It is normal for some newborn babies to lose weight in their first week of life. At one week old, Jenny's weight is 6.8 pounds. That is 3.7% lighter than she was at birth. What was the baby's birth weight?
Round your answer to the nearest tenth.
Based on the information, it can be inferred that the baby weighed 7.06 pounds at birth.
How to calculate how much the baby weighed at birth?To calculate how much the baby weighed at birth we must take into account the information we have available
Current Weight: 6.8 lbs.
% lost: 3.7%
According to the above, we must calculate what percentage the current weight is equal to:
100% - 3.7% = 96.3%
Now we must make a rule of three to find the weight of the baby at birth:
96.3 - 6.8
100 - ?
100% * 6.8 pounds / 96.3% = 7.06 pounds
According to the above, the baby was born thinking 7.06 pounds, that is, she lost 0.26 pounds.
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Find the exact length of the midsegment of the trapezoid with the vertices S(-2, 4), T(-2,-4), U(3,-2), V(13,10)
The exact length of the midsegment of the trapezoid is √29 units.
What is Distance?The length along a line or line segment between two points on the line or line segment.
Distance=√(x₂-x₁)²+(y₂-y₁)²
The midsegment of a trapezoid is the line segment that connects the midpoints of the two non-parallel sides. Let's first find the midpoints of the sides SU and TV.
The midpoint of SU can be found as:
((Sx + Ux)/2, (Sy + Uy)/2) = ((-2 + 3)/2, (4 - 2)/2) = (1/2, 1)
Similarly, the midpoint of TV can be found as:
((Tx + Vx)/2, (Ty + Vy)/2) = ((-2 + 13)/2, (-4 + 10)/2) = (5.5, 3)
Now we can find the length of the midsegment that connects these two midpoints.
Distance=√(x₂-x₁)²+(y₂-y₁)²
So the length of the midsegment is:
d = √(5.5 -0.5)²+ (3 - 1)²)
= √25 + 4= = √29
Therefore, the exact length of the midsegment of the trapezoid is √29 units.
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What is the compound interest on a $10,000 investment that earns 6% compounded monthly for 5 years?
Answer:
$13,488.50
Step-by-step explanation:
annual rate 6%
so every month = 6/12 = 0.5%
compounding monthly so every month the money grows at (1+0.5%)
for 5 years, it's 60 months
10,000 * (1+0.5%)^60 = $13,488.50
What is the perimeter? Step by step.
Answer: 36
Step-by-step explanation:
to find the length, find the hypotenuse of a triangle formed by the x-axis and the distance the parallelogram is from the x-axis.
hypotenuse= [tex]a^{2}+b^{2} =c^{2}[/tex]
the distance from -6 to -3 is 3 units
the distance from 0 to 4 is 4 units
[tex]3^{2} +4^{2} =9+16=25[/tex]
then [tex]\sqrt{25} =5[/tex]
therefore the length of the parallelogram is 5 units
repeat on other side
the distance from -3 and 9 is 12 units
the distance from 0 and 5 is 5 units
[tex]12^{2} +5^{2} =144+25=169[/tex]
then [tex]\sqrt{169} =13[/tex]
therefore the width of the parallelogram is 13 units
now to find the perimeter add all side lengths of the given shape
since parallelograms have equal lengths and widths add 13+13+5+5
therefore the perimeter of the parallelogram is 36
A model rocket is launched with an initial upward velocity of 50m / s The rocket's height (meters) after seconds is given by the following h = 50t - 5t ^ 2
The complete question
A model rocket is launched with an initial upward velocity of 50m/s. The rocket's height h (in meters) after t seconds is given by the following. h=50t-5t².
Find all values of t for which the rockets height is 20 meters.
The values of t for which the rockets height is 20 meter are, (10 + 2√21) / 2 and (10 - 2√21) / 2
What is velocity ?Velocity is a vector quantity that represents the rate of change of an object's position. It is defined as the derivative of the position vector with respect to time and has units of meters per second (m/s). Velocity includes both speed and direction, and is an important concept in physics and engineering.
We can find the values of t for which the rocket's height is 20 meters by setting h equal to 20 and solving for t.
h = 50t - 5t² = 20
Expanding the equation, we have:
50t - 5t² = 20
Adding 5t² to both sides:
50t = 20 + 5t²
Dividing by 5 both the sides,
10t = 4 + t²
t² - 10t + 4 = 0
t = (10 + 2√21) / 2
and t = (10 - 2√21) / 2
So the values of t for which the rocket's height is 20 meters are
(10 + 2√21) / 2 and (10 - 2√21) / 2
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The student population at the local high school is 1,375 and is decreasing by 2% each year. what will the student population be after 7 years?
I REQUEST HELP! PLS HELP ME W THIS Q!!! WILL GIVE BRAINLIEST!
Answer:
[tex]x\geq 5\\x > 4\\[/tex]
Answer:
x ≥ 5
x > 4
x < 6
Step-by-step explanation:
The inequalities for which 5 is the lowest integer value that x could take are:
x is greater than or equal to 5. (Since x can be 5 in this case.)x > 4. (Since 5 is the lowest integer value for x, and 5 is not greater than 4, x must be greater than 4.)x is less than 6. (Since 5 is less than 6, and x is the lowest integer value that is less than 6, x must satisfy this inequality.)Therefore, the correct options are:
x is greater than or equal to 5.
x > 4.
x is less than 6.
wen and five friends equally share 1/3 of a pan of snack bars. which expression shows how much of the pan each person gets?
The solution is, 1/3 ÷ 6, expression shows how much of the pan each person gets.
What is division?Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
wen and five friends equally share 1/3 of a pan of snack bars.
so, we get,
the expression is 1/3 ÷ 6
This is because there are 6 friends in all and you are splitting 1/3 of the pan snack bars to each of them.
So, what your splitting/cutting/dividing would be the dividend (1/3) and then the friends would be the divisor (6)
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help its due tmr please
On evaluating, the function f(x) and g(x) the values of f(g(3)) = - 11 and f(g(x)) = -35x + 22.
Evaluating functions:A relation between a collection of inputs and outputs is known as a function. A function is an association between inputs in which each input is connected to approximately one output. To find f(a) for a given function f(x) we simply substitute 'a' instead of 'x' in the given function f(x).
Here we have
f(x) = 7x - 5 and g(x) = - 5x + 4
10. f(g(3))
To find g(3) take x = 3 in g(x)
=> g(3) = - 5(3) + 4 = - 15 + 4 = 11
=> g(3) = - 11
To find f(g(3)) take x = g(x) = - 11 in f(x)
f(g(3)) = 7(-11) - 5 = - 77 - 5 = - 82
∴ The value of f(g(3)) = - 11
11. f(g(x)
To find f(g(x)) take x = g(x)
=> f(g(x) = 7(-5x + 4) - 5
=> f(g(x)) = -35x + 28 - 5
=> f(g(x)) = -35x + 22
∴ f(g(x)) = -35x + 22
Therefore,
On evaluating, the function f(x) and g(x) the values of f(g(3)) = - 11 and f(g(x)) = -35x + 22.
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Select all that apply Which of the following is true regarding the application of Chebyshev's theorem and the Empirical Rule? Check all that apply. Chebyshev's theorem applies to any set of values. Chebyshev's theorem works for symmetrical, bell-shaped distributions. Both work for skewed distributions. ClChebyshev's theorem applies only to symmetrical, bell-shaped distributions
Ther statement that is true regarding the application of Chebyshev's theorem and the Empirical Rule is B.Chebyshev's theorem works for symmetrical, bell-shaped distributions.
What is Chebyshev's theorem and the Empirical Rule?The Empirical Rule is an approximation that only works with data sets that have a relative frequency histogram with a bell-shaped distribution. The percentage of measurements that fall within one, two, and three standard deviations of the mean is estimated.
It is true that Chebyshev's Theorem holds true for all conceivable data sets. Both do not require a sample standard deviation for the data.
Therefore, option B is correct.
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A video game system and several games are sold for $612. The cost of the games is
times as much as the cost of the system. Find the cost of the
system and the cost of the games.
Cost of the video game system:
Cost of the games:
URGENT PLEASE HELP.
finish this sentence to make it true: the maximum number of times you can overload a method in a class definition...
overload it by doing it again and again.
The table shows the distance that Rachel jogged last weekend. How much farther did Rachel jog on Sunday than on Saturday?
The number of miles further that Rachel was able to jog on Sunday more than Saturday was 10 miles.
How to find the distance ?On Saturday, the table shows that Rachel jogged a total of 15 miles. On Sunday, Rachel was able to jog 25 miles.
This means that Rachel was able to jog more miles on Sunday than she was able to jog on Saturday. The difference in the miles was :
= Miles jogged on Sunday - Miles jogged on Saturday
= 25 - 15
= 10 miles
In conclusion Rachel jogged 10 miles more on Sunday than Saturday.
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A wire 14 cm long is cut into two pieces. The longer piece is 4 cm longer than the shorter piece. Find the length of the shorter piece of wire
Answer:
5cm
Step-by-step explanation:
Let x represent the shorter wireif the shorter wire = x
therefore the longer wire = x+4
Write an equation[tex] x + x + 4 = 14[/tex]
Subtract 4 from both sides
[tex]x + x + 4 - 4 = 14 - 4[/tex]
[tex]x + x = 10[/tex]
[tex]2x = 10[/tex]
Divide both sides by 2
[tex] \frac{2x}{2} = \frac{10}{2} [/tex]
[tex]x = 5[/tex]
A chemist has three different acid solutionsThe first acid solution contains 25% acid, the second contains 45\% and the third contains 65%. He wants to use three solutions to obtain a mixture of 224 liters containing 35% acid, using 3 times as much of the 65% solution as the 45% solution. How many liters of each solution should be used?
The chemist should use __ liters of 25% solution, ___ liters of 45% solution, and ____ liters of 65% solution
Answer:
160 L of 25%16 L of 45%48 L of 65%Step-by-step explanation:
You want the number of liters of 25%, 45%, and 65% acid solution required to make a mixture that is 224 L of a 35% acid solution, using 3 times as much of the 65% solution as of the 45% solution.
SetupThere are numerous ways this mixing problem can be formulated. The calculator display in the attachment shows one of them: 3 equations in 3 unknowns.
Here, we choose to use one variable. Let x represent the amount of 45% solution. Then 3x is the amount of 65% solution, and (224 -4x) is the amount of 25% solution. The amount of acid in the final mix is ...
0.25(224 -4x) + 0.45x + 0.65(3x) = 0.35·224
SolutionThe equation can be simplified to ...
1.4x +56 = 78.4
1.4x = 22.4
x = 16 . . . . . . . . . liters of 45% solution
3x = 48 . . . . . . . . liters of 65% solution
224 -4x = 224 -64 = 160 . . . . liters of 25% solution
The chemist should use ...
160 L of 25%16 L of 45%48 L of 65%<95141404393>
Jane mixes the juice in jug A with the water in jug B.
What is the capacity of her mixture in litres?
Jug A
millilitres
-1000
-900
-800
-700
-600
عاااالسالسا
-500
-400
-300
-200
-100
Jug B
Litres
The capacity of her mixture in liters is 1.6 L
What is capacity?Capacity describes your ability to do something or the amount something can hold.
Given that, Jane mixes the juice in jug A with the water in jug B, we need to find that, what is the capacity of her mixture in liters,
We know that,
1 L = 1000 ml
Jug A = 400 × 1L / 1000 ml = 0.4 L
Jug B = 12 / 10 L = 1.2 L
Total = 0.4 + 1.2 = 1.6 L
Hence, the capacity of her mixture in liters is 1.6 L
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13) A cutlery manufacturer packs 200 teaspoon into boxes holding either 4 spoons or six spoons.there are 48 full boxes.
are 48 full boxes,
a) If there are a four-spoon boxes and y six spoons boxes use the information to find two equations relating to x and y
relating x and y.
b) How many boxes hold four spoons
Answer:
Step-by-step explanation:
890
brainest if correct!!
To the nearest hundredth, what is the length of linesegmentAB?
Answer: 5.83 units. please give brainliest
Step-by-step explanation: Using the distance formula, we can find the distance between the two points A(1, -5) and B(-4, -2):
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
d = sqrt((-4 - 1)^2 + (-2 - (-5))^2)
d = sqrt((-5)^2 + 3^2)
d = sqrt(25 + 9)
d = sqrt(34)
To the nearest hundredth, the length of line segment AB is approximately 5.83 units.
6 times of the age of a daughter is the age of her mother. If the difference of their ages be 35years find the age of the mother.
Answer:
the age of her mother is 35 yrs old
Step-by-step explanation:
Let the age of daughter be x and mother be 6x
Now,
By question
6x -x=35
or, 5x =35
or,x=35/5
or x =5
Lastly,
age of daughter=x=5
age of mother =6x
=6*5
=35
If I have a car that can move at a speed of 6 km/h
and the distance from Talas to Bishkek is 2 km,
how long will the car drive? (in minutes)
Answer: 20 minutes
Step-by-step explanation:
Employee Salaries Employee Salary [before raise] Raise Jane $41,400 4% John $44,000 4.5% Jack $39,400 3% What is the total of all three raises?
need answer
Answer:
The total of all three raises is $1,890. Jane's raise is $1,660 (4% of $41,400), John's raise is $1,980 (4.5% of $44,000), and Jack's raise is $1,250 (3% of $39,400).
Taxi company a charges 4$ plus 0.5x per mile and taxi company b charges 5 $ plus 0.25x per mile
Graph it do they intersect?
The graphs of the linear equations will intercept at the point (4, 6)
Do the graphs intercept?We know that taxy company a charges $4 plus $0.5 per mile, so the cost for x miles is:
A = 4 + 0.5x
While taxy company be charges $5 plus $0.25 per mile, so the cost for x miles will be:
B = 5 + 0.25x
The graphs will intersect at the x value such that the two linear equations are equal:
A = B
This happens when:
4 + 0.5x = 5 + 0.25x
0.5x - 0.25x = 5 - 4
0.25x = 1
x = 1/0.25 = 4
And the cost is:
B = 5 + 0.25*4 = 6
So the graphs intercept at the point (4, 6)
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You are playing a solitaire game in which you are dealt three cards without replacement from a simplified deck of 10 cards (marked 1 through 10). You win if one of your cards is a 10 or if all of your cards are odd. How many winning hands are there?
The total number of winning hands are 276.
What is the probability?Probability is defined as the ratio of favorable outcomes to all other possible outcomes of an event. The symbol x can be used to express the quantity of successful outcomes for an experiment with 'n' outcomes. The probability of an event can be calculated using the following formula.
Probability of an event = Number of favourable outcomes/Total number of outcomes = x/n.
In the given question,
If the first card drawn is a 10, then there are
[tex]P_9^2=\frac{9!}{(9-2)!} =9*8=72 hands[/tex]
There are 9 possible numbers if the second card is a 10, and there are 8 possible numbers if the third card, giving us,
[tex]9*8= 72 hands[/tex]
If the third card is 10 then there are 9 possible numbers for the first card and 8 possible numbers for
second card, it gives us
[tex]9*8= 72 hands[/tex]
And there are 5 odd cards, and it gives us:
[tex]P_5^3=\frac{5!}{(5-3)!} =5*4*3=60 hands[/tex]
So, we have that in total we have
72+72+72+60=276 winning hands.
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Two identical rectangular prisms and two identical cubes are joined.
Answer the questions to find the new solid’s surface area.
The new solid's surface area, which is 490 cm², is created by combining two identical cubes, each of which has a surface area of 294 cm².
What is the Total Surface Area of a Cube?The total area of a cube's faces that cover it is the surface area of the object. The cube's surface area is calculated as six times the square of its side lengths. 6a², where an is the cube's side length, serves as its representation. In essence, it is the overall surface area.
Total surface area of a cube = 6a², where a is the length of each of the sides.
Let the surface area of each identical cube = 294 cm²
The length of each side be
6a² = 294
simplifying the above equation, we get
a² = 294/6
a² = 49
a = √49
a = 7 cm
Surface area of the new solid
= surface area of the two identical cubes - 2(area of the surface where both are joined)
Surface area of the new solid = 2(294) - 2(7²) = 490 cm²
Therefore, the surface area of the new solid be 490 cm².
The complete question is;
Two identical rectangular prisms and two identical cubes are joined. Answer the questions to find the new solid’s surface area. The numbers are 9 and 4.
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In a certain molecule, atom X is bonded to H. The force of attraction for X’s nucleus on the shared valence electron is 2.2 x 10-8 N. If the radius of atom X is 1.02 x 10-10 m, predict the number of protons in X’s nucleus. Predict the identity of atom X. Show your set-up.
An atom X has 3 protons in its nucleus. An atomic number of 3 corresponds to the element lithium (Li).
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.
We can use Coulomb's law to predict the number of protons in X's nucleus. Coulomb's law states that the force of attraction between two charges is proportional to the product of the charges and inversely proportional to the square of the distance between them.
⇒ F = k (q₁ q₂) / r²
Where, F is the force of attraction, k is the Coulomb constant (8.99 x 10⁹ Nm²/C²), q₁ and q₂ are the magnitudes of the charges, and r is the distance between them.
We can rearrange the equation to solve for the charge:
⇒ q₂ = (F * r²) / (k * q₁)
In this case, q1 is the charge on the electron, which is -1.60 x 10⁻¹⁹ C. The radius of atom X, r, is given, and the force of attraction, F, is also given.
So, we have:
⇒ q₂ = (2.2 x 10⁻⁸ N * (1.02 x 10⁻¹⁰ m)²) / (8.99 x 10⁹ Nm²/C^2 * -1.60 x 10⁻¹⁹ C)
Solving for q₂, we find that;
q₂ = +5.4 x 10⁻¹⁹ C.
This is the charge on the nucleus of atom X. The number of protons in the nucleus of atom X can be found by dividing the charge by the charge of a proton:
⇒ N = q₂ / qp
Where N is the number of protons and qp is the charge on a proton, which is +1.60 x 10⁻¹⁹ C.
So, we have:
N = (5.4 x 10⁻¹⁹ C) / (1.60 x 10⁻¹⁹ C) = 3.375
Hence, the number of protons must be a whole number, the closest whole number to 3.375 is 3. This means that atom X has 3 protons in its nucleus. The identity of atom X can be determined based on its atomic number, which is equal to the number of protons in its nucleus. An atomic number of 3 corresponds to the element lithium (Li).
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you are given the following information about a population:• There are two alleles: C and c.• C codes for green hair and c codes for white hair.• C is dominant over c.• The frequency of the c allele is 0.3.• The population is comprised of 100 individuals.Assuming the population is in Hardy-Weinberg equilibrium, how many individuals have green hair?
In this population of 100 individuals, approximately 49 individuals will have green hair due to the dominant allele CC and approximately 42 individuals will have green hair due to the dominant allele Cc. The total number of individuals with green hair is 49 + 42 = 91.
What is the quadratic equation?
A quadratic equation in one variable is a mathematical sentence of degree 2 that can be written in the following standard form. a+ bx + c = 0, where a, b, and c are real numbers and a 0.
The Hardy-Weinberg equilibrium is an idealized model of a population that assumes that the frequency of alleles remains constant from generation to generation in the absence of external forces.
According to this model, the frequency of a particular genotype can be calculated using the following formula:
p² + 2pq + q² = 1
where p is the frequency of the dominant allele (C) and q is the frequency of the recessive allele (c). In this case, p = 1 - q = 1 - 0.3 = 0.7, and q = 0.3.
The frequency of individuals with the genotype CC (green hair) is given by p², or 0.7² = 0.49.
The frequency of individuals with the genotype Cc (green hair) is given by 2pq, or 2 * 0.7 * 0.3 = 0.42.
Hence, in this population of 100 individuals, approximately 49 individuals will have green hair due to the dominant allele CC and approximately 42 individuals will have green hair due to the dominant allele Cc. The total number of individuals with green hair is 49 + 42 = 91.
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Lainey is sliding down a water slide that is 336 feet long at a rate of 48 feet per second. How long will it take Lainey to travel from the top to the bottom of the slide?
A.
-288 seconds
B.
288 seconds
C.
7 seconds
It will it take Lainey 7 seconds to travel from the top to the bottom of the slide. Option C
How to calculate the speed from the top to the bottom of the slide
Using the formula for calculating speed
The formula for Speed is given as [Speed = Distance ÷ Time].
To calculate the time, the speed formula can be molded as:
Time = Distance ÷ Speed].
Given Distance = 336 feet
Given speed = 48 feet per second
Time = Distance ÷ Speed
= 336 ÷ 48 = 7 seconds
Hence, the time it will take Lainey to travel from the top to the bottom of the slide is 7 seconds
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(- 6, 8) and (- 8, 2)
Answer:
Step-by-step explanation:
m= 3
Given
�
(
�
)
=
�
3
+
�
�
−
4
f(x)=x
3
+kx−4, and the remainder when
�
(
�
)
f(x) is divided by
�
−
3
x−3 is
5
5, then what is the value of
�
k?
Answer:
Step-by-step explanation:
Given
Mr B aged 52 years, has earned rupees 75,00,000 out of his business. His ex- wife gifted him cash in account worth rupees 6 lakh. He spent a total of rupees 15 lakh during a family trip. He won a lottery of 19 lakh rupees. Out of happiness he gifted his wife cash of rupees 450000. He bought a life insurance policy and paid a premium of 50000 annually. He paid tuition fee for his daughter for rupees 50000. He invested rupees 80000 in PPF. One of his existing life insurance policy got matured and he received a total of rupees 32 lakh. Seeing his health conditions the doctor adviced him a medical test of rupees 6000 following he bought a health insurance for rupees 27000. Calculate his taxable income and tax liability
The taxable income of the family is 1,15,37,000, the tax liability is given as 34,61,100.
How to solve for the taxable incomeMr. B's taxable income calculation:
Income from Business: 75,00,000
Gift received: 6,00,000
Lottery winnings: 19,00,000
Maturity amount of life insurance: 32,00,000
Total Income: 1,32,00,000
Expenditures:
Family trip: 15,00,000
Gift to wife: 4,50,000
Life insurance premium: 50,000
Tuition fee: 50,000
PPF investment: 80,000
Medical test fee: 6,000
Health insurance premium: 27,000
Total Expenditures: 16,63,000
Taxable Income: 1,15,37,000 (Total Income - Total Expenditures)
Tax liability calculation:
Taxable Income Tax Rate Up to (in Rupees)
2.5 Lakhs NIL
2.5 Lakhs to 5 Lakhs 5% (12,500)
5 Lakhs to 7.5 Lakhs 10% (25,000)
7.5 Lakhs to 10 Lakhs 15% (37,500)
10 Lakhs to 12.5 Lakhs 20% (50,000)
12.5 Lakhs to 15 Lakhs 25% (62,500)
Above 15 Lakhs 30%
In this case, Mr. B's taxable income is 1,15,37,000, which falls in the tax bracket of above 15 Lakhs, so his tax liability would be 30% of 1,15,37,000 = 34,61,100.
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