{\frac{7!}{4!3!} \times \frac{5!}{1!4!}}{\frac{12!}{5!7!}} \][/tex]
[tex]\[ = \frac{\frac{7 \times 6 \times 5}{3 \times 2 \times 1} \times \frac{5}{1}}{\frac{12 \times 11 \times 10 \times 9 \times 8}{5 \times 4 \times 3 \times 2 \times 1}} \][/tex]
[tex]\[ = \frac{35 \times 5}{792} \][/tex]
[tex]\[ = \frac{175}{792} \][/tex]
[tex]\[ \approx 0.221\][/tex]
c. Probability of selecting 5 females:
Since there are only 7 female finalists, it's impossible to select 5 females out of them for 5 positions. So, the probability is 0.
d. Probability of at least 4 females:
This includes the cases of selecting 4 females and 5 females.
[tex]$\begin{aligned} & P(\text { at least } 4 \text { females })=P(4 \text { females, } 1 \text { male })+P(5 \text { females }) \\ & =\frac{175}{792}+0 \\ & =\frac{175}{792} \\ & \approx 0.221\end{aligned}$[/tex]
So, the probabilities are:
a. Approximately 0.442
b. Approximately 0.221
c. 0
d. Approximately 0.221
Select all irrational numbers
[tex]
\sqrt{9}=3\notin\mathbb{I} \\
\sqrt{12}=2\sqrt{3}\in\mathbb{I} \\
\sqrt{16}=4\notin\mathbb{I} \\
\sqrt{20}=2\sqrt{5}\in\mathbb{I} \\
\sqrt{25}=5\notin\mathbb{I}
[/tex]
Hope this helps.
Of the numbers shown, only √12 and √20 are irrational.
Here's why:
* Rational numbers: A rational number can be expressed as a fraction `p/q`, where `p` and `q` are integers and `q ≠ 0`.
* Irrational numbers: An irrational number cannot be expressed as a fraction `p/q`. It has a decimal representation that continues infinitely without repeating.
* √9 = 3: 3 is a rational number because it can be expressed as the fraction 3/1.
* √12: The square root of 12 cannot be simplified as a fraction. Its decimal representation is non-repeating and infinite (approximately 3.464), making it irrational.
* √16 = 4: 4 is a rational number because it can be expressed as the fraction 4/1.
* √20: The square root of 20 cannot be simplified as a fraction. Its decimal representation is non-repeating and infinite (approximately 4.472), making it irrational.
* √25 = 5: 5 is a rational number because it can be expressed as the fraction 5/1.
Therefore, the only irrational numbers in the image are √12 and √20.
A rectangular area of 36 f t2 is to be fenced off. Three sides will use fencing costing $1 per foot and the remaining side will use fencing costing $3 per foot. Find the dimensions of the rectangle of least cost. Make sure to use a careful calculus argument, including the argument that the dimensions you find do in fact result in the least cost (i.e. minimizes the cost function).
Answer:
x = 8,49 ft
y = 4,24 ft
Step-by-step explanation:
Let x be the longer side of rectangle and y the shorter
Area of rectangle = 36 ft² 36 = x* y ⇒ y =36/x
Perimeter of rectangle:
P = 2x + 2y for convinience we will write it as P = ( 2x + y ) + y
C(x,y) = 1 * ( 2x + y ) + 3* y
The cost equation as function of x is:
C(x) = 2x + 36/x + 108/x
C(x) = 2x + 144/x
Taking derivatives on both sides of the equation
C´(x) = 2 - 144/x²
C´(x) = 0 2 - 144/x² = 0 ⇒ 2x² -144 = 0 ⇒ x² = 72
x = 8,49 ft y = 36/8.49 y = 4,24 ft
How can we be sure that value will give us a minimun
We get second derivative
C´(x) = 2 - 144/x² ⇒C´´(x) = 2x (144)/ x⁴
so C´´(x) > 0
condition for a minimum
2. Which coordinate divides the directed line segment from –10 at J to 23 at K in the ratio of 2 to 1? Explain.
A. 1
2. 11
C. 12
Answer:
12
Step-by-step explanation:
x=(-10×1+23×2)÷(2+1)=36/3=12
Final answer:
The coordinate that divides the line segment from -10 at J to 23 at K in the ratio of 2 to 1 is C) 12.
Explanation:
The coordinate that divides the line segment from -10 at J to 23 at K in the ratio of 2 to 1 is 12.
To find this coordinate, we can use the concept of a section formula. Let the ratio be m:n. The coordinate divided is [tex](\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n})[/tex]. Substituting the values, we get [tex](\frac{2 ( 23) + 1 ( -10)}{2+1}, \frac{2 (0) + 1 ( 2)}{2+1})[/tex] = (12, 0).
Therefore, the required coordinate that divides the line segment in the ratio of 2 to 1 is C) 12.
Amaya has a store credit of 50.86 she plans to purchase a video game for $24.97 and a golf club accessory for $6.99 how much store credit will she have left
Amaya will have $18.90 store credit left.
Step-by-step explanation:
Available store credit = $50.86
Cost of video game = $24.97
Cost of golf club accessory = $6.99
Total amount spent = Cost of video game + cost of golf club accessory
[tex]Total\ amount\ spent=24.97+6.99\\Total\ amount\ spent=\$31.96[/tex]
Remaining store credit = Available store credit - total amount spent
[tex]Remaining\ store\ credit=50.86-31.96\\Remaining\ store\ credit=\$18.90[/tex]
Amaya will have $18.90 store credit left.
Keywords: Addition, subtraction
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Write the equation of the linear relationship in slope-intercept form, using decimals as needed.
x 25 35 45 55
y 92.5 87.5 82.5 77.5
The equation that represents this relationship is y = ?
The equation of the linear relationship given the x and y coordinates is calculated in slope-intercept form by finding the slope and y-intercept. In this case, the equation of the line is y = -0.5x + 95.
Explanation:In mathematics, the equation of a linear relationship can be represented in the slope-intercept form, which is y = mx + c.
Where, 'm' is the slope of the line and 'c' is the y-intercept.
Given the x and y coordinates, we can calculate the slope 'm' using the formula, m = (y2 - y1) / (x2 - x1).
For example: m = (87.5-92.5) / (35-25) = -5 / 10 = -0.5. So the slope 'm' is -0.5.
Now we can find the y-intercept 'c' by substituting the known x,y coordinates and the slope into the equation and solving for 'c'. Let's take x = 25 and y = 92.5, substituting these values, we will get c = y - mx = 92.5 - (-0.5 * 25) = 95.
So, the equation of the straight line in slope-intercept form is y = -0.5x + 95.
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For every 60 phone calls that Linda made in a month, she received 70 phone calls. What is the ratio in simplest form of the number of calls made to the number of calls received by Linda that month?
Ans6:7
wer:
Step-by-step explanation:
Greatest Common Factornof 60 and 70 is 10.
60÷10 / 70÷10 =6/7
There are three nursing positions to be filled at Lilly Hospital. Position 1 is the day nursing supervisor, position 2 is the night nursing supervisor; and position 3 is the nursing coordinator position. There are 10 candidates qualified for 3 of the positions. Determine the number of different ways that 3 positions can be filled by these applicants.a.30.b.720.c. none of these choices.d. 10.e. 120
Answer:
The correct option is B) 720.
Step-by-step explanation:
Consider the provided information.
We have 10 candidates those qualified for 3 of the positions.
There are three nursing positions to be filled at Lilly Hospital. Position 1 is the day nursing supervisor, position 2 is the night nursing supervisor; and position 3 is the nursing coordinator position.
For Position 1 we have 10 choices, if we select 1 out of 10 candidates we are left with 9 candidates.
For position 2 we have 9 candidates, if we select 1 out of 9 candidates we are left with 8 candidates.
For position 3 we have 8 candidates.
Therefore, the number of ways are: [tex]10\times 9\times 8=720[/tex]
The number of different ways that 3 positions can be filled by these applicants is 720.
Hence, the correct option is B) 720.
Correct Option Is (e. 120.) The number of different ways that 3 positions can be filled by the applicants is 120.
Explanation:To determine the number of different ways that 3 positions can be filled by these applicants, we can use the concept of combinations. Since there are 10 candidates and the order of the positions does not matter, we can use the combination formula. The number of combinations of 10 candidates taken 3 at a time is given by:
C(10, 3) = 10! / (3!(10-3)!)
Simplifying this expression, we get:
C(10, 3) = 10! / (3!7!)
Calculating the factorial values, we have:
C(10, 3) = 10 * 9 * 8 / (3 * 2 * 1) = 120
Therefore, the number of different ways that 3 positions can be filled by these applicants is 120.
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If you wanted to view data in reports by different user categories such as Bronze, Gold, and Platinum status levels, what Google Analytics feature would you set up to collect this data?
A. Customer Filter
B. Customer Dimension
C. Custom Metric
D. Event Tracking
Answer:
B. Customer Dimension
Step-by-step explanation:
Custom dimensions is used to collect and analyze data that Analytics doesn't capture. You can send value to custom dimensions with a variable that pulls data from web page or use layer to pass specific values.
If you want to view data by different user such as Bronze , Gold , Platinum level Google Analytics feature set up the Custom Dimensions to collect the data.
The G. Analytics feature I would set up to collect this data is B. Customer Dimension
What is the customer dimension?Custom dimensions are used to gather and examine information that Analytics is unable to. A variable that retrieves information from a web page can be used to deliver value to custom dimensions, or a layer can be used to provide certain values. Sales data is broken down into individual customers via the customer hierarchy in the customer dimension.
To comply with reporting standards, the hierarchy between the root element All Customers and the individual customer might be arranged arbitrarily.
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A sumo wrestling ring is circular and has a circumference of 4.6\pi \text{ meters}4.6π meters4, point, 6, pi, start text, space, m, e, t, e, r, s, end text. What is the area AAA of the sumo wrestling ring in square meters? Give your answer in terms of \piπpi. A=A=A, equals \text{m}^2m 2
Answer:
The area of the sumo wrestling ring is [tex]5.29 \pi[/tex]
Step-by-step explanation:
The circumference of the circular sumo wrestling ring is [tex]4.6\pi[/tex], that means its radius [tex]r[/tex] is:
[tex]2\pi r=4.6\pi[/tex]
[tex]r=\frac{4.6}{2} =\boxed{2.3\:meters.}[/tex]
Now once we have the radius [tex]r[/tex] of the sumo wrestling ring we can find its area [tex]A[/tex] by the following formula:
[tex]A=\pi r^2[/tex]
Putting in the value of [tex]r=2.3\:meters[/tex] we get:
[tex]A=\pi (2.3m)^2=\boxed{5.29\pi\:\:m^2}[/tex]
Therefore the area of the sumo wrestling ring is [tex]{5.29\pi\:\:m^2[/tex]
Answer:
5.29pi
Step-by-step explanation:
A total of 517 tickets were sold for the school play. They were either adult tickets or student tickets. There were 67 more student tickets sold than adult tickets. How many adult tickets were sold?
The number of adult tickets sold for the school play was 225.
Explanation:This is a problem of simple algebra. Let's denote the number of adult tickets sold as a. It is stated in the problem that 67 more student tickets were sold than adult tickets. Therefore, we can denote the number of student tickets sold as a + 67. The problem also tells us that a total of 517 tickets were sold. Hence, we can form an equation: a + a + 67 = 517. Simplifying this equation gives us 2a + 67 = 517. And solving for a (the number of adult tickets) we subtract 67 from both sides to get 2a = 450, then divide by 2, gives us a = 225. So, 225 adult tickets were sold.
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A golf-course architect has sixsix linden trees, fourfour white birch trees, and threethree bald cypress trees to plant in a row along a fairway. In how many ways can the landscaper plant the trees in a row, assuming that the trees are evenly spaced?
Answer: There are 60060 ways to do so.
Step-by-step explanation:
Since we have given that
Number of linden trees = 6
Number of white birch trees = 4
Number of bald cypress trees = 3
Total number of trees = 6 +4 +3 =13
So, Number of ways that the landscaper plant that trees are evenly spaced is given by
[tex]\dfrac{13\!}{6!\times 4!\times 3!}\\\\=60060[/tex]
Hence, there are 60060 ways to do so.
What is the area of the rectangle
Answers
60 units
66 units
70 units
74 units
Answer:
The answer to your question is 74 u²
Step-by-step explanation:
Process
1.- Find the 4 vertices
A (-2, 8)
B (0, -4)
C (4, 9)
D (6, -3)
2.- Find the length of the base and the height
[tex]d = \sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }[/tex]
Distance AB = \sqrt{(0 + 2)^{2} + (-4 - 8)^{2} }[/tex]
dAB = [tex]\sqrt{4 + 144}[/tex]
dAB = [tex]\sqrt{148}[/tex]
Distance BD = \sqrt{(6 - 0)^{2} + (-3 + 4)^{2} }[/tex]
dBD = [tex]\sqrt{36 + 1}[/tex]
dBD = [tex]\sqrt{37}[/tex]
3.- Find the area
Area = base x height
Area = [tex]\sqrt{148} x \sqrt{37}[/tex]
Area = [tex]\sqrt{5476}[/tex]
Area = 74 u²
Lucy goes to a department store and spends $90 on clothing.She buys a dress for $30,a hat for $12, and also buys a jacket.How much does the jacket cost?
Answer:
$48
Step-by-step explanation:
$30+$12=$42
$90-$42=$48
Answer: she spent $48 on the jacket
Step-by-step explanation:
Lucy goes to a department store and spends $90 on clothing. This means that all the money she spent at the store is $90
She buys a dress for $30,a hat for $12, and also buys a jacket.
Let $x = the cost of the jacket. Therefore, total amount spent at the store = amount spent on dress + amount spent on hat + amount spent on jacket. It means that
90 = 12 + 30 + x
x = 90 - 12 -30 = $48
he brain volumes (cm cubedcm3) of 20 brains have a mean of 1103.81103.8 cm cubedcm3 and a standard deviation of 121.9121.9 cm cubedcm3. Use the given standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or significantly high. For such data, would a brain volume of 1367.61367.6 cm cubedcm3 be significantly high?
Answer: We can say that brain volume of 1367.6 cubic cm would be significantly high.
Step-by-step explanation:
Since we have given that
n = 20 brains
Mean = 1103.8 cubic. cm
Standard deviation = 121.9 cubic. cm
According to range rule of thumb, the usual values must lie within 2 standard values from the mean.
So, it becomes,
[tex]\bar{x}-2\sigma\\\\=1103.8-2\times 121.9\\\\=1103.8-243.8\\\\=860[/tex]
and
[tex]\bar{x}+2\sigma\\\\=1103.8+2\times 121.9\\\\=1103.8+243.8\\\\=1225.7[/tex]
We can see that 1376.6 does not lie within (860,1225.7).
So, we can say that brain volume of 1367.6 cubic cm would be significantly high.
A rectangle is drawn on a coordinate grid. The equation for one side of the rectangle is 2x – 5y = 9. Which could be the equation of another side of the rectangle?
Answer:
[tex]25x+10y+18=0[/tex]
Step-by-step explanation:
We are given that a rectangle in which the equation of one side is given by
[tex]2x-5y=9[/tex]
We have to find the equation of another side of the rectangle.
We know that the adjacent sides of rectangle are perpendicular to each other.
Differentiate the given equation w.r.t.x
[tex]2-5\frac{dy}{dx}=0[/tex] ([tex]\frac{dx^n}{dx}=nx^{n-1}[/tex])
[tex]5\frac{dy}{dx}=2[/tex]
[tex]\frac{dy}{dx}=\frac{2}{5}[/tex]
Slope of the given side=[tex]m_1=\frac{2}{5}[/tex]
When two lines are perpendicular then
Slope of one line=[tex]-\frac{1}{Slope\;of\;another\;line}[/tex]
Slope of another side=[tex]-\frac{5}{2}[/tex]
Substitute x=0 in given equation
[tex]2(0)-5y=9[/tex]
[tex]-5y=9[/tex]
[tex]y=-\frac{9}{5}[/tex]
The equation of given side is passing through the point ([tex]0,-\frac{9}{5})[/tex].
The equation of line passing through the point [tex](x_1,y_1)[/tex] with slope m is given by
[tex]y-y_1=m(x-x_1)[/tex]
Substitute the values then we get
[tex]y+\frac{9}{5}=-\frac{5}{2}(x-0)=-\frac{5}{2}x[/tex]
[tex]y=-\frac{5}{2}x-\frac{9}{5}[/tex]
[tex]y=\frac{-25x-18}{10}[/tex]
[tex]10y=-25x-18[/tex]
[tex]25x+10y+18=0[/tex]
Hence, the equation of another side of rectangle is given by
[tex]25x+10y+18=0[/tex]
Answer:
y=2/5x-9
I just answered this and got it right.
Step-by-step explanation:
Consider an employee's whose earnings, in dollars, are according to the continuous stream f(t)=5,000e0.1t for t>0, where t is measured in years. How many years will it take them to earn a combined total of $100,000? Give your answer in years to the nearest year.
It will take approximately 10.986 years for the employee to earn a combined total of $100,000. Rounding to the nearest year, it will take approximately 11 years for the employee to reach this earnings milestone.
To determine how many years it will take for the employee to earn a combined total of $100,000, we need to set up and solve the following integral:
[tex]\[ \int_{0}^{t} 5000e^{0.1\tau} \, d\tau = 100,000 \][/tex]
Here, [tex]\( t \)[/tex] represents the time in years. The integral represents the accumulated earnings from the start (0 years) to t years based on the continuous stream function[tex]\( f(\tau) = 5000e^{0.1\tau} \).[/tex]
Let's solve this integral:
[tex]\[ \int_{0}^{t} 5000e^{0.1\tau} \, d\tau = \left. \frac{5000}{0.1}e^{0.1\tau} \right|_{0}^{t} \][/tex]
Evaluate this at the upper and lower limits:
[tex]\[ \frac{5000}{0.1}e^{0.1t} - \frac{5000}{0.1}e^{0.1 \times 0} \][/tex]
Simplify:
[tex]\[ 50000(e^{0.1t} - 1) \][/tex]
Now, set this expression equal to the target earnings of $100,000 and solve for t :
[tex]\[ 50000(e^{0.1t} - 1) = 100,000 \][/tex]
Divide both sides by 50000:
[tex]\[ e^{0.1t} - 1 = 2 \][/tex]
Add 1 to both sides:
[tex]\[ e^{0.1t} = 3 \][/tex]
Now, take the natural logarithm (ln) of both sides:
[tex]\[ 0.1t = \ln(3) \][/tex]
Solve for t:
[tex]\[ t = \frac{\ln(3)}{0.1} \][/tex]
Using a calculator:
[tex]\[ t \approx \frac{1.0986}{0.1} \]\[ t \approx 10.986 \][/tex]
At a recent track meet the fastest time in the 40-yard dash was 4.37 seconds on the slowest time was 5.08 seconds what is the difference between the fastest and slowest time
The difference between the fastest and slowest time in the 40-yard dash is 0.71 seconds.
Explanation:The difference between the fastest and slowest time in the 40-yard dash can be found by subtracting the slowest time from the fastest time. In this case, the fastest time was 4.37 seconds and the slowest time was 5.08 seconds. To find the difference, we subtract 5.08 seconds from 4.37 seconds.
The difference between the fastest and slowest time is 0.71 seconds.
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Use Descartes' Rule of Signs to determine the possible numbers of positive and negative real zeros of f (x )equals x cubed plus 5 x squared plus 7 x plus 6f(x)=x3+5x2+7x+6. What are the possible numbers of positive real zeros?
Answer:
0
Step-by-step explanation:
All of the terms have positive signs, so there are no sign changes. Zero sign changes means there are zero positive real roots.
What is the difference between an inscribed and a circumscribed shape?
Answer:
An inscribed shape is drawn inside of another shape . A circumscribed shape is the shape drawn on the outside or around another shape .
Telephone calls arrive at a doctor’s office according to a Poisson process on the average of two every 3 minutes. Let X denote the waiting time until the first call that arrives after 10 a.m.
(a) What is the pdf of X?
(b) Find P(X > 2).
Answer:
a) [tex]f(x)=\frac{2}{3}e^{-\frac{2}{3}x}[/tex] when [tex]x\geq 0[/tex]
[tex]f(x)=0[/tex] otherwise
b) [tex]P(X<2)=0.2636[/tex]
Step-by-step explanation:
First of all we have a Poisson process with a mean equal to :
μ = λ = [tex]\frac{2}{3}[/tex] (Two phone calls every 3 minutes)
Let's define the random variable X.
X : ''The waiting time until the first call that arrives after 10 a.m.''
a) The waiting time between successes of a Poisson process is modeled with a exponential distribution :
X ~ ε (λ) Where λ is the mean of the Poisson process
The exponential distribution follows the next probability density function :
I replace λ = a for the equation.
[tex]f(x)=a(e)^{-ax}[/tex]
With
[tex]x\geq 0[/tex]
and
[tex]a>0[/tex]
[tex]f(x)=0[/tex] Otherwise
In this exercise λ= a = [tex]\frac{2}{3}[/tex] ⇒
[tex]f(x)=(\frac{2}{3})(e)^{-\frac{2}{3}x}[/tex]
[tex]x\geq 0[/tex]
[tex]f(x)=0[/tex] Otherwise
That's incise a)
For b) [tex]P(X>2)[/tex] We must integrate between 2 and ∞ to obtain the probability or either use the cumulative probability function of the exponential
[tex]P(X\leq x)=0[/tex]
when [tex]x<0[/tex]
and
[tex]P(X\leq x)=1-e^{-ax}[/tex] when [tex]x\geq 0[/tex]
For this exercise
[tex]P(X\leq x)=1-e^{-\frac{2}{3}x}[/tex]
Therefore
[tex]P(X>2)=1-P(X\leq 2)[/tex]
[tex]P(X>2)=1-(1-e^{-\frac{2}{3}.2})=e^{-\frac{4}{3}}=0.2636[/tex]
(A) The pdf of X, the waiting time until the first call after 10 a.m., is f(x; 2/3) = (2/3) * e^(-(2/3) * x), and, (B) the probability that X > 2 (the first call arrives more than 2 minutes after 10 a.m.) is approximately 0.264.
(a) To find the probability density function (pdf) of X, we first need to understand the arrival rate of the calls, which follows a Poisson process. In our case, the arrival rate (λ) is two calls every 3 minutes, which could also be expressed as 2/3 of a call per minute.
For a Poisson process, the waiting times between arrivals are exponentially distributed. Therefore, the pdf for X, the waiting time until the first call, is given by the exponential distribution function.
The exponential distribution has the following pdf:
f(x; λ) = λ * e^(-λ * x)
In our case, substituting λ = 2/3 (the arrival rate per minute), the pdf of waiting time X becomes:
f(x; 2/3) = (2/3) * e^(-(2/3) * x)
(b) The second part of the question asks for the probability that the waiting time until the first call, X, is greater than 2 minutes.
For an exponential distribution, the cumulative distribution function (CDF), which gives the probability that a random variable is less than or equal to a certain value, is as follows:
F(x; λ) = 1 - e^(-λ * x)
We need P(X > 2), but it's easier to compute P(X <= 2), and then subtract that from 1.
So, we first find the cumulative probability that the waiting time is 2 minutes or less, using our given λ and x = 2:
P(X <= 2) = F(2; 2/3) = 1 - e^(-(2/3) * 2)
After calculating, this probability is approximately 0.736.
Therefore, the probability that waiting time X is greater than 2 minutes, P(X > 2), is simply 1 minus this result, which approximately equals to 0.264.
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Find the cotangent, cosine, and tangent of both angles A and B.
If you could put it in this format:
Cotangent -
Cosine -
Tangent -
that would be epic :^D
Answer:
[tex]\displaystyle \frac{5}{12} = cot∠B \\ 2\frac{2}{5} = cot∠A \\ \\ 2\frac{2}{5} = tan∠B \\ \frac{5}{12} = tan∠A \\ \\ \frac{5}{13} = cos∠B \\ \frac{12}{13} = cos∠A[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{OPPOSITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOSITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOSITE} = csc\:θ \\ \frac{ADJACENT}{OPPOSITE} = cot\:θ \\ \\ \frac{10}{24} = cot∠B → \frac{5}{12} = cot∠B \\ \frac{24}{10} = cot∠A → 2\frac{2}{5} = cot∠A \\ \\ \frac{24}{10} = tan∠B → 2\frac{2}{5} = tan∠B \\ \frac{10}{24} = tan∠A → \frac{5}{12} = tan∠A \\ \\ \frac{10}{26} = cos∠B → \frac{5}{13} = cos∠B \\ \frac{24}{26} = cos∠A → \frac{12}{13} = cos∠A[/tex]
I am joyous to assist you anytime.
The office building is 48 floors high. Half of the floors have 18 windows each and half of the floors have 36 windows each. How many windows does the building have in all?
Answer:
1296 windows
Step-by-step explanation:
HALF of the floors, means
HALF of 48, that is:
48 * 0.5 = 24
Thus, we can say:
24 floors each have 18 windows, and
24 floors each have 36 windows
Total Number of Windows:
24 * 18 = 432 windows
24 * 36 = 864 windows
Total = 432 + 864 = 1296 windows
Answer:
1296 windows are present in the building
Explanation:
Given the office building is 48 floors high
Half of floors have 18 windows each
Then , half of floors =[tex]\frac{48}{2}[/tex] = 24 floors
Total windows on half of the floors, that is 24 floors
= [tex]18\times 24[/tex]
= 432 windows
Also, half of the floors have 36 windows each
Total windows on rest half floors (24 floors)
=[tex]36 \times 24[/tex]
= 864 windows
Total windows = 432 + 864 = 1296 windows
Therefore, 1296 windows are present in the building