State if the pair of triangles are similar. If so, state how you know they are similar and complete the similarity statement.
Answers
The triangles ∆UTS and ∆UBA are similar, hence we can write the similarity statement as:"Triangle ∆UTS is similar to triangle ∆UBA."
How to determine if triangles ∆UTS and ∆UBA are similarTo determine if triangles ∆UTS and ∆UBA are similar, we need to check if their corresponding angles are congruent and if their corresponding sides are proportional.
If ∆UTS is similar to ∆UBA, the following conditions must be true, then each angle in ∆UTS must have a corresponding congruent angle in ∆UBA. Also, the ratio of the lengths of corresponding sides in ∆UTS and ∆UBA must be equal.
AB/ST = 984/1271 = 0.7742
UB/UT = 768/994 = 0.7742
UA/US = 648/837 = 0.7742
AB/ST = UB/UT = UA/US
Therefore triangles ∆UTS and ∆UBA are similar, hence we can write the similarity statement as:"Triangle ∆UTS is similar to triangle ∆UBA."
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Related Questions
What are the domain and range of the function f(x) = -log(5-x)+9?
Answers
The domain of the function is all real numbers less than 5, and the range is all real numbers greater than or equal to 9.
The given function is f(x) = -log(5-x) + 9.
To determine its domain and range, we need to consider the restrictions on x and the possible values of f(x).
Domain:
The domain refers to the set of all valid inputs or values of x for which the function is defined.
In this case, the function contains a logarithmic term, -log(5-x), which is only defined for positive values inside the logarithm.
Therefore, we must ensure that the expression 5-x is greater than zero:
5 - x > 0
Solving this inequality, we find:
x < 5
Hence, the domain of the function is (-∞, 5).
Range:
The range refers to the set of all possible output values or values of f(x). Since the logarithm term can take any positive value, and we add 9 to it, the range of the function is shifted upward by 9 units.
The range can be defined as all real numbers greater than or equal to 9:
Range: [9, +∞)
To summarize, the domain of the function f(x) = -log(5-x) + 9 is (-∞, 5), and the range is [9, +∞), indicating that f(x) can take any value greater than or equal to 9.
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Classify each polynomial by degree and number of terms.
10
8x4
5x²-7x+9
2x³ +3
1. Quartic monomial
2. Cubic binomial
3. Quadratic trinomial
4. Quintic quadnomial
Answers
Answer:
10: Zero-degree monomial.
8x^4: Quartic monomial.
5x² - 7x + 9: Quadratic trinomial.
2x³ + 3: Cubic binomial.
Step-by-step explanation:
10: This is a constant term, and it can be classified as a zero-degree monomial.
8x^4: This is a monomial with a degree of 4, and it contains one term. It can be classified as a quartic monomial.
5x² - 7x + 9: This is a polynomial with three terms. The highest power of the variable, x, is 2, so it is a quadratic polynomial. Therefore, it can be classified as a quadratic trinomial.
2x³ + 3: This is a polynomial with two terms. The highest power of the variable, x, is 3, so it is a cubic polynomial. Hence, it can be classified as a cubic binomial.
10: Zero-degree monomial.
8x^4: Quartic monomial.
5x² - 7x + 9: Quadratic trinomial.
2x³ + 3: Cubic binomial.
Heather is making chocolate biscuits
she has:
2kg of flour
1kg of butter
340g of icing sugar
200g of chocolate
here is the list of ingredients for making 20 biscuits.
100g of flour
120g of butter
80g of icing sugar
25g of chocolate
work out how mnany bisuits she can make
Answers
Therefore, Heather can make a maximum of 4 biscuits with the given ingredient quantities.
To determine how many biscuits Heather can make, we need to compare the amount of each ingredient required for a single biscuit to the total amount of ingredients she has.
Let's calculate the number of biscuits she can make based on the ingredient quantities provided:
First, we need to find the ratio of each ingredient required per biscuit:
Flour: 100g per biscuit
Butter: 120g per biscuit
Icing sugar: 80g per biscuit
Chocolate: 25g per biscuit
Next, we divide the total amount of each ingredient by the respective ratio to find the maximum number of biscuits she can make:
Flour: 2kg / 100g = 20 biscuits
Butter: 1kg / 120g = 8.33 biscuits (approximately)
Icing sugar: 340g / 80g = 4.25 biscuits (approximately)
Chocolate: 200g / 25g = 8 biscuits
Since we can only make a whole number of biscuits, the limiting factor is the icing sugar. Heather can only make 4 biscuits since she has 4.25 times the required amount of icing sugar.
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X^2 + x -72 rewrite the giving expression
Answers
Answer:
(x + 9)(x - 8)
Step-by-step explanation:
Factorising the expression
x² + x - 72
consider the factors of the constant term (- 72) which sum to give the coefficient of the x- term (+ 1)
the factors are + 9 and - 8 , since
9 × - 8 = - 72 and 9 - 8 = + 1 , then
x² + x - 72 = (x + 9)(x - 8) ← in factored form
Which expression is equivalent to StartRoot 8 x Superscript 7 Baseline y Superscript 8 Baseline EndRoot? Assume x greater-than-or-equal-to 0.
x y squared StartRoot 8 x cubed EndRoot
2 x cubed y cubed StartRoot x y squared EndRoot
2 x cubed y Superscript 4 Baseline StartRoot 2 x EndRoot
4 x cubed y Superscript 4 Baseline StartRoot x EndRoot
Answers
The expression that is equivalent to StartRoot [tex]8 x^7 y^8[/tex] EndRoot is ([tex]2 x^3 y^4[/tex] StartRoot 2 x EndRoot)^2.
To understand why this is the case, let's break down each expression and simplify them step by step:
StartRoot [tex]8 x^7 y^8[/tex] EndRoot:
We can rewrite 8 as [tex]2^3[/tex], and since the square root can be split over multiplication, we have StartRoot [tex](2^3) x^7 y^8[/tex] EndRoot. Applying the exponent rule for square roots, we get StartRoot [tex]2^3[/tex] EndRoot StartRoot [tex]x^7[/tex] EndRoot StartRoot [tex]y^8[/tex] EndRoot.
Simplifying further, we have 2 StartRoot [tex]2 x^3 y^4[/tex] EndRoot StartRoot [tex]2^2[/tex] EndRoot StartRoot [tex]x^2[/tex] EndRoot StartRoot [tex]y^4[/tex] EndRoot. Finally, we obtain 2 [tex]x^3 y^4[/tex] StartRoot 2 x EndRoot, which is the expression in question.
([tex]2 x y^2[/tex] StartRoot 8 x^3 EndRoot)^2:
Expanding the expression inside the parentheses, we have [tex]2 x y^2[/tex]StartRoot [tex](2^3) x^3[/tex] EndRoot. Applying the exponent rule for square roots, we get [tex]2 x y^2[/tex] StartRoot [tex]2^3[/tex] EndRoot StartRoot [tex]x^3[/tex] EndRoot.
Simplifying further, we have [tex]2 x y^2[/tex] StartRoot 2 x EndRoot. Squaring the entire expression, we obtain ([tex]2 x y^2[/tex] StartRoot 2 x EndRoot)^2.
Therefore, the expression ([tex]2 x^3 y^4[/tex] StartRoot 2 x EndRoot)^2 is equivalent to StartRoot [tex]8 x^7 y^8[/tex] EndRoot.
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New flowers are being planted in an empty area of a landscaped garden. The
map shows the area that is being planted. If walkway A and walkway B are
parallel, what is the distance from F to G on walkway C?
Answers
The distance from F to G on walkway C is approximately 19.21 units.
To determine the distance from point F to point G on walkway C, we can use the information provided in the map and apply some basic geometric principles.
Looking at the map, we can see that walkway A and walkway B are parallel. Let's use this information to find the distance from F to G on walkway C.
First, let's identify the relevant points on the map. We have point F on walkway C and point G on walkway C. The map also shows two intersecting lines, representing walkways A and B, but we don't need to consider those for this particular calculation.
To find the distance from F to G on walkway C, we need to focus on the segment of walkway C that connects F and G. Based on the map, we can see that the segment of walkway C is perpendicular to both walkway A and walkway B.
Since walkway A and walkway B are parallel, and the segment of walkway C is perpendicular to both, we can conclude that the segment FG forms a right triangle with walkway A and walkway B.
In a right triangle, we can use the Pythagorean theorem to find the length of one side (FG) if we know the lengths of the other two sides.
Let's assume the length of the segment FG is represented by the variable 'd' (which we need to find).
From the map, we can see that the distance from F to walkway A is 15 units. Similarly, the distance from G to walkway B is 12 units.
Applying the Pythagorean theorem, we have:
d^2 = 15^2 + 12^2
d^2 = 225 + 144
d^2 = 369
Taking the square root of both sides, we find:
d ≈ √369
d ≈ 19.21
As a result, it takes 19.21 units to get from F to G on walkway C.
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12
Find x.
20
X
x = [ ?
X
Answers
The calculated length x of the right triangle is 16
Finding the length x of the right triangleFrom the question, we have the following parameters that can be used in our computation:
The right triangle
The length x of the right triangle can be calculated using the following Pythagoras theorem
x² = difference of squares of the other sides
Using the above as a guide, we have the following:
x² = (20)² - (12)²
Evaluate
x² = 256
Take the square roots
x = 16
Hence, the length x of the right triangle is 16
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100 Points! Multiple choice geometry questions. Photo attached. Thank you!
Answers
Answer:
[tex]\textsf{8.} \quad \textsf{(A)}\;\;\overline{XB}[/tex]
[tex]\textsf{9.} \quad \textsf{(D)}\;\;\overleftrightarrow{BD}[/tex]
Step-by-step explanation:
RadiusThe radius is the distance from the center of a circle to any point on its circumference.
The center of the given circle is point X.
Therefore, the radii in the given circle are line segments XB, XA and XC.
[tex]\hrulefill[/tex]
TangentA tangent is a straight line that touches a circle at only one point.
The line BD touches the circle at point B.
Therefore, the tangent of the given circle is line BD.
Answer:
8. A
9. D
Step-by-step explanation:
The radius is a straight line from the midpoint to the circle's circumference.
A Tangent is a line going through the circumference of the circle.
Find the missing side.
N
41° 15
Z=
Round to the nearest tenth.
Remember: SOHCAHTOA
Answers
Answer:
To the nearest tenth, we have,
z = 19.9
Step-by-step explanation:
The missing side is the hypotenuse,
And we are given the side adjacent to the angle,
z = hupotenuse = H = ?
Adjacent = A = 15
Angle = α = 41
Since we have to find hypotenuse and we are given adjacent,
Using SOHCAHTOA,
We know the angle and adjcent but need to find Hypotenuse,
So, we use CAH
or,
cos(α) = A/H
cos(α) = 15/z
(since z = hypotenuse)
zcos(α) = A
z = A/(cos(α))
z = 15/cos(41)
z = 19.8752
To the nearest tenth, we get,
z = 19.9
What is the domain of the function y=2 x-6
Answers
Answer: The domain of the expression is all real numbers except where the expression is undefined.
Step-by-step explanation:
HELP ME PLEASE.
The figure below shows a rectangle ABCD having diagonals AC and DB:
Jimmy wrote the following proof to show that the diagonals of rectangle ABCD are congruent:
Jimmy's proof:
Statement 1: In triangle ADC and BCD, AD = BC (opposite sides of a rectangle are congruent).
Statement 2: Angle ADC = Angle BCD (angles of a rectangle are 90°
Statement 3:
Statement 4: Triangle ADC and BCD are congruent (by SAS postulate)
Statement 5: AC = BD (by CPCTC)
Which statement below completes Jimmy's proof? (1 point)
• AB=AB (reflexive property of equality)
• AB=AB (transitive property of equality)
O DC=DC (reflexive property of equality)
O DC=DC (transitive property of equality)
Answers
Statement 1: In triangle ADC and BCD, AD = BC (opposite sides of a rectangle are congruent).
Statement 2: Angle ADC = Angle BCD (angles of a rectangle are 90°).
Statement 3: DC = DC (reflexive property of equality).
Statement 4: Triangle ADC and BCD are congruent (by SAS postulate).
Statement 5: AC = BD (by CPCTC).
The statement that completes Jimmy's proof is:
DC = DC (reflexive property of equality)
The reflexive property of equality states that any quantity is equal to itself. In this case, statement 3 is stating that the diagonal DC is equal to itself, which is true by the reflexive property of equality.
Therefore, the completed proof is:
Statement 1: In triangle ADC and BCD, AD = BC (opposite sides of a rectangle are congruent).
Statement 2: Angle ADC = Angle BCD (angles of a rectangle are 90°).
Statement 3: DC = DC (reflexive property of equality).
Statement 4: Triangle ADC and BCD are congruent (by SAS postulate).
Statement 5: AC = BD (by CPCTC).
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PLEASE I NEED HELP the question is,
In the diagram of triangle LAC and triangle DNC below, LA = DN, CA = CN, and DAC is perpendicular to LCN.
a) Prove that triangle LAC = triangle DNC.
b) Describe a sequence of rigid motions that will map triangle LAC onto triangle DNC.
Answers
Answer:
1244 DCD
Step-by-step explanation:
1st Semester - Summer 2023
Quiz Active
Abc
1
2 3
4
When summarizing the
5
6 7
TIME R
51
of a plot, one should notice the key ideas about how the conflict builds.
Answers
When summarizing the plot, it is important to pay attention to the key ideas and how the conflict develops over time. The given pattern suggests a narrative structure where the plot unfolds gradually, revealing information and building tension.
The plot starts with an introduction (line 1) and then introduces the conflict or problem (lines 2 and 3). As the plot progresses, the conflict continues to develop, possibly reaching a climax or a turning point (line 4). Afterward, the plot moves towards a resolution or conclusion (lines 5, 6, and 7).
The pattern presented in the given example showcases the basic elements of a plot, including the exposition, rising action, climax, falling action, and resolution. The plot begins by setting the stage and introducing the characters and setting (line 1). Then, the conflict is introduced or developed, creating tension and driving the narrative forward (lines 2 and 3).
The plot further progresses with the development of the conflict, possibly reaching a high point or turning point (line 4). Finally, the plot moves towards its resolution or conclusion, providing closure to the story (lines 5, 6, and 7). By understanding these key ideas and the progression of the conflict, one can effectively summarize the plot and capture its essential elements.
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Mr. John recently bought 2 cords of wood from a local contractor
(delivered in a dump truck). After the pile was dropped off, he stacked
the wood and wondered if he really received the 2 standard cords of
wood (see diagram) or if the company sold him less wood than he
ordered.
Note: a cord of wood if defined as 4ft X 4ft’ X 8ft stack
Mr. John ended up stacking to piles of wood this past week.
Mr. John ended up with two piles of wood with the following sizes
PILE #1: 72” X 167” X 16”
PILE #2: 65” X 266” X 16”
QUESTIONS:
1. Did Mr. John get more or less than 2 cords of wood (as defined in
the diagram above)?
2. If a standard piece of wood is 5” X 5” X 12”. How pieces of actual
wood did he receive based on his stacked piles?
3. If the cost for both cords of wood was actually $250/cord,
What was the cost per a standard piece of wood?
Answers
1. Mr. John received more than 2 cords of wood based on the sizes of the stacked piles.
2. Based on the stacked piles, Mr. John received approximately 11,974 pieces of actual wood.
3. The cost per standard piece of wood is approximately $0.0417.
1. To determine if Mr. John received more or less than 2 cords of wood, we need to calculate the volume of each pile and compare it to the volume of a standard cord of wood.
Calculating the volume of each pile:
PILE #1:
Volume = 72 inches * 167 inches * 16 inches = 1,523,584 cubic inches
PILE #2:
Volume = 65 inches * 266 inches * 16 inches = 2,068,480 cubic inches
Calculating the volume of a standard cord of wood:
Volume of a standard cord = 4 feet * 4 feet * 8 feet = 128 cubic feet
Since 1 foot = 12 inches, the volume in cubic inches is 128 * 12 * 12 * 12 = 221,184 cubic inches.
Comparing the volumes:
Pile #1: 1,523,584 cubic inches
Pile #2: 2,068,480 cubic inches
Standard cord: 221,184 cubic inches
It is evident that both piles have significantly more volume than a standard cord of wood. Therefore, Mr. John received more than 2 cords of wood.
2. To determine the number of standard pieces of wood received, we need to calculate the number of pieces that can be obtained from the total volume of the piles.
Total volume of the piles = Volume of Pile #1 + Volume of Pile #2
Total volume = 1,523,584 cubic inches + 2,068,480 cubic inches = 3,592,064 cubic inches
Volume of a standard piece of wood = 5 inches * 5 inches * 12 inches = 300 cubic inches
Number of standard pieces of wood received = Total volume of the piles / Volume of a standard piece of wood
Number of pieces = 3,592,064 cubic inches / 300 cubic inches = 11,973.55 pieces (rounded to the nearest whole number)
Therefore, Mr. John received approximately 11,974 pieces of actual wood based on his stacked piles.
3. To calculate the cost per standard piece of wood, we need to divide the total cost of the two cords by the number of standard pieces received.
Total cost for both cords of wood = 2 cords * $250/cord = $500
Cost per standard piece of wood = Total cost / Number of standard pieces
Cost per piece = $500 / 11,974 = $0.0417 (rounded to four decimal places)
Therefore, the cost per standard piece of wood is approximately $0.0417.
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Humpback whales migrate up to 25,000 kilometers per year from polar waters to tropical waters. An observer
measures a humpback whale traveling a distance of 13.5 kilometers in 30 minutes.
What is the average speed of the humpback whale in km/h?
Answers
Average speed of the humpback whale: 27 kilometers per hour.
To calculate the average speed of the humpback whale, we can use the formula:
Average speed = Total distance / Total time
Given that the humpback whale traveled a distance of 13.5 kilometers in 30 minutes, we need to convert the time to hours. There are 60 minutes in an hour, so 30 minutes is equal to 0.5 hours.
Now, we can substitute the values into the formula:
Average speed = 13.5 kilometers / 0.5 hours
Average speed = 27 kilometers per hour
Therefore, the average speed of the humpback whale is 27 kilometers per hour.
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Find an equation of the line that passes through (2, -2) and parallel to the line passing through (4, 5) and (6, 4).
Answers
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the second line
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{4}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{4}}} \implies \cfrac{ -1 }{ 2 } \implies - \cfrac{1}{2}[/tex]
so we're really looking for the equation of a line whose slope is -1/2 and it passes through (2 , -2)
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{-2})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{1}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{- \cfrac{1}{2}}(x-\stackrel{x_1}{2}) \implies y +2 = - \cfrac{1}{2} ( x -2) \\\\\\ y+2=- \cfrac{1}{2}x+1\implies {\Large \begin{array}{llll} y=- \cfrac{1}{2}x-1 \end{array}}[/tex]
Answer:
Line passing through (4, 5) and (6, 4):
[tex]m = \frac{4 - 5}{6 - 4} = - \frac{1}{2} [/tex]
Line passing through (2, -2) and with slope -1/2:
-2 = (-1/2)(2) + b
-2 = -1 + b, so b = -1
y = (-1/2)x - 1
-2y = x + 2
-x - 2y = 2
x + 2y = -2
The distance around a circle is called the ______.
A. volume
B. area
C. circumference
D. diameter
Answers
The answer is:
C. circumference
Work/explanation:
Here's the correct answer:
The distance around a circle is called the circumference.
How to find the circumference :
Use [tex]\sf{C=2\pi r}[/tex] or [tex]\sf{C=\pi d}[/tex]Hence, c is correct.ead the situations below and determine which relationship is not functional.
Situation 1: a cell phone bill to the amount of minutes used
Situation 2: the perimeter of a square to the length of one of the sides of a square
Situation 3: the total amount of money charged monthly on credit cards to the number of credit cards owned
Situation
does not represent a function.
This is because
.
Answers
There can be multiple outputs (monthly charges) for a given input (number of credit cards), violating the definition of a function. hence, Situation 3 does not represent a function.
Situation 3: the total amount of money charged monthly on credit cards to the number of credit cards owned does not represent a function.
In a function, each input (or x-value) should have a unique output (or y-value). However, in this situation, the total amount of money charged monthly on credit cards depends on the number of credit cards owned. It is possible to have different credit card numbers but still have the same total amount of money charged monthly.
For example, two people could own different numbers of credit cards but have the same monthly charges.
As a result, the definition of a function can be violated by having many outputs (monthly charges) for a single input (number of credit cards).
Because of this, case 3 does not represent a function.
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Factor −5x2 + 10x.
PLS HURRY NEED THIS DUE TODAY
Answers
Answer:
C. 5x(-x + 2)
Step-by-step explanation:
To factor the expression -5x² + 10x, we need to look for a common factor that can be factored out.
Finding a common factor involves identifying a term or expression that can be factored out from each term of a given expression.
Both terms have the common factor of 5x, so we can factor out 5x:
5x(-x + 2)
Therefore, the factored form of -5x² + 10x is -5x(x - 2).
[tex]\hrulefill[/tex]
Additional notes:
If we expand the expressions in the given answer options, we get:
A. −5x(x + 2) = -5x² - 10x
B. 5(−x² + 10x) = -5x² + 50x
C. 5x(−x + 2) = -5x² + 10x
D. x(5x + 10) = 5x² + 10x
Hence confirming that the correct answer is option C.
To factor [tex]-5x^2+10x[/tex], we can begin by factoring out the greatest common factor, which is [tex]-5x[/tex]:
[tex]-5x^2 + 10x = \boxed{-5x(x - 2)}[/tex]We can check our answer by distributing [tex]-5x[/tex] to the expression inside the parentheses:
[tex]\begin{aligned}-5x(x - 2)& = (-5x)(x) + (-5x)(-2)\\& = -5x^2 + 10x\end{aligned}[/tex][tex]\therefore[/tex] The answer is [tex]-5x(x-2)[/tex].
[tex]\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}[/tex]
A teaching hospital in South-West Part of Nigeria receives on the average 5 pregnant women with high blood pressure per week. What is the probability that on a particular week, the teaching hospital will receive:
1.) No high BP pregnant woman
Answers
Answer:
The probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068
Step-by-step explanation:
We use the Exponential distribution,
Since we are given that on average, 5 pregnant women with high blood pressure come per week,
So, average = m = 5
Now, on average, 5 people come every week, so,
5 women per week,
so, we get 1 woman per (1/5)th week,
Hence, the mean is m = 1/5 for a woman arriving
and λ = 1/m = 5 = λ
we have to find the probability that it takes higher than a week for a high BP pregnant woman to arrive, i.e,
P(X>1) i.e. the probability that it takes more than a week for a high BP pregnant woman to show up,
Now,
P(X>1) = 1 - P(X<1),
Now, the probability density function is,
[tex]f(x) = \lambda e^{-\lambda x}[/tex]
And the cumulative distribution function (CDF) is,
[tex]CDF = 1 - e^{-\lambda x}[/tex]
Now, CDF gives the probability of an event occuring within a given time,
so, for 1 week, we have x = 1, and λ = 5, which gives,
P(X<1) = CDF,
so,
[tex]P(X < 1)=CDF = 1 - e^{-\lambda x}\\P(X < 1)=1-e^{-5(1)}\\P(X < 1)=1-e^{-5}\\P(X < 1) = 1 - 6.738*10^{-3}\\P(X < 1) = 0.9932\\And,\\P(X > 1) = 1 - 0.9932\\P(X > 1) = 6.8*10^{-3}\\P(X > 1) = 0.0068[/tex]
So, the probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
A. The volume of the hemisphere with a diameter of 48 yards is approximately 1001.1 cubic yards.
B. The volume of the sphere with a circumference of a great circle approximately equal to 26 meters is approximately 359.4 cubic meters.
A. To find the volume of a hemisphere, we first need to calculate the radius. The diameter is given as 48 yards, so the radius is half of that, which is 24 yards.
The formula for the volume of a hemisphere is (2/3)πr^3, where r is the radius. Plugging in the values:
Volume = (2/3) * π * (24^3)
Volume ≈ 1001.1 cubic yards (rounded to the nearest tenth)
Therefore, the volume of the hemisphere is approximately 1001.1 cubic yards.
B. To find the volume of a sphere, we need to know the radius. Since the circumference of a great circle is given as approximately 26 meters, we can use the formula C = 2πr, where C is the circumference and r is the radius.
We can rearrange the formula to solve for the radius: r = C / (2π). Plugging in the circumference:
r = 26 / (2π)
r ≈ 4.134 meters (rounded to the nearest thousandth)
The formula for the volume of a sphere is (4/3)πr^3. Substituting the radius:
Volume = (4/3) * π * (4.134^3)
Volume ≈ 359.4 cubic meters (rounded to the nearest tenth)
Therefore, the volume of the sphere is approximately 359.4 cubic meters.
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
The probability that a point chosen at random lies on the shaded region is given as follows:
4/7.
How to calculate a probability?The parameters that are needed to calculate a probability are listed as follows:
Number of desired outcomes in the context of a problem or experiment.Number of total outcomes in the context of a problem or experiment.Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
The area of the shaded region in this problem is given as follows:
4² = 16.
The total area of the figure is given as follows:
16 + 2 x 1/2 x 3 x 4 = 28.
Hence the probability is given as follows:
16/28 = 4/7.
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For the attached graph two questions:
1. What does the slope of the line represent, in context of the problem?
2. What does the y intercept represent, in context of the problem?
Answers
The slope of the line represents the speed in miles per hour
The y intercept represents the initial distance
What does the slope of the line representfrom the question, we have the following parameters that can be used in our computation:
The graph
Where, we have
x = time in hours
y = distance in miles
The slope is
slope = change in y/x
So, we can conclude that the slope is the speed
What does the y intercept representBy definition, the y intercept is the initial value of the graph
In this case;
y intercept = initial distance
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Given the attached graph and the equation of the line in the slope intercept form?
Answers
The slope, "m," indicates the rate of change of the line, while the y-intercept, "b," represents the value of y when x equals zero.
I apologize, but as a text-based AI model I'm unable to directly view or analyze any attached images or graphs. However, if you provide me with the equation of the line in the slope-intercept form or describe the relevant details from the graph, I can certainly help you with a response within the given word limit.
The slope-intercept form of a linear equation is given by y = mx + b, where "m" represents the slope of the line and "b" represents the y-intercept, the point where the line intersects the y-axis.
Using this equation, you can determine the slope and y-intercept by comparing the given equation with the slope-intercept form.
Once you provide me with the equation or necessary information, I'll be able to assist you further in understanding the line and its characteristics.
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Please awnser asap I will brainlist
Answers
The number of vans, small truck and large truck they can buy is 130, 65 and 65 respectively.
How many of each vehicles can be bought?Total cost of vehicles = $10 million
Total number of vehicles = 260
Cost of each commercial van = $25,000
Cost of each small truck = $50,000
Cost of each large truck = $50,000
Let
c = commercial van
s = small truck
l = large truck
v = 2s
s = l
So,
v + s + l = 260
2s + s + s = 260
4s = 260
divide both sides by 4
s = 260/4
s = 65
Therefore,
v = 2s
= 2(65)
= 130
s = l
l = 65
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(-1,1,5)
9
8
7-
6
5
4
3₂
-3-2-1₁
(1,5)
(0,3)
Which exponential function is represented by the graph?
Of(x)=2(3¹)
Of(x)=3(3)
Of(x)=3(2)
O f(x) = 2(2¹)
Answers
The value of the equation that defines the function is f(x) = 3(5/3)ˣ
Finding an equation defining the functionFrom the question, we have the following parameters that can be used in our computation:
(0, 3) and (1, 5)
An exponential function is represented s
y = abˣ
Where,
a = y when x = 0
So, we have
y = 3bˣ
Using the other point, we have
3b = 5
This gives
b = 5/3
So, we have
f(x) = 3(5/3)ˣ
Hence, the equation defining f is f(x) = 3(5/3)ˣ
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100 Points! Geometry question. Find x and y. Photo attached. Please show as much work as possible. Thank you!
Answers
The calculated values of x and y in the figure are x = 2 and y = 4
How to calculate x and y in the figurefrom the question, we have the following parameters that can be used in our computation:
The figure
Where, we have
equal side lengths
This means that
2y - 1 = 3y - 5
Evaluate
y = 4
Next, we have
x + 3 = 3/2x + 2
So, we have
1/2x = 1
This gives
x = 2
Hence, the values of x and y in the figure are x = 2 and y = 4
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Please help me. I don't even know where to start.
Answers
The sum diverges to negative infinity.
Does the sum exist?Here we want to find the value of the sum:
[tex]\sum_{m=1}^{ \infty}} (-11/2)*(3/2)^{m + 1}[/tex]
So, that sum goes for infinite values of m, that is bad because you can see that the term with an exponent is larger than 1.
So when m is a really large value, then the term will also be a really large value, which means that the fuction eventually diverges to negative inifnity.
The usual rule that we need to check is that, for large values of m, as m increases, the absolute value of each term decreases.
Here this cleraly does not happen, so the sum diverges.
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A bag contains 8 red marbles, 3 blue marbles, and 1 green marble. Find P(not blue).
A. 9
B. 4/3
C. 1/4
D. 3/4
Please select the best answer from the choices provided.
Answers
8+3+1=12
1-3/12=3/4
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
Rounded to the nearest tenth of a percent, the probability is approximately 27.8%.
To determine if the event of rolling a pair of dice and getting doubles or a sum of 6 is mutually exclusive, we need to assess whether the two outcomes can occur simultaneously or if they are mutually exclusive.
Let's analyze the two outcomes separately:
1. Getting doubles: When rolling a pair of dice, getting doubles means that the numbers on both dice are the same. The possible outcomes for getting doubles are (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6). There are a total of 6 outcomes that satisfy this condition.
2. Getting a sum of 6: To get a sum of 6, the numbers on the two dice should add up to 6. The possible outcomes for this condition are (1,5), (2,4), (3,3), (4,2), and (5,1). There are a total of 5 outcomes that satisfy this condition.
Now, to determine if the two outcomes are mutually exclusive, we need to check if there are any outcomes that satisfy both conditions. In this case, the outcome (3,3) satisfies both conditions (doubles and sum of 6).
Since there is one outcome that satisfies both conditions, we can conclude that the event of rolling a pair of dice and getting doubles or a sum of 6 is not mutually exclusive.
To find the probability of this event, we need to determine the total number of possible outcomes when rolling a pair of dice. Each die has 6 sides, so there are 6 possible outcomes for each die, resulting in a total of 6 * 6 = 36 possible outcomes when rolling a pair of dice.
The probability is calculated by dividing the number of favorable outcomes (satisfying the condition) by the total number of possible outcomes.
Favorable outcomes = 6 (for doubles) + 5 (for sum of 6) - 1 (for the overlapping outcome) = 10
Probability = Favorable outcomes / Total number of outcomes = 10 / 36 ≈ 0.2778
Rounded to the nearest tenth of a percent, the probability is approximately 27.8%.
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