The answer given question : Is 50%,probability of each child inheriting two copies of the mutated gene is 25%. And the Overall, without additional information about the genetic makeup of the second-generation partners, it is impossible to determine the exact probability of occurrence of PKU in their children.
phenylketonuria (PKU) is an inherited disorder caused by a mutation in a gene that produces an enzyme called phenylalanine hydroxylase. This enzyme is necessary for the breakdown of the amino acid phenylalanine, and without it, phenylalanine can build up to toxic levels in the body, leading to brain damage and other serious health problems.
PKU is an autosomal recessive disorder, which means that a person must inherit two copies of the mutated gene (one from each parent) in order to develop the condition. If only one copy of the mutated gene is inherited, the person is a carrier of the disorder but does not develop PKU.
Given that one of the four children in the first generation has PKU, we can assume that both parents are carriers of the disorder. The probability of each of their children inheriting a single copy of the mutated gene (i.e., becoming carriers like their parents) is 50%, and the probability of each child inheriting two copies of the mutated gene (i.e., developing PKU) is 25%.
The occurrence of PKU in the second generation will depend on the genetic makeup of the partners who have children. If both partners are carriers, there is a 25% chance that each of their children will develop PKU. If one partner is a carrier and the other is not, there is no chance that their children will develop PKU, but each child will have a 50% chance of being a carrier
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A radio station broadcasts a signal over an area with a 45-mile radius. What is the area of the region that receives the radio signal to the nearest tenth?
Rounded to the nearest tenth, the area of the region that receives the radio signal is approximately 6,366.2 square miles.
What is the region's signed area?Consider a plane region described by a xy-plane graph. The signed area of the region is defined as the area of the graph on or above the x-axis. The negative area of the graph is defined as the area below the x-axis.
The formula A = πr² gives the area of a circle with radius r. In this case, the radio station broadcasts over a 45-mile radius, so the region that receives the radio signal is:
A = π(45)²
A ≈ 6,366.2 square miles
The area of the region that receives the radio signal is approximately 6,366.2 square miles when rounded to the nearest tenth.
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Which is true about an equilateral triangle?
no sides have equal measure
one angle is obtuse
all angle measures are equal
only two sides have equal measure
Answer: all angles are equal
Step-by-step explanation:
in a equilateral triangle all angles will be 60°
Part III: Use the point given for line p and the slope you found in Part II to write an
equation for line p in point-slope form: Y-Y₁ = m(x-x₁). (1 point)
The slope of line q is equal to 3.
The slope of line q is equal to -1/3.
An equation for line p in point-slope form is y + 5 = -1/3(x - 6).
An equation for line p in slope-intercept form is y = -1/3x - 3.
What is the slope-intercept form?Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c ....equation 1.
Where:
m represents the slope.x and y are the points.c represents the y-intercept or initial value.From the information provided, we have the following linear equation in slope-intercept form for line q:
y = 3x + 5 ....equation 2.
By comparing equation 1 and equation 2, we can logically deduce the following:
Slope (m) = 3
Since line p is perpendicular to line q, the slope of line p is the negative reciprocal of the slope of line q;
m₁ × m₂ = -1
3 × m₂ = -1
Slope, m₂ of line p = -1/3.
At data point (6, -5), a linear equation of this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - (-5) = -1/3(x - 6)
y + 5 = -1/3(x - 6)
By simplifying further, the slope-intercept form is given by;
y + 5 = -1/3(x - 6)
3y + 15 = -x + 6
3y = -x - 9
y = -1/3x - 3
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Complete Question:
Line p contains point (6, -5) and is perpendicular to line q. The equation for line q is y = 3x + 5. Write an equation for line p.
Find the slope of line q.
Find the slope of line p. (Write the negative reciprocal of the slope you found in Part I.)
Use the point given for line p and the slope you found in Part II to write an equation for line p in point-slope form: y - y1 = m (x - x1)
Use your equation from Part III to write an equation for line p in slope-intercept form: y = mx + b.
Prove that a nonempty set W is a subspace of a vector space V if and only if ax + by is an element of W for all scalar a and b and all vectors x and y in W.In one direction, assume W is a subspace and show by using closure axioms that ax + by is an element of W. In the other direction, assume ax + by is an element of W for all scalars a and b and all vectors x and y in W, and verify that W is closed under addition and scalar multiplication.(i) If W is a subspace of V, then use scalar multiplication closure to show that ax and by are in W. Now, use additive closure to get the desired result.(ii) Conversely, assume ax + by is in W. By cleverly assigning specific values to a and b, show that W is closed under addition and scalar multiplication.
If W is a subspace of V, then ax + by is an element of W since it satisfies the closure axioms of a vector space. Specifically, scalar multiplication closure confirms that ax and by are in W, and additive closure confirms that their sum, ax + by, is also in W.
Conversely, if ax + by is an element of W for all scalars a and b and all vectors x and y in W, then W must be closed under both addition and scalar multiplication.
To demonstrate this, we can assign a particular value to a or b, set the other to 1, and substitute the corresponding vectors x and y from W to get the equation ax + by = a(x) + b(y). This equation confirms that W is closed under addition and scalar multiplication, making it a subspace of V.
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What is D(50) − (D(15) ∪ D(20))?
The expression "D(50) - (D(15) ∪ D(20))" refers to the set difference between the set D(50) and the union of sets D(15) and D(20).
The set difference is the operation that gives you the elements that are in the first set (D(50)) but not in the second set (D(15) ∪ D(20)). Note that this prompt draws on Set Theory.
What is Set Theory?Set Theory is a branch of mathematics concerned with the study of sets, their properties, and their relationships.
In set theory, a set is a collection of distinct objects, and the set difference operation, represented by the minus sign (-), returns the elements that are in the first set but not in the second set.
The union of sets, represented by the symbol ∪, is the operation that gives you the set of all elements that are in at least one of the sets being considered.
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stuck on this question plsss helpp
Answer:
2 vases of lilacs
3 vases of irises
Step-by-step explanation:
7( lilacs ) × 2( vases) = 14 flowers
5( irises ) × 3( vases) = 15 flowers
14 + 15 = 29 flowers
the base of a triangle is 8 ft less than its height. if the area is 120 ft2, find the base and the height of this triangle. use an equation to solve this problem.
The height of the triangle is 20 and base of the triangle is 12.
"Information available from the question"
The base of a triangle is 8 ft. less than its height.
If the area is 120 [tex]ft^2.[/tex]
We have to find the base and the height of this triangle.
Now, According to the question:
Let the height be x then if the base is 8 ft. less, then the base is x - 8.
We know that:
Area of the triangle is : (b × h)/2
Area of the triangle is : (x (x - 8)) /2
120 [tex]ft^2[/tex] = ([tex]x^{2} -8x[/tex])/2
240 = [tex]x^{2} -8x[/tex]
[tex]= > x^{2} -8x-240=0[/tex]
For solving equation, Use the quadratic formula :
x = (-b ± [tex]\sqrt{b^2-4ac}[/tex]) / 2a
a = 1
b = -8
c = -240
x = (-(-8) ± [tex]\sqrt{(-8)^2-4.1(-240)})/2.1[/tex]
By solving, we get
x = (8 ± 32)/2
We get the values :
x = 20 and x = -12
We know x = −12 can't be a solution as length can't be negative.
Base = x - 8
Base = 20 - 8
Base = 12
Hence, The height of the triangle is 20 and base of the triangle is 12.
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PLEASE HELP FAST!!!! IT IS URGENT!!!! The distribution of professional baseball player salaries has a mean of $3.2 million. An analyst believes that the mean salary for teams on the East Coast is different. The analyst randomly selects 30 baseball players from teams on the East Coast and records their annual salaries. The mean salary for the players in the sample is $3.9 million with a standard deviation of $2.1 million. Do the data provide convincing evidence at the level that the mean salary for the baseball players on the East Coast is different from $3.2 million? What hypotheses should the analyst use to conduct a significance test?
The hypothesis tested are given as follows:
[tex]H_0: \mu = 3.2, H_a: \mu \neq 3.2[/tex]
What are the null and alternative hypothesis?The claim for this problem is given as follows:
"The mean salary for the baseball players on the East Coast is different from $3.2 million".
At the null hypothesis, we test if the claim is false, that is, if the mean salary is equals to 3.2 million, hence:
[tex]H_0: \mu = 3.2[/tex]
At the alternative hypothesis, we test if the claim is true, that is, if the mean salary is different of 3.2 million, hence:
[tex]H_a: \mu \neq 3.2[/tex]
The [tex]\mu[/tex] symbol, without the bar, is used, as we are testing for the population mean, not sample mean, hence the first option is the correct option.
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1. It is claimed that less than 25% of adults prefer Italian food as their favorite ethnic food. A
survey of 1122 adults resulted in 314 who say that Italian food is their favorite ethnic food.
Find the value of the test statistic z using
z=^p-p
——-
Square root of pq
—-
n
Oz=2.31
Oz=-2.31
Oz=2.01
Oz=-2.01
The value of the test statistic z is, 2.31.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
It is claimed that less than 25% of adults prefer Italian food as their favorite ethnic food.
And, A survey of 1122 adults resulted in 314 who say that Italian food is their favorite ethnic food.
Now,
⇒ P = 25%
⇒ q = 100% - 25% = 75%
⇒ n = 1122
Hence, We get;
⇒ z = (314/1122 - 25%) / √(25% 75% / 1122)
⇒ z = 2.31
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A group of 6 friends are playing poker one night, and one of the friends decides to try out a new game. They are using a standard 52-card deck. The dealer is going to deal the cards face up. There will be a round of betting after everyone gets one card. Another round of betting after each player gets a second card, etc. Once a total of 7 cards have been dealt to each player, the player with the best hand will win. However, if any player is dealt one of the designated cards, the dealer collects all cards, shuffles, and starts over.
The designated cards are: Queen of Clubs, 10 of Hearts. The players wish to determine the likelihood of actually getting to play a hand without mucking the cards and starting over.
In how many ways can you deal the cards WITHOUT getting one of the designated cards? (Hint: Consider how may cards are in the deck that are NOT one of the designated cards and consider how many cards need to be dealt in order for each player to have 7 cards.)
In how many ways can you deal each player 7 cards, regardless of whether the designated cards come out?
What is the probability of a successful hand that will go all the way till everyone gets 7 cards? (Round your answer to 4 decimal places.)
Recall, while using your calculator, that E10 means to move the decimal place 10 places to the righ
a) The number of ways to deal the cards without getting one of the designated cards are equals to the 2250829575120.
b) The number of ways to deal each player 7 cards, regardless of whether the designated cards come out are equals to the 21945588357420.
c) The probability of a successful hand that will go all the way till everyone gets 7 cards is 0.1026.
Six friends group is playing poker one night. They have a standard 52-card deck. So, here, total number of possible outcomes of game = 52
Now, the designated cards are , Queen of Clubs, 10 of Hearts. So,
a) Number of cards are in the deck that are not one of the designated cards
= 52 - 2 = 50
Number of cards that need to be dealt in order for each player to have 7 cards
= 5× 7 = 35
Thus total possible number of ways
= ⁵⁰C₃₅ = 2250829575120, which are ways to deal the cards without getting one of the designated cards.
b) Number of cards are in the deck = 52
Number of cards that need to be dealt in order for each player to have 7 cards = 5× 7 = 35
Thus total possible number of ways
= ⁵²C₃₅ = 21945588357420
Which are ways to deal each player 7 cards, regardless of whether the designated cards come out.
c) The probability of a successful hand that will go all the way till everyone gets 7 cards is = Number of ways to deal the cards without getting one of the designated cards/Total number of ays to deal the cards
= 2250829575120/21945588357420
= 0.10256410256
Hence, required probability is 0.1026.
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PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS ANSWER THESE QUESTIONS, PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEE
I will be your loyal s l a v e for all eternity
1. What is the equation for a line in slope-intercept form that is perpendicular to y= 1/4x-5
2. Write the equation of the line in slope-intercept form that goes through (3,8) and is parallel to y=-3x+1.
Answer:
1) y = - 4x + b;2) y = - 3x + 17.--------------------------------
Question 1Given line:
y = 1/4x - 5We know that perpendicular lines have opposite-reciprocal slopes.
Perpendicular line to the given has a slope of m = - 1 / (1/4) = - 4.
Let the y-intercept be b, then the line is:
y = - 4x + bQuestion 2Given line:
y = - 3x + 1We know parallel lines have equal slopes.
The parallel line to the given has a slope of m = - 3 and passes through point (3, 8).
Set the point-slope equation:
y - 8 = - 3(x - 3)Convert this into slope-intercept form:
y - 8 = - 3x + 9y = - 3x + 9 + 8y = - 3x + 17Take a picture or describe a place/instance/event that might influence your heart rate. Start with a heart rate of 90bpm, decide how many beats per minute your situation might increase or decrease your heart rate – DO NOT DISCLOSE YOUR NUMBER. Calculate the number of 0.04s boxes there would be between R-R intervals on an ECG trace. Write that number in your answer. - choose something that might increase your heart rate
Using unitary method, we can calculate the number of 0.04s boxes between R-R intervals on an ECG trace for our chosen event.
The unitary method is a mathematical technique that involves finding the value of one unit of a given quantity and then using it to find the value of a different quantity. In this case, we want to find the change in heart rate per second, so we need to determine how many beats per second our chosen event increases our heart rate by.
To calculate the duration of each R-R interval, we can use the following formula:
R-R interval duration = 1 / heart rate (in seconds)
Assuming our starting heart rate is 90 bpm and our event increases our heart rate by y beats per second, we can calculate the new heart rate as follows:
New heart rate = 90 bpm + (y * 60) bpm
We can then calculate the duration of each R-R interval using the formula above.
Finally, to find the number of 0.04s boxes between R-R intervals on an ECG trace, we can convert the R-R interval duration to a number of 0.04s boxes. Each 0.04s box on an ECG trace represents 0.04 seconds, so we can use the following unitary method:
1 second = 25 0.04s boxes
R-R interval duration (in seconds) = x seconds
Number of 0.04s boxes = x * 25
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Anthony painted 2triangles of the same size on the top corners of his house flag for sports day. What is the total area of both triangles?
The total area of both triangles is the product of the height and base of the flag.
What is a triangle?The connecting of three noncolinear points results in a triangle, which is a three-sided closed-plane object. Triangles can be classified into three categories based on their side properties: equilateral, scalene, and isosceles.
Given, Anthony painted 2triangles of the same size on the top corners of his house flag for sports day.
We are aware of A parallelogram can be divided into two comparable triangles by dividing it along its diagonal.
A planar figure with opposite sides that are parallel and of equal length is called a parallelogram.
Since the area of a parallelogram is equal to its base times its height, the combined area of the two triangles will be the same.
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the number is divisible by 6, 8, and 10 and has no repeated digits
120 is the number divisible by 6, 8, and 10.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
The common multiples to 6, 8, and 10.
6 x 20 = 120
8 x 15 = 120
10 x 12 = 120
So,
120 is divisible by 6, 8, and 10.
Thus,
120 is the number.
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-5 < 9 -6x???????????
Answer:
7/3>x
Step-by-step explanation:
-5<9-6x
subtract 9 from both sides
-14<-6x
divide by 6
14/6<x
simplified its 7/3<x
but since we divided by a negative we switch the sign
final answer is 7/3>x
find the value of x. SIMPLEST RADICAL FORM
Answer:
Step-by-step explanation:
56
The original price of a lawn mower was $199.99. During a midsummer sale, the lawn mower is on sale for $139.99. What is the discount rate?
Answer:
60 dollars
Step-by-step explanation:
I say this because it's simple math 199.90 - 139.99 its obviously 60
A tent is in the shape of a triangular prism. About how much canvas, including the floor, is used to make the tent? Draw a net if necessary.
The total area of the canvas needed would be 21.4 square yards.
What is the surface area of triangular pyramid?The formula to calculate the total surface area of a triangular pyramid is -
T.S.A. = {1/2}(a × b) + {1/2}(b × s).
Given is a tent is in the shape of a triangular prism.
The total area of the canvas would be -
A{C} = 2{1/2 x 2 x 1.7} + 2{3 x 2} + {3 x 2}
A{C} = (2 x 1.7) + 12 + 6
A{C} = 3.4 + 18
A{C} = 21.4 square yards
Therefore, the total area of the canvas needed would be 21.4 square yards.
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Answer:6
Step-by-step explanation:beacuse it it
Suppose x is a normally distributed random variable with μ=10 and σ=2. Find each of the following probabilities.
a. P(x ≥ 12.5) b. P(x ≤ 9) c. P(10.88 ≤ x ≤ 15.3) d. P(4.72 ≤ x ≤ 12.46)
The value of the probabilities are
a. P(x ≥ 12.5) is 6.68%
b. P(x ≤ 9) is 2.28%
c. P(10.88 ≤ x ≤ 15.3) is 61.38%
d. P(4.72 ≤ x ≤ 12.46) is 99.45%
Probability is the measure of the likelihood of an event occurring. It is a way of quantifying uncertainty and predicting the likelihood of an outcome. In this question, we will use the normal distribution to calculate probabilities.
The mean is the center of the distribution, and the standard deviation measures the spread of the distribution.
a. P(x ≥ 12.5):
Using a standard normal distribution table, we find that the area to the right of 12.5 is 0.0668. This means that the probability of x being greater than or equal to 12.5 is 0.0668 or 6.68%.
b. P(x ≤ 9):
Using a standard normal distribution table, we find that the area to the left of 9 is 0.0228. This means that the probability of x being less than or equal to 9 is 0.0228 or 2.28%.
c. P(10.88 ≤ x ≤ 15.3):
Using a standard normal distribution table, we find that the area to the left of 15.3 is 0.9987 and the area to the left of 10.88 is 0.3849. Therefore, the area between 10.88 and 15.3 is
=> 0.9987 - 0.3849 = 0.6138.
This means that the probability of x being between 10.88 and 15.3 is 0.6138 or 61.38%.
d. P(4.72 ≤ x ≤ 12.46):
Using a standard normal distribution table, we find that the area to the left of 12.46 is 0.9946 and the area to the left of 4.72 is 0.0001. Therefore, the area between 4.72 and 12.46 is
=> 0.9946 - 0.0001 = 0.9945.
This the probability of x being between 4.72 and 12.46 is 0.9945 or 99.45%.
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A rectangle has a length of 30 feet less than five times its width if the area of the rectangle is 360 ft.² find the length of the rectangle
Answer:
[tex]l = 30[/tex] OR [tex]l=-60[/tex]
Step-by-step explanation:
We can solve this problem with a system of equations by creating 2 equations from the information given.
1. "a length of 30 feet less than 5 times its width"
[tex]l = 5w - 30[/tex]
2. "the area of the rectangle is 360 ft²"
[tex]l\cdot w = 360[/tex]
To solve for the rectangle's length, we can create a substitution for w by dividing both sides of the second equation by length ([tex]l[/tex]).
[tex]l\cdot w = 360\\\overline{\ \ l\ \ } \ \ \ \: \ \overline{\ l \ \ }[/tex]
[tex]w = \dfrac{360}{l}[/tex]
Then, we can substitute this value back into the first equation and solve for [tex]l[/tex].
[tex]l = 5(\dfrac{360}{l}) - 30[/tex]
↓ distribute the 5
[tex]l(l) = \left(\dfrac{1800}{l} - 30\right)l[/tex]
↓ multiply both sides by [tex]l[/tex]
[tex]l^2 = 1800 - 30l[/tex]
↓ move all [tex]l[/tex]'s to one side
[tex]l^2 + 30l = 1800[/tex]
To solve this quadratic, we can complete the square.
↓ add (30/2)² to both sides
[tex]l^2 + 30l + \left(\dfrac{30}{2}\right)^2 = 1800 + 15^2[/tex]
↓ simplify 15²
[tex]l^2 + 30l + 225 = 1800 + 225[/tex]
↓ factor the left side as a perfect square
[tex](l + 15)^2 = 2025[/tex]
↓ take the square root of both sides
[tex]l + 15 = \pm \sqrt{2025}[/tex]
[tex]l + 15 = \pm 45[/tex]
↓ split into 2 equations
[tex]l + 15 = 45[/tex] OR [tex]l + 15 = -45[/tex]
[tex]\boxed{l = 30}[/tex] OR [tex]\boxed{l=-60}[/tex]
For the following exercises, determine whether each of the following relations is a function_ 1.y =2x + 8 2. {(2, 1), (3,2), (-1,1), (0, -2)}
For the following exercises, evaluate the function f(x) = -3x2 + 2x at the given input: 3. f(-2) 4. f(a)
The value of the evaluated function f(x) = -3x² + 2x at
(i) f(-2) is -16 ;
(ii) f(a) is -3a² + 2a .
The Function is represented as : f(x) = -3x² + 2x ;
(i) We have to evaluate the above function at f(-2),
So, we substitute x = -2 into the function:
we get ;
⇒ f(-2) = -3(-2)² + 2(-2)
⇒ f(-2) = -12 - 4 = -16 .
So , f(-2) = -16 .
(ii) Next we have to evaluate f(a),
So , we substitute x = a into the function:
⇒ f(a) = -3a² + 2a
So , f(a) = -3a² + 2a .
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The given question is incomplete , the complete question is
For the following exercises, evaluate the function f(x) = -3x² + 2x ; at the given input: (i) f(-2) (ii) f(a) .
How many solutions does the system of
equations below have?
-2x - 3y + z = 7
-x - y + 3z = -10
-2x - y - z = 13
no solution
one solution
infinitely many
solutions
The system of equations has infinitely many solutions.
What is a system of equations?
A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.
Here, we have
Given:
-2x - 3y + z = 7
-x - y + 3z = -10
-2x - y - z = 13
We have to how many solutions the system of equations has.
Arranging the above equations in form of a matrix and finding the determinant, we get,
Δ = [tex]\left|\begin{array}{ccc}-2&-3&1\\-1&-1&3\\-2&-1&-1\end{array}\right|[/tex]
= -2(1+3) +3(1+6) +1(1-2)
= - 4 + 21 -1 = 16
Δ₁ = [tex]\left|\begin{array}{ccc}7&-3&1\\-10&-1&3\\13&-1&-1\end{array}\right|[/tex]
= 7(1+4) +3(10-39) +1(10+13)
= 35 - 87 + 23
= -29
Hence, the system of equations has infinitely many solutions.
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What is the y-intercept of the graph of y = 2.5*?
a. 2.5
b. 1
ΟΑ
О в
О с
OD
C. 0
d. -1
OT
Ü
Please select the best answer from the choices provided
Point of y-intercept is (0,1)
What is y-intercepts?In a graph, the point where the line or curve crosses the axis is called the intercept. If a point crosses the x-axis it is x-intercepts. If a point crosses y-axis it is y-intercepts.
Given the function is [tex]y=2.5^{x}[/tex]
y-intercept is the point where the graph of the function crosses the y-axis.
To find the point of y-intercept put x=0 in the given function, we get
if x=0 then [tex]y=2.5^{0}[/tex] ⇒ y=1.
The function crosses at the point 1 in the y-axis.
Hence, point of y-intercept is (0,1)
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Which of the following is/are assumptions for linear regression? Please select all that apply. It's possible that there is only one correct answer. Y| X = x (the conditional distribution of Y given X = x) is a normal distribution. X and Y are independent. The errors e1,e2, e; have the same variance. The expectation of each error e; is O
As per the information provided, option B) The errors e1,e2, e; have the same variance is the assumptions for linear regression.
Regression analysis is a linear technique used to model the relationship between a scalar response and/or one or more explanatory variables, also known as the dependent and independent variables here.
Simple linear regression and multiple linear regression are two terms used to describe the process when there is only one explanatory variable present. This statement is different from multivariate linear regression, which thus predicts multiple correlated dependent variables as opposed to a single scalar variable present.
The first regression analysis technique that attracted a lot of research attention and was frequently applied in practical situations was linear regression. This is because models with linear rather than non-linear dependence on their unknown parameters are easier to fit, and it is also easier to determine the statistical properties of the resulting estimators.
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Malcolm trains on his kayak every weekend. He paddles upstream (against current) for 3 ½ hours and then returns downstream (with current) in 2hrs 6 minutes. If the river flows at 3km/ h, find:
* The paddling speed in still water
* The distance he paddles upstream.
The probability she pulls out a purple piece of candy would be 0.22.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is Sam's fathers collection.
We can write the equations for upstream and downstream as -
x - y = 7/2
x + y = 21/10
Solving the equations graphically -
{x} = 2.8
{y} = 0.7
In still water, the speed would be -
S = 3 - 0.7
S = 2.3 Km/h
Distance peddled upstream -
D = 2.8 x 3.5 = 9.8 Km
Therefore, the speed in still water would be 2.3 Km/h and the distance peddled upstream would be 9.8 Km.
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C
Flagpole a and flagpole c are both casting a shadow that ends at point s.
The distance (x) between the flagpoles is 12 ft.
The distance (y) from flagpole c to point s is 10 ft.
The height of flagpole a is 13.2 ft.
What is the height of flagpole c?
Show all your work.
The height of flagpole c is given as follows:
66 ft.
What are similar triangles?Similar triangles are triangles that share these two features presented as follows:
Congruent angle measures.Proportional side lengths.For each flagpole, the parameters are given as follow:
Flagpole a: Distance of 12 - 10 = 2 ft, height of 13.2 ft.Flagpole c: Distance of 10 ft, height of h ft.The triangles are similar, hence the proportional relationship to obtain the height of flagpole's c is given as follows:
2/10 = 13.2/h
Applying cross multiplication, the height is obtained as follows:
2h = 10 x 13.2.
h = 132/2
h = 66 ft.
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In the ratio of yellow marbles to blue marbles, 6:2, the quantities 6 and 2 are called?
The quantities 6 and 2 are called proportions
How to determine the name of the quantitiesFrom the question, we have the following parameters that can be used in our computation:
In the ratio of yellow marbles to blue marbles, 6:2,
This means that
Yellow : Blue = 6 : 2
Using the above as a guide, we have the following:
For every 6 yellow marbles, there are 2 blue marbles
This means that 6 and 2 are the proportions
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This figure was created by using two semi-circles and one rectangle. Find the area of the figure in square inches.
The area of the figure is 596.625 in².
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
We will consider the figure to have a rectangle and a circle.
Rectangle:
Length = 28 in
Breadth = 15 in
Area = 28 x 15 = 420 in²
Semicircle:
Diameter = 15 in
Radius = 7.5 in
Area = 1/2 πr²
= 1/2 x 3.14 x 7.5²
Area = 176.625/2
Area = 88.3125
There are two semicircles so,
= 2 x 88.3125
= 176.625 in²
Now,
Area of the figure.
= 420 + 176.625
= 596.625 in²
Thus,
596.625 in² is the area of the figure.
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make w the subject of the formula y-aw=2w-1
dont answer y+1/a+2 cuz it doesnt work
A bond has a 1,9% interest rate compounded quarterly. A stock has a 7.2% interest rate compounded
annually.
Which of the following shows how to transform the function representing the value of the bond from
quarterly compounding interest to annually compounding interest? Assume t is the time in quarters, and
that there is an initial investment of $1 in each account.
The way to transform the function such that the bond goes from quarterly compounding interest to annually compounding interest is = 1 + ( 1 + rate / 4 )ⁿ ˣ ⁴.
How to find the value ?The bond is said to be compounded quarterly. There would therefore be four compounding periods in a single year because there are four quarters in a year.
The formula would have been:
= Initial investment + ( 1 + rate ) ^ number of years
The adjusted formula to account for the quarters becomes :
= 1 + ( 1 + rate / 4 )ⁿ ˣ ⁴
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