Answers
The value of x for the given parallelogram is 4.8 cm.
According to the question,
We have the following information:
We have a parallelogram with base x cm, height 2.5 cm and area 12 square centimeters.
(More to know: in a parallelogram, the opposite sides are equal and parallel to each other. Opposite angles of parallelogram are equal and the sum of consecutive angles is 180°.)
We know that the following formula is used to find the area of the parallelogram:
Area of parallelogram = Base*height
x*2.5 = 12
x = 12/2.5
x = 4.8 cm
Hence, the value of x is 4.8 cm.
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Related Questions
7 The nth term of a sequence is u, = 10 x 3" Write down the first four terms in the sequence.
Answers
The first four terms in the sequence are 30, 90, 270 and 810 respectively.
How to determine the termsWe have that the nth term of the sequence is expressed as;
U = 10 × 3 ^n
Where;
n = number of terms
To determine the first terms, let's substitute the value of n as 1, we get;
U = 10 × 3^1
Multiply the values
U₁ = 30
The second terms, n = 2
U₂ = 10 × 3²
U₂ = 10 × 9
Multiply through
U₂ = 90
The third year, n = 3
U₃ = 10 × 3³
Find the cube of the value and multiply the values
U₃ = 270
The fourth year, n = 4
U₄ = 10 × 3^4
U₄ = 10 × 81
Multiply through
U₄ = 810
Thus, the numbers are 30, 90, 270, 810
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what are the coordinates of the image of vertex after a reflection of r x-axias (x,y)
Answers
The coordinates of the image of vertex after a reflection of r x-axias (x,y) is (x, -y).
To get the coordinates of a point reflected on the x - axis, some important rules be considered here:
1. The x - coordinate of the reflected point is the same as the x - coordinate of the original point.
2. The y - coordinate of reflected point has opposite sign of y-coordinate of original point.
Example:
(1,9) when reflected on the x - axis it will be (1,-9).
Therefore the coordinates of the image of vertex after a reflection of r x-axias (x,y) is (x, -y).
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A car starts from point P at time t= 0 and travels at 45 mph.
Write an expression d(t) for the distance the car travels from P.
Graph y = d(t)
What is the slope of the graph in (b)? What does it have to do with the car?
Create a scenario in which t could have negative values
Create a scenario in which the y-intercept of y= d(t) could be 30.
Answers
Answer:
Step-by-step explanation:
Let y be the distance the car travels, in miles. Let t be the time traveled, in hours. The speed is 45 m/h. We know that the distance the car travels is given by the equation:
Distance = (speed)*(time)
Using the assigned variables, we can rewrite this as:
d(t) = (45 m/h)(t hours)
We want an equation that will tell us the position of the car, y, at any time, t, including t = 0, the start.
d(t) = ?
At time = 0, the starting point of the car is P. We can write:
d(0) = P
For x[tex]\geq[/tex]0, we would find the car at:
d(t) = P + (45)*t
The 45 is in units of miles/hour, t is in hours and d is in miles. Let's assume an intital position, P, for this car to be 10 miles. P = 10 miles.
The function is: d(t) = 10 + (45)*t
If we leave the units in, it can be written as: d(t) = (10 miles) + (45 miles/hr)*t(in hr)
We can see that the term "(45 miles/hr)*t(in hr)" will eventually reduce to just miles one we enter the time in hours, since the hours cancel out.
The graph of this function is attached. The line crosses the y axis at 10 (miles) when time, t, is 0 : the car has not started.
The slope of the graph can be determined by calculating the Rise/Run of the line. Pick any two points. I'll choose: (2,100) and (4,190).
Rise (change in y) is (190-100) = 90
Run (change in x) is (4 - 2) = 2
Slope = Rise/Run = (90/2) or 45.
The slope has the same value as the speed, as it should. The slope is telling us the rate of change, which for this graph, is the speed of the car. The y-intersect is (0, 10). The car is at 10 miles at the start (t=0).
To create a scenario where could have a negative value requires some imagination. There is really no such thing as negative time, except in time travel movies. But we can define t, perhaps, as the start of a race. (High noon, for example). If the cars were allowed to start moving before noon as long as they started back (negative direction) from the starting point of the race. If t is defined as "hours after 12:00 noon" then a value of t = -1 means 11:00 AM. If the car were approaching the staring line at 45 miles/hour, ahread of the official start time, the graph would make sense. Not the race, so much, but the graph would be accurate.
James knows that he eventually wants to buy a motocycle, and the model he has in mind cost $5000. he has found a bank that will let him open a saving account with 7% interest that is compounded monthly. if he wants to buy his motocycle in 5 years ( he's still nervious) how much money should he invest in the account now
Answers
He should invest $86.29 in the account now, which has a 7% interest compounded monthly.
Compound interest refers to the amount of interest added on the principal amount plus interest. The formula for compound interest is:
B = P(1 + r/n)^t
where B is the ending balance, P is the principal amount or original balance, r is the interest rate in decimal form, n = number of times interest is compounded monthly, and t is the time in number of months
Based on the given information, P is the unknown and
B = $5000
t = 5 years = 60 months
r = 7% = 0.07
n = 1
Plug in the values and solve for P or the amount that should be invested today.
B = P(1 + r/n)^t
$5000 = P(1 + 0.07/1)^60
$5000 = P(1.07)^60
P = $5000/(1.07)^60
P = $86.29
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The length of a rectangle is the sum of the width and 2. The area of the rectangle is 63 units. What is the width, in units, of the rectangle?
Answers
Answer:
WITDTH=7
Step-by-step explanation:
width = w
length = w + 2.
w(w + 2) = 63 (area)
quadratic equation in w:
w2 + 2w = 63
w2 + 2w - 63 = 0
FACTOR:
(w + 9)(w - 7) = 0
9-7=2
9x(-7) = -63
Two possible solutions:
w + 9 = 0 (solution w = -9) or
w - 7 = 0 (solution w = 7)
The width must be positive, the answer is 7 units.
length = w+2
length = 9
Larissa is standing at point L Pj is standing at point P and Raelynn is standing at points are on segment LR as shown in the figure If LR equals 12 and PR equals 4, find LP. explain
Answers
If LR equals 12 and PR equals 4, then: LP = 8 because LP + PR = LR according to the Segment Addition Postulate, and 8 + 4 = 12 using substitution.
What is the Segment Addition Postulate?The Segment Addition Postulate states that when there are two endpoints on a line segment (L) and (C), a third point (P) would lie on the line segment (LR), if and only if the magnitude of the distances between the endpoints satisfy the requirements of this equation LP + PR = LR.
This ultimately implies that, the Segment Addition Postulate is only applicable on a line segment that contains three collinear points.
By applying the Segment Addition Postulate to the given endpoints, the value of LP is given by:
LP + PR = LR
LP = LR - PR
Substituting the given parameters into the formula, we have;
LP = 12 - 4
LP = 8.
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Complete Question:
Larissa is standing at point L. Pj is standing at point P and Raelynn is standing at points are on segment LR as shown in the figure If LR equals 12 and PR equals 4, find LP. explain
LP = 16 because 12 + 4 = 16 according to the addition property of equality.
LP = 8 because 12 - 4 = 8 according to the subtraction property of equality.
PR = 16 because LR + LP = PR according to the Segment Addition Postulate, and 12 + 4 = 16 using substitution.
PR = 8 because LP + PR = LR according to the Segment Addition Postulate, and 8 + 4 = 12 using substitution.
Answer: Lp = 8
Step-by-step explanation:
Got it right
Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. after 11 hours of burning, a candle has a height of 19.4 centimeters. after 23 hours of burning, its height is 12.2 centimeters. what is the height of the candle after 15 hours?
Answers
The height of the candle after 15 hours of burning is 17 cm.
According to the question,
We have the following information:
Height of the candle after 11 hours of burning = 19.4 cm
Height of the candle after 23 hours of burning = 12.2 cm
Now, we will find the rate at which the height of the candle is decreasing. It means that we will find the decrease in height per centimeter.
Difference between hours and height:
23-11 = 12 hours
19.4-12.2 = 7.2 cm
So, we have:
12 hours = 7.2 cm
1 hour = 7.2/12
1 hour = 0.6 cm
So, the height is decreasing at the rate of 0.6 cm per hour.
Now, we have to find the height after 15 hours.
Height at 11 hours = 19.4 cm
Difference between 15 hours and 11 hours is 4 hours.
Change in height = 0.6*4 cm
Decrease in height = 2.4 cm
So, the height after 15 hours:
19.4-2.4
17 cm
Hence, the height of the candle after 15 hours of burning is 17 cm.
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a random sample of 26 checking accounts at a bank showed an average daily balance of $300 and a standard deviation of $45. the balances of all checking accounts at the bank are normally distributed. develop a 95% confidence interval estimate for the mean of the population.
Answers
The confidence interval estimate for the mean of the population at 95% is [$282.70, $317.30].
Confidence interval is defined as the range of values where a parameter might fall at a given confidence level. It can be calculated using the formula below.
CI = μ ± z x (SD / √n)
where CI = confidence interval
μ = sample mean
z = found by using a z-score table
SD = sample standard deviation
n = sample size
At 95% confidence level, the area in each tail of the standard normal curve is 2.5, and the cumulative area up to the second tail is 97.5.
(100 - 95) / 2 = 2.5
100 - 2.5 = 97.5
Find 0.975 in the z-table to get the value of z.
At p = 0.95, z = 1.96
Plug in the values and solve for the confidence interval.
CI = μ ± z x (SD / √n)
CI = 300 ± 1.96 x (45 / √26)
CI = 300 ± 17.30
CI = [$282.70, $317.30]
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What is the equation in standard form of the line that passes through the point (6,-1) and is perpendicular to the line represented by 8x + 3y=1
Answers
The required equation of line in standard form that passes through the point (6,-1) and is perpendicular to the line represented by 8x + 3y = 1 is
y = (3/8)x - 13/4
How to find equation of line if one point and equation of perpendicular line is given?
To find the equation of line which is perpendicular to another line
Find slope of the required line using m₁. m₂ = -1Using the given point find y-intercept by substituting in the equation of line.According to the given question:
Let the required equation of line be y = mx + b
where m is the slope of line and b is the y-intercept
Now, 8x + 3y = 1 is perpendicular to the line. Hence, the slopes of both line will satisfy m₁. m₂ = -1
Standard form of the given line is
y = (-8/3)x + 1/3
∴ m₁ = -8/3
Finding m₂, (-8/3). m₂ = -1
∴ m₂ = 3/8 ------ (1)
Using the given point (6, -1) to find y-intercept in the equation
y = (3/8)x + b
-1 = (3/8)(6) + b
∴ b = -13/4
Therefore the required equation of line in standard form is
y = (3/8)x - 13/4
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The length of the base of a triangle with
constant area varies inversely as the height.
When the base is 18 cm long, the height is 7
cm. Find the length of the base when the
height is 6 cm.
Answers
The length of the base when the height is 6 cm is 21 cm .
In the question ,
it is given that ,
the length of the base(b) of the triangle varies inversely with the height(h) ,
which is represented as
b ∝ 1/h
b = k/h
where k is the constant of variation
given that when b = 18 , h is = 7
18 = k/7
k = 18 × 7
k = 126
Substituting , the value of k = 126 in the equation b = k/h ,
we get ,
b = 126/h
So, the length of the Base When h = 6,
b = 126/6
b = 21
Therefore, the length of the base when the height is 6 cm is 21 cm .
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If B=x^{2}+ 2 and C=2+2x^{2}find an expression that equals 2B+C in standard form.
Answers
The expression that equals 2B+C in standard form is 4x² + 6
How to determine the expression?From the question, we have the following parameters that can be used in our computation:
B = x² + 2
C = 2 + 2x²
The expression to calculate is given as
2B + C
Substitute the known values in the above equation, so, we have the following representation
2B + C = 2x² + 4 + 2 + 2x²
Evaluate the like terms
2B + C = 4x² + 6
Hence, the expression is 4x² + 6
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each face of a cube is given a single narrow stripe painted from the center of one edge to the center of the opposite edge. the choice of the edge pairing is made at random and independently for each face. what is the probability that there is a continuous stripe encircling the cube?
Answers
The probability that there is a continuous stripe encircling the cube is 3/16.
A single, thin stripe is painted from the center of one edge to the center of the other edge on each face of a cube. Each face's edge pairing is selected independently and at random.
For each of the cube's six faces, there are two possible stripe orientations, resulting in a total of 2 x 6 = 64 possible stripe permutations. Since there are three sets of parallel faces, the stripe orientation for the remaining faces is determined uniquely by the pair of faces that does not contribute to the encircling stripe. Additionally, there are two possible orientations for the stripe on each face that is non-contributing.
A continuous stripe surrounds the cube as a consequence of a total of
3 * 2 * 2 = 12 stripe variations.
The necessary probability is 12/64, which equals 3/16.
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help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Dimensions of the area enclosed is 800 * 800 and the maximum area = 6,40,000 square yards.
Given:
Liana has 3200 yards of fencing to enclose a rectangular area.
Let l and b be the length and width.
we know that:
perimeter of rectangle = 2(l+b)
2l + 2b = 3200
l+b = 1600
b = 1600 - l
Area of rectangle A = lb
= l*1600-l
= 1600 l - l^2
Apply derivative:
dA/dl = 1600 - 2l
1600 - 2l = 0
1600 = 2l
l = 1600/2
l = 800
l+b = 1600
b = 1600 - 800
= 800
Area = 800*800
= 6,40,000
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together, katya and mimi have 480 pennies in their piggy banks. after katya loses 1/2 and mimi losses 2/3of her pennies, they have an equal number of pennies left. how many pennies did they lose altogether?
Answers
The number of pennies they lose altogether is 288 pennies.
How to find the number of pennies they lost together?
Together, Katya and Mimi have 480 pennies in their piggy banks.
Therefore, there total amount of pennies is 480.
After Katya loses 1/2 of her pennies and Mimi loses 2/3 of her pennies, they have an equal number of pennies left.
Therefore,
let
x = number of pennies Katya have
y = number of pennies Mimi have
Hence,
x + y = 480
x = 480
Katya pennies left = x - 1 / 2x = 1 / 2x
Mimi pennies left = y - 2 / 3 y = 1 / 3 y
1 / 2 x = 1 / 3 y
2y = 3x
y = 3 / 2 x
Substitute the value in equation(i)
x + 3 / 2 x = 480
2.5x = 480
x = 480 / 2.5
x = 192
Therefore,
192 + y = 480
y = 480 - 192
y = 288
The number of pennies they lose can be calculated as follows;
Katya losses = 1 / 2 × 192 = 96
Mimi losses = 2 / 3 × 288 = 192
Therefore, they lost 96 + 192 = 288 pennies altogether.
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Andrew owns stock in Hyren Airlines and as a result gets paid dividends worth $539.70 every year. If Andrew owns 105 shares of Hyren Airlines, how big is the dividend each share yields?
Answers
Answer: $5.14
Step-by-step explanation:
divide $539.70 by 105 to get the answer
so 539.70 divide by 105 is 5.14
step1 get rid of the decimal but you will ad it later so
53970
/ 105
=514
step2 move the decimal 2 places to the left.
Noble-gas notation: [ar]3s1 [he]2s22p63s1 [ne]3s23p4 [ne]3s1
Answers
In longhand notation, the electron configuration is
1s² 2s² 2p6 3s¹
Noble gas configuration
[ Ne ] 3s¹
Complete question:
Choose the electron configuration for sodium (Na) in both longhand notation and noble-gas notation.
What is electron configuration?
The arrangement of electrons in atomic or molecular orbitals of an atom, molecule, or other physical structure is referred to as the electron configuration in atomic physics and quantum chemistry.
In longhand notation, the electron configuration is
1s² 2s² 2p^6 3s¹
Noble gas configuration
[ Ne ] 3s¹
Here, the configuration 1s² 2s² 2p^6 is replaced by [ Ne ].
[ Ne ] represents the electron configuration of [ Ne ].
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Answer:
D) [Ne]3s1
☆
EDGE2023; Good Luck :D!!!
Decide whether each equation is true for all, one, or no values of x.
Answers
Answer:
Theres nothing to see?
Step-by-step explanation:
Answer:
First is one value of x
Second is no values of x
Third is all values of x
Step-by-step explanation:
Please give brainliest!
Little Johnny spent $240 on candy today. If his amount is 2/5 the amount of money his dad gave him, how much did his dad give him orginally
Answers
Answer: 600$
Step-by-step explanation:
2/5 of 600 is 240
19)
By which rule are these triangles congruent?
A)aas
B)asa
C)sas
D) SSS
Answers
Step-by-step explanation:
Angel side angle rule (ASA)
Geometry pls help me
Answers
The radius of the given circle is 7.5 units.
What is the radius?A circle or sphere's radius is any line segment that connects the object's center to its perimeter in classical geometry; in more contemporary usage, it also refers to the length of such line segments. The word "radius" is derived from Latin and means "ray" as well as "the spoke of a chariot wheel."The diameter of a circle cuts through the center while the radius extends from the center to the edges of the circle. The diameter of a circle effectively divides the shape in half.So, use the Pythagorean theorem:
Where, c² = a² + b².We know that, AB² = AC² + CB².Now, calculate as follows:
AB² = AC² + CB²AB² = 12² + 9²AB² = 144 + 81AB² = 225AB = √225AB = 15
So, the diameter is 15 units.
Then the radius is:
15/2 = 7.5 unitsTherefore, the radius of the given circle is 7.5 units.
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Fill in the blanks below in order to justify whether or not the mapping shown
represents a function.
Set A
Submit Answer
+
2
Ń
9.
The mapping diagram above
where there
Set B
5
C
a function since
C
in
attempt 1 out of 2
Answers
A construction crew needs to pave a road that is 209 miles long. The crew paves 8 miles of the road each day. The length, L (in miles), that is left to be paved after d days is given by the following function.
L(d)=209-8d
Question a.)
If 154 miles of the road is left to be paved, how many days has the crew been paving the road?
Question b.)
How many miles of the road does the crew have left to pave after 13 days?
Answers
Answer:
a) 6 7/8 days
b) 105 miles
Step-by-step explanation:
Given that L(d) = 209 -8d miles of road remain to be paved after d days, you want to know (a) the number of days paving if 154 miles remain, and (b) remaining miles after 13 days.
a) Paving daysWe want to find d such that L(d) = 154.
L(d) = 154
209 -8d = 154 . . . . . . substitute for L(d)
209 -154 = 8d . . . . . add 8d-154
55/8 = d = 6 7/8 . . . divide by 8
The crew has been paving for 6 7/8 days if 154 miles remain.
b) Remaining milesAfter 13 days, the remaining miles will be ...
L(13) = 209 -8·13 = 209 -104
L(13) = 105
After 13 days, the crew has 105 miles left to pave.
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in a certain industrial facility, accidents occur infrequently. it is known that the probability of an accident on any given day is 0.005 and accidents are independent of each other. what is the probability that in any given period of 400 days there will be an accident on one day? use binomial approximation to poisson distribution.
Answers
The probability that in any given period of 400 days there will be an accident on one day is 0.2707
Given that;
In a certain industrial facility, accidents occur infrequently. it is known that the probability of an accident on any given day is 0.005 and accidents are independent of each other.
n = 400, p = 0.005
Poisson distribution is given by;
e P(x) = (λˣe^λ ) / x!
Here, Mean(λ) = np
= 400*0.005
=2
The probability that there will be an accident on one day;
(P(x = 1)) = (λxe-λ)/x!
= 2*e-2
= 0.2707
The probability that in any given period of 400 days there will be an accident on one day is 0.2707
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What is the area of a triangle if the vertices are at
A(-11, 4)
B(-7, 8)
C(-4, 4)
Answers
Answer:
14 square units
Step-by-step explanation:
You want the area of the triangle whose vertices are the points A(-11, 4), B(-7, 8), C(-4, 4).
Area formulaThe area of a triangle is given by the formula ...
A = 1/2bh
where b is the base of the triangle, and h is the height, the1 perpendicular distance to the opposite vertex.
DimensionsThe diagram shows one side is the horizontal line AC. The length of that is the difference of the x-coordinates of the end points:
b = -4 -(-11) = 7
The opposite vertex, B, has a y-coordinate of 8, so the height of the triangle is ...
h = 8 -4 = 4
ApplicationWe now have the information we need to use the area formula:
A = 1/2(7)(4) = 14 . . . . square units
The area of ∆ABC is 14 square units.
__
Additional comment
You can use the diagram and count grid squares to find the dimensions of the triangle.
nikolai and teresa are trying to decide which restaurant they should take their friend thomas to for his birthday. nikolai wants to take thomas to a vietnamese restaurant (which serves generous portions of inexpensive but delicious food), and teresa wants to take thomas to a french restaurant (which serves expensive and beautifully presented food). to resolve the issue, they decide to flip a coin. if nikolai wins the coin toss they will take thomas to the vietnamese restaurant and the next time a friend of theirs has a birthday they will take her or him to the french restaurant teresa likes. if teresa wins the coin toss, they will go to the french restaurant first and the vietnamese restaurant later. the conflict style they used is best described as:
Answers
The conflict style they used is Collaboration.
Given, that Nikolai wants to take Thomas to a Vietnamese Restaurant (which serves generous portions of inexpensive but delicious food), and Teresa wants to take Thomas to a French restaurant (which serves expensive and beautifully presented food)
To resolve the issue, they decide to flip a coin.
If Nikolai wins the coin toss they will take Thomas to the Vietnamese restaurant and the next time a friend of theirs has a birthday they will take her or him to the French restaurant Teresa likes and If Teresa wins the coin toss, they will go to the French restaurant first and the Vietnamese restaurant later.
Here, we can see that this is a win-win situation as both can go to their favorite restaurant.
So, the conflict style they used is Collaboration. As, Collaboration generates solutions that satisfy both the parties’ needs.
Hence, the conflict style they used is Collaboration.
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Hershey’s Chocolate World is located in Hershey, PA. The cost, , for any large chocolate bars is per bar, . Write a rule to represent this relationship.
. Hershey’s Chocolate World is located in Hershey, PA. The cost, c, for any large chocolate bars is $ 2.25 per bar, b. Write a rule to represent this relationship.
Answers
The equation to represent the expression is C ( b ) = 2.25b , where C ( b ) is the cost of b number of chocolate bars
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the cost of b chocolate bars be = C
Let the cost of 1 bar of chocolate bar be = $ 2.25
Let the number of chocolate bar be = b
Now , the equation to find the cost of b number of chocolate bars is ,
The cost of b number of chocolate bar =
cost of 1 bar of chocolate bar x number of chocolate bar
So , the equation is
The cost of b number of chocolate bar = 2.25b
So , the equation to find the cost of b number of chocolate bars is ,
Cost of b chocolate bars C = cost of b number of chocolate bar
C ( b ) = 2.25b
Therefore , the expression is C ( b ) = 2.25b
Hence , The equation to represent the expression is C ( b ) = 2.25b , where C ( b ) is the cost of b number of chocolate bars
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The function f(x) = x2 is graphed above. Which of the graphs below represents the function g(x) = x2 + 3 ?
Answers
Using a translation, the graph of the function f(x) = x² + 3 is given by the image at the end of the answer.
What is a translation?Among the many transformations that a function or a figure can undergo is a translation, and other examples are reflections, rotations and dilation.
The difference of a translation from these other transformations is that the only thing that changes for the function is the position. The inclination, orientation and length all remains constant.
The four possible types of a translation are given as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.The parent function in this problem is given as follows:
f(x) = x².
Which has the U format of a parabola and a vertex at the origin (3,3).
The translated function is given as follows:
g(x) = x² + 3.
The addition by 3 means that the function was translated up 3 units, as shown in the image given at the end of the answer.
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You have 7,160 grams of a radioactive kind of bismuth. How much will be left after 10 days if
its half-life is 5 days?
grams
Answers
The solution is 1790 grams
The amount of bismuth left after 10 days if the half life is 5 days will be
1790 grams
What is half-life of an element?
The half-life of a radioactive isotope is the amount of time it takes for one-half of the radioactive isotope to decay. The half-life of a specific radioactive isotope is constant; it is unaffected by conditions and is independent of the initial amount of that isotope.
Half-life (symbol t½) is the time required for a quantity (of substance) to reduce to half of its initial value
The decay constant λ is = 0.693/t½
where t½ is the half-life of the element
Given data ,
Let the half life of the element be represented as t½
The value of t½ = 5 days
Now , the initial amount of bismuth N₀ = 7160 grams
The number of days t = 10 days
The amount of bismuth left after 10 days = N( t )
Now , the value of N( t ) is given by the formula ,
N( t ) = N₀ ( 1/2 )^ t/ t½
Substituting the values in the equation , we get
N( t ) = 7160 ( 1/2 )^10/5
N( t ) = 7160 ( 1/2 )²
N( t ) = 7160 / 4
N( t ) = 1790 grams
Therefore , the value of N( t ) is 1790 grams
Hence , the amount of bismuth left is 1790 grams
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Match the following definitions with the correct term.
Answers
Answer:
that's biology but
Step-by-step explanation:
autotrophs make their owner food
heterotrophs can't make their own food
photosynthesis is the 3rd one
photosynthesis happens in the chloroplast
photosynthesis makes glucose
I can go in depth about any of these, ask me if needed
Pls solve all the question as per the questions given below
Answers
1a) The additional information required using SAS Congruency postulate is; ∠AOB ≅ ∠BOD
1b) The additional information required using ASA Congruency postulate is BC ≅ QR
2a) The symbolic form of the congruent triangles is written as;
ΔABC ≅ ΔADC
2b) The congruence rule used is SAS Congruency postulate.
How to use congruency postulates?1a) We want to prove that the triangles are congruent by SAS Congruency postulate. SAS congruency postulate means Side - Angle - Side. Thus, the additional information is;
∠AOB ≅ ∠BOD
1b) We want to prove that triangle ABC is congruent to triangle PQR by ASA Congruency. We have that;
∠Q = ∠B and ∠R = ∠C. Thus;
The additional information is BC ≅ QR
2a) The symbolic form of the congruent triangles is written as;
ΔABC ≅ ΔADC
2b) The congruence rule used here is SAS Congruency postulate.
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