Answer:
x equals [tex]\frac{11}{2}[/tex]
Hope this helps!
Step-by-step explanation:
Cross multiply to get ( 4x + 8 = 6x - 3 ) = ( 2x = 11 ) = ( x = [tex]\frac{11}{2}[/tex] ).
Answer:
11/2 or 5.5 (5 1/2 mixed)
Step-by-step explanation:
Cross multiplication ( a/b = c/d = a*d = c*b
(x+2)*4 = 3(2x-1) =
4x + 8 = 6x - 3
Move -3 to the left side (becomes positive since it is a negative)
4x + 8 + 3 = 6x
Move 4x to the other side
8+3 = 6x - 4x
Combine Like Terms
11 = 2x
Divide by 2
11/2 = x
The diameter of a circle is___________the length of its radius
Answer:
hey kid the answer is twice
the diameter of a circle is twice the length of its radius
Step-by-step explanation:
Answer: (2 times) the length of the radius
Step-by-step explanation:
r= 2D
see attachment
I don't know how to do 14
The surface area of the figure in item 14 is given as follows:
1112.8 mm².
What is the surface area of a rectangular prism?The surface area of a rectangular prism of height h, width w and length l is given by:
S = 2(hw + lw + lh).
This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.
The figure in item 14 is composed as follows:
Rectangular prism of dimensions 5 mm, 13 mm and 13 mm.Four triangles of base 13 mm and height 10.3 mm.Hence the surface area of the figure is given as follows:
S = 5 x 13 x 13 + 4 x 0.5 x 10.3 x 13
S = 1112.8 mm².
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Pls pls pls help 20 points will be given
Answer:
1: 9
2: 16
3: 225
4: 196
5: 25
6: 256
Step-by-step explanation:
Math :)
)
2. A deli offers a lunch consisting of a soup,
salad, and sandwich from the menu shown
in the table. A customer randomly chooses
lunch consisting of a soup, salad, and
sandwich. Construct and use a tree diagram
to determine the sample space of the event.
How many possible outcomes are in the
sample space? (Example 2)
Salad
Soup
Tortellini
Lentil
Caesar
Macaroni
Sandwich
Roast Beef
Ham
Turkey
Show
your work
here
So, there are 18 possible outcomes in the sample space.
What is sample space?In probability theory, the sample space of an experiment is the set of all possible outcomes that can occur. It is denoted by the symbol S and represents the total set of possible results that can be obtained from a given experiment.
For example, when rolling a standard six-sided die, the sample space is {1, 2, 3, 4, 5, 6}, because those are the only possible outcomes of the experiment. Similarly, when flipping a coin, the sample space is {heads, tails}.
The sample space is an essential concept in probability theory because it helps to determine the likelihood or probability of various outcomes occurring in a given experiment.
Here's the tree diagram for the given problem:
markdown
Copy code
Lunch
/ | \
Soup Salad Sandwich
/ | |
Tortellini Lentil Caesar
/ | \
Roast Beef Ham Turkey
The possible outcomes in the sample space are all the combinations of soup, salad, and sandwich.
There are 2 options for soup (Tortellini, Lentil), 3 options for salad (Caesar, Macaroni, Garden), and 3 options for sandwich (Roast Beef, Ham, Turkey). Therefore, the total number of possible outcomes in the sample space is:
2 x 3 x 3 = 18
So, there are 18 possible outcomes in the sample space.
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use the substitution method
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
Which equation would demonstrate the inverse property?
A. B. C. D
Option D : The equation that demonstrates the inverse property is D. 3/4 x 4/3= 1, which shows that the multiplication of the reciprocal of a number equals 1.
According to the multiplicative property known as the inverse property, the result of multiplying any non-zero number by its inverse or reciprocal will equal the multiplicative identity, which is 1.
The inverse property of multiplication states that for any non-zero number a, its inverse or reciprocal, when multiplied by a, will result in 1. The reciprocal of a number is the number that when multiplied by the original number results in 1.
For example, the reciprocal of 3 is 1/3 because 3 x 1/3 = 1.
Similarly, the reciprocal of 4/3 is 3/4 because (4/3) x (3/4) = 1.
So, if we multiply 3/4 by its reciprocal 4/3, we get:
(3/4) x (4/3) = (3 x 4) / (4 x 3) = 12 / 12 = 1
This shows that the product of 3/4 and 4/3 is 1, which is the multiplicative identity. Hence, this equation demonstrates the inverse property of multiplication.
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Which equation would demonstrate the inverse property?
A. (3x4) + (3x5) = 3(4+5)
B. 3x5 = 5x3
C. 3x4x5= (3x4)x5
D. 3/4 x 4/3= 1
(Translations LC)
Use the graph to answer the question.
Answer:
put 5 units up
if someone could help I would appreciate it! the first q was done in a group and I don't understand what's happening . will give brainliest
Step-by-step explanation:
1) x^2 - 4x + 1
re-arrange into vertex form y = a ( x-h)^2 + k where h, k is the vertex
y = (x^2 -4x) +1 'complete the square'
( take 1/2 of x coeff square it and add and subtract it )
(x^2 - 4x +4) - 4 + 1 reduce it
y= (x-2)^2 -3 shows vertex is 2, -3
Back to original equation
x^2 -4x + 1 using Quadratic Formula x = 2 ± sqrt (3) = 3.73 and .268
line of symmetry = x value of vertex x = 2
Range is -3 ≤ y ≤ + ∞
domain is - ∞ ≤ x ≤ + ∞
2) Similar to above....try it yourself
franco and cristina bought a sofa at the sale price of $1,344 the original price of the sofa was $1,920. what was the n percent of the discount
Answer: 70%
Step-by-step explanation:
make x=the percent of the discount.
$1,920 x=$1,344
x =$1,344÷ $1,920
x =0.7 or 70%
a tank with a capacity of 100 gallons initially contains 50 gallons of water with 10 pounds of salt in solution. fresh water enters at a rate of 2 gallons per minute and a well-stirred mixture is pumped out at the same rate. compute the amount of salt (in pounds) in the tank 10 minutes after the process begins.
The amount of salt in the tank 10 minutes after the process begins is 9.6 pounds.
As per the given information,
a tank with a capacity of 100 gallons initially contains 50 gallons of water with 10 pounds of salt in solution. Freshwater enters at a rate of 2 gallons per minute and a well-stirred mixture is pumped out at the same rate. Compute the amount of salt (in pounds) in the tank 10 minutes after the process begins.
We know that
Amount of salt in the tank = Salt concentration x Volume of water
Amount of salt at t = 0 in the tank = 10 pounds
Volume of water at t = 0 in the tank = 50 gallons
Amount of salt at time t in the tank can be calculated by the following formula.
Amount of salt in the tank at time t = (Amount of salt at t = 0) - (Freshwater enters at rate × Salt concentration in the tank)
Now, let's calculate the amount of salt in the tank after 10 minutes.
Calculate the volume of water in the tank after 10 minutes
The rate of freshwater enters into the tank is 2 gallons per minute
So, the volume of water that entered the tank in 10 minutes = 2 × 10 = 20 gallons
Initial volume of water in the tank = 50 gallons
Volume of water in the tank after 10 minutes
= Initial volume + Freshwater enters - Freshwater pumped out
= 50 + 20 - 20
= 50 gallons
Calculate the salt concentration in the tank after 10 minutes.
Initially, the salt concentration = (Amount of salt at t = 0) / (Volume of water at t = 0) = 10/50 = 0.2 lbs/gallon
Now, the amount of salt at time t = 10 min = 10 - 2 × 0.2 = 9.6 lbs
So, the salt concentration after 10 minutes = 9.6 / 50 = 0.192 lbs/gallon
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The vertices of triangle PQR are P(3,4), Q(5,8) and R(7,4). State the coordinates of the midpoint S of side PR
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ P(\stackrel{x_1}{3}~,~\stackrel{y_1}{4})\qquad R(\stackrel{x_2}{7}~,~\stackrel{y_2}{4}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 7 +3}{2}~~~ ,~~~ \cfrac{ 4 +4}{2} \right) \implies \left(\cfrac{ 10 }{2}~~~ ,~~~ \cfrac{ 8 }{2} \right)\implies \stackrel{ \textit{\LARGE S} }{(5~~,~~4)}[/tex]
is x^2+3x+4 linear or quadratic
Answer:
Quadratic
Step-by-step explanation:
I have no idea how to explain it except that it follows the standard ax² + bx + c format
Quadratic is the answer to your question! :)
Brody and his children
Went into a movie theater and he bought 44. T0 worth of drinks and pretzels. Each drink costs $6 abd each pretzel costs $3. 25 he bought a total of 12 drinks and pretzels all together
Brody bought 2 drinks and 10 pretzels. Let's use algebra to solve this problem. Let d be the number of drinks that Brody bought, and let p be the number of pretzels that he bought. We know that he bought a total of 12 drinks and pretzels, so:
d + p = 12
We also know that each drink costs $6 and each pretzel costs $3.25, and he spent a total of $44.10 on drinks and pretzels. So:
6d + 3.25p = 44.10
We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for p:
p = 12 - d
Substituting this into the second equation, we get:
6d + 3.25(12 - d) = 44.10
Simplifying:
6d + 39 - 3.25d = 44.10
2.75d = 5.10
d = 1.85 (rounded to two decimal places)
Since d represents the number of drinks, we can't have a fractional value for it. However, we can round it to the nearest whole number and use that to solve for p:
d ≈ 2
p = 12 - d = 12 - 2 = 10
Therefore, Brody bought 2 drinks and 10 pretzels. We can check that this solution satisfies both equations:
2 + 10 = 12 (first equation)
6(2) + 3.25(10) = 44.10 (second equation)
Therefore, our solution is correct
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Brody and his children went into a movie theater and he bought $44.50 worth
of drinks and pretzels. Each drink costs $6 and each pretzel costs $3.25. He
bought a total of 12 drinks and pretzels altogether. Determine the number of
drinks and the number of pretzels that Brody bought
Let h(x)=,[tex]\sqrt{3x^{2} -5x+2}[/tex] find the domain and range for h(x). Write in set builder notation.
In set-builder nοtatiοn, we can write:
Dοmain οf h(x): { x ∈ R | x ≤ 1/3 οr x ≥ 2/3 }
Range οf h(x): { y ∈ R | y ≥ 0 }
What is Functiοn?In mathematics, a functiοn is a rule that maps each element in οne set, called the dοmain, tο a unique element in anοther set, called the range. It is a relatiοn between a set οf inputs and a set οf pοssible οutputs with the prοperty that each input is related tο exactly οne οutput.
The dοmain οf h(x) is the set οf all values οf x that make the functiοn well-defined, i.e., there shοuld be nο negative number inside the square rοοt.
Tο find the dοmain οf h(x), we set the expressiοn inside the square rοοt tο be nοn-negative and sοlve fοr x:
3x² - 5x + 2 ≥ 0
Factοrizing the quadratic expressiοn, we get:
(3x - 2)(x - 1) ≥ 0
The sοlutiοn set fοr this inequality is given by the interval:
x ≤ 1/3 οr x ≥ 2/3
Therefοre, the dοmain οf h(x) is:
{ x ∈ R | x ≤ 1/3 οr x ≥ 2/3 }
The range οf h(x) is the set οf all pοssible values that the functiοn can take. Since the square rοοt is always nοn-negative, the range οf h(x) is:
{ y ∈ R | y ≥ 0 }
In set-builder nοtatiοn, we can write:
Dοmain οf h(x): { x ∈ R | x ≤ 1/3 οr x ≥ 2/3 }
Range οf h(x): { y ∈ R | y ≥ 0 }
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Pls someone help me i need this
The formula for the volume of the shaded region is given as follows:
V = π/3[(R² - r²)(H - h)]
How to obtain the volume a cone?The volume of a cone of radius r and height h is given by the equation presented as follows, which the square of the radius is multiplied by π and the height, and then divided by 3.
V = πr²h/3.
Hence, for the large cone, the volume is given as follows:
Vl = πR²H/3.
For the smaller cone, the volume is given as follows:
Vs = πr²h/3.
Hence the volume of the shaded region is given as follows:
V = Vl - Vs
V = πR²H/3 - πr²h/3
V = π/3[(R² - r²)(H - h)]
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A magician makes potions by combining maple syrup from a magical maple tree with ordinary water. The magician starts with a large supply of two potions: a red potion, which is 60% magical syrup by volume (and the rest is just water), and blue potion, which is 30% magical syrup by volume.
(a) Find the amount of red potion (in mL) that must be added to 500 mL of blue potion in order to produce potion that is 40% magical syrup by volume.
(b) Find the amounts of red potion and blue potion (in mL) that can be combined in order to produce 100 mL of a potion that is 54% magical syrup by volume.
(c) Does there exist a combination of red potion and blue potion that can produce a potion that is 75% magical syrup by volume?
need help
In system equation method,
a) Amount of red portion = 240 ml.
b) There are 300 mL of blue potion used and 100 mL of red potion used.
c) There is a ratio of 2 (blue potion):1 (red potion), there will be a 35% amount of magical syrup.
What is equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
(a) We can use a system equation here to solve this.
Let x=amount of red potion used
Let y=total amount of potion in solution
Then,
=>200 + x = y
=> 0.15(200) + 0.75x = 0.25y
0.15(200) because 15% of the blue potion=.15 and there is 200mL.
0.75x because 75% of the red potion=.75 and there is x amount of it
0.25y because we want 25% of the total potion=.25 and there is y amount of it.
We can substitute for y in the second equation:
=>0.15(200) + 0.75x = 0.25(200 + x)
=> 30 + 0.75x = 50 + 0.25x
=> -20 = -0.5x
=> x = 40
Knowing that x=40, we know that y=240, meaning our answer is 240.
b.) We can again use a system for this problem
Let x=Amount of red potion
Let y=Amount of blue potion
=> x + y = 400
=> 0.3(400) = 0.15y + 0.75x
0.3(400)=30% of the 400 mL
0.15y=15% of the magic syrup
0.75x=75% of the magic syrup
We can substitute for x in this equation:
=>120 = 0.15y + 0.75(400 - y)
120 = 0.15y + 300 - 0.75y
-180 = -0.6y
y = 300, x = 100
There are 300 mL of blue potion used and 100 mL of red potion used.
c.) Let x=amount of red potion
Let y=amount of blue potion
=> 0.15x + 0.75y = 0.35(x + y)
0.35(x+y) because the total amount of the potion is x+y
=>0.15x + 0.75y = 0.35x + 0.35y
0.4y = 0.2x
2y = x
Whenever there is a ratio of 2 (blue potion):1 (red potion), there will be a 35% amount of magical syrup.
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Which expressions are equivalent to
−
7
+
3
(
−
4
�
−
3
)
−7+3(−4e−3)minus, 7, plus, 3, left parenthesis, minus, 4, e, minus, 3, right parenthesis ?
Choose all answers that apply:
The expressions -4(3e+4) is equivalent to -7+3(-4e-3)
How to find the equivalent expressions?Given expression:
[tex]-7+3(-4e-3)[/tex]
Expand expression:
[tex]-7-12e-9[/tex]
Regroup like terms:
[tex]-12e-9-7[/tex]
= [tex]-12e-16[/tex]
Factor -4 to get:
[tex]-4(3e+4)[/tex]
What is mathematical expression?A mathematical expression is a combination of numbers, symbols, and/or variables that represent a mathematical statement. It can be a simple expression like "2 + 3," or a more complex one like "sin(x) + 3y^2 - 7."
Expressions can be used to perform calculations, represent relationships between different quantities, or describe geometric shapes and structures. They are an essential tool in mathematics and are used in a wide range of fields, including science, engineering, finance, and economics.
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Complete question:
Which expressions are equivalent to -7+3(-4e-3)?
Choose all answers that apply:
(Choice A)
-4(3e+4)
(Choice B)
12e
(Choice C)
None of the above
In this triangle, what is the value of x? Enter your answer, rounded to the nearest tenth, in the box. 63 degrees 85 cm
Using the sine's function in the given triangle, the value of x is 75.7 respectively.
What is the triangle?
A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon.
There are three sides and three angles in every triangle, some of which may be the same.
The angle total of a triangle will always be equal to 180°.
A quadrilateral can be divided in half from corner to corner to form a triangle because the angle total of a quadrilateral is equal to 360°.
A triangle is effectively half of a quadrilateral, therefore it makes sense that its angle measurements are also half. 180° is one-half of 360°.
So, right triangles are used to depict figures like this one, which has a hypotenuse of 85, a base of x, and a top angle of 63°.
The hypotenuse and the side that faces the angle are both present.
The sine function's opposite/hypotenuse ratio is as follows:
sin 63° = x/85
Now, solve as follows:
sin 63° = x/85
85(sin 63°) = x
75.7 = x
Therefore, using the sine's function in the given triangle, the value of x is 75.7 respectively.
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Complete question:
In this triangle, what is the value of x? Enter your answer, rounded to the nearest tenth, in the box.
y = 3x + 19
8x + 2y = -18
Answer: i don't know what type of answer ur looking for but
the answer for substitution is x=-4, y=7
Step-by-step explanation:
y = 3x + 19
8x + 2y = - 18 ====> y = -4x - 9
Equate the two expressions of 'y'
3x + 19 = - 4x- 9
7x = -28
x = -4 then y = 3x + 19 = 3(-4) + 19 = 7
(-4, 7)
Solving Exponential Equations with Logarithms Solve each equation. Round your answers to the nearest ten-thousandth.
1) 3^b = 17 2) 12^r= = 13
3) 9^n = 49 4) 16^v = 67
5) 3^a = 69
Answer:
1. =2.5759 ; 2. =0.8290 ; 3. =2 ; 4. =1.7959 ; 5. = 3.9138
Step-by-step explanation:
1. Taking logarithm with base 3 on both sides, we get:
b = log₃(17)
b ≈ 2.5759
2. Taking logarithm with base 12 on both sides, we get:
r = log₁₂(13)
r ≈ 0.8290
3. Taking logarithm with base 9 on both sides, we get:
n = log₉(49)
n = 2
4.Taking logarithm with base 16 on both sides, we get:
v = log₁₆(67)
v ≈ 1.7959
5.Taking logarithm with base 3 on both sides, we get:
a = log₃(69)
a ≈ 3.9138
Please Help! Dilations about origin!
The coordinate location of the point S' is (-1.5, 4).
The scale factor of the dilation is 0.25.
How to find the coordinate location of the point S'?To find coordinate location of the point S' after a dilation using a scale factor of 0.5 , we can use the following formula:
S' = scale factor * S
where S' is the image of S and S is the preimage. The coordinate of S is (-3, 8)
Substituting the values, we get:
S' = 0.5 * (-3, 8)
S' = (-1.5, 4)
Thus, the coordinate location of the point S' is (-1.5, 4).
PART 2
The scale factor of the dilation is given by:
scale factor = coordinate of image / coordinate of preimage
Let's pick one of the coordinates (you can use either x or y coordinate). We pick B:
scale factor = B'/B
scale factor = 1/4 = 0.25
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What is the x-intercept of the line shown below? Enter your answer as a coordinate pair
Answer:
The x-intercept is (1, 0).
Javier and his brothers are going to ride go-karts. They decide whoever
picks a red king from a standard deck of cards gets to ride first. What is the
probability of drawing a red king?
(B)
(A)
1
13
2
13
1
26
1
52
The probability of getting a red king card from the deck of cards is 1/26.
Define probability?The probability formula can be used to determine the likelihood of an event by only dividing the favourable number of possibilities by the entire number of possible outcomes.
As there can never be more favourable outcomes than there are possible outcomes, the probability of an event happening can range from 0 to 1. As a result, 0 cannot represent the percentage of successful outcomes.
Given,
We have a deck of cards.
So, total no of cards = 52
Now, no of red cards = 26.
Now total no. of kings = 4.
Total no. of red kings = 2
Probability of picking a red king from the deck =
2/52
=1/26
Therefore, the probability of getting a red king card from the deck of cards is 1/26.
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Reagan's house is due west of Oakdale and due south of Bloomington. Oakdale is 21 kilometers from Reagan's house and 29 kilometers from Bloomington. How far is Bloomington from Reagan's house, measured in a straight line? kilometers
9 kilom-eters, is Bloomin-gton from Reag-an's house, measured in a str-aight line.
What is unitary method?"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."
We always count the unit or amount value first and then calculate the more or less amount value.
For this reason, this procedure is called a unified procedure.
Many set values are found by multiplying the set value by the number of sets.
A set value is obtained by dividing many set values by the number of sets.
=29-20
=9 km
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Suav wants to use a sheet of fiberboard 27 inches long to create a skateboard ramp with a 19 degree angle of elevation from the ground. How high will the ramp rise from the ground at its highest end?
The ramp will rise 16.8 inches from the ground at its highest end, when the angle of elevation is 19 degrees and the length of the fiberboard is 27 inches.
To calculate the height of the ramp at its highest end:
1. First, calculate the length of the hypotenuse of the triangle formed by the ramp, using the Pythagorean Theorem. This can be done by squaring the length of the ramp (27 inches) and the angle of elevation (19 degrees) and adding them together. The result is 750.41 inches.
2. Next, take the square root of the result from step 1. This gives us 27.45 inches, which is the length of the hypotenuse.
3. Then, subtract the length of the ramp from the length of the hypotenuse. This gives us 8.45 inches.
4. Finally, divide the result from step 3 by 2. This gives us the height of the ramp at its highest end, which is 16.8 inches.
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Use geogebra to record m∠ead. also find and record m∠adc and m∠aec. you don’t need geogebra to find m∠adc and m∠aec. explain why not.
Answer:
In GeoGebra, m∠EAD = 120°. Both m∠ADC and m∠AEC are 90° because the tangent to a circle is perpendicular to the radius drawn from the point where the tangent touches the circle.
Step-by-step explanation:
plato :>
the length of a rectangle is three times its width. If the area of the rectangle is 300 m², find its perimeter.
Answer:
Let's assume that the width of the rectangle is 'w' meters.
According to the problem, the length of the rectangle is three times its width, so the length is:
l = 3w
The area of the rectangle is given as 300 m², so we have:
lw = 300
Substituting the value of 'l' in terms of 'w', we get:
(3w)w = 300
Simplifying the above equation, we get:
3w^2 = 300
Dividing both sides by 3, we get:
w^2 = 100
Taking the square root on both sides, we get:
w = 10
So the width of the rectangle is 10 meters.
Using the value of 'w', we can find the length of the rectangle:
l = 3w = 3(10) = 30
So the length of the rectangle is 30 meters.
The perimeter of the rectangle is given by:
P = 2(l + w)
Substituting the values of 'l' and 'w', we get:
P = 2(30 + 10) = 2(40) = 80
Therefore, the perimeter of the rectangle is 80 meters.
Step-by-step explanation:
Calculate the number of expected double crossover progeny- Express your answer to the nearest whole number: 3uCF Previous Answers Correct To calculate the expected number of double crossovers use the product law: Multiply the single crossover probabilities and then multiply by the tota number of progeny: Using the map distances provided, the expected number of double crossovers is 0.305 x 0.155 x 1000
The number of expected double crossover progeny when multiply by the total number of progeny is 47.
When chromosomal pieces are swapped out twice, it is known as a double crossover. In the case of a double crossing, the two ends of the chromosome are still parental, but another sister chromatid sequence has "swapped" into the space between the crossovers;
When homologous chromosomes are combined, crossovers happen.
Chromatids from various chromosomes can be aligned. Exchange chromatids from, for example, segments a collision between two identical chromosomes occurs at an similar spot along their respective lengths. they are After swapping the segments, the chromatids have split between the point of contact and the chromatids' tips.
We have,
number of double crossovers is 0.305 x 0.155 x 1000
so 0.305 x 0.155 x 1000 = 47
So number of expected double crossover progeny is 47.
Test cross:
Progeny whithered wing smooth body and speck body
Genetic distance between sm and sp is 15.5
15.5 = 2x + 33 /1000 x 100
155 = 2x + 33
2x = 155-33
x = 122/2
x = 61.
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Jeff has a life insurance policy,
and his insurance company
expects that it would have to put
$2,225,000 into a bank account
if it ever had to make payments
on the policy. The insurance
company also expects interest
rates to be at 1.4% at that time.
How much will the life insurance
policy pay to Jeff's beneficiaries
per year?
The life insurance policy will pay $2,256,150 to Jeff's beneficiaries per year. The solution has been obtained by using the simple interest.
What is simple interest?
A way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time is by using simple interest. The principal amount in a basic interest calculation is constant.
We are given that Jeff has to put $2,225,000 into a bank account if it ever had to make payments on the policy and the company also expects interest rates to be at 1.4% at that time.
So, from this we get,
⇒ Total Interest = $2225000 × 1.4% × 1
⇒ Total Interest = $31,150
Amount payable by company = $2225000 + $31,150
Amount payable by company = $2,256,150
Hence, the life insurance policy will pay $2,256,150 to Jeff's beneficiaries per year.
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What is the missing length?
5.3 cm
12 cm
area = 128.885 cm²
W =
centimeters
The missing length w of the given trapezium with the area of 128.885 cm² is found to be: w = 14.9 cm.
Explain about the trapezium?A closed-form, two-dimensional quadrilateral with two parallel, opposite sides is called a trapezium. The bases and legs of a trapezium are referred to as parallel and non-parallel, respectively. Four sides as well as four corners make up the trapezium.
The term "isosceles trapezium" refers to a trapezium with equal-length legs, meaning that the 2 non parallel sides are equal.
Area of Trapezium = ½ (Sum of parallel sides) × (Height between parallel sides)
128.885 = ½(5.3 + 12) × w
128.885 * 2 = 17.3 w
w = 128.885 * 2 / 17.3
w = 14.9
Thus, the missing length w of the given trapezium with the area of 128.885 cm² is found to be: w = 14.9 cm.
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