In pigs, the length of pregnancies varies according to a Normal distribution with mean 114 days and standard deviation 5 days, approximately 2.28% of pig pregnancies are longer than 124 days.
We can start by standardizing the value 124 using the formula:
z = (x - μ) / σ
where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.
So in this case:
z = (124 - 114) / 5 = 2
Using a standard normal distribution table or calculator, we can find that the proportion of values greater than 2 is approximately 0.0228.
Therefore, approximately 2.28% of pig pregnancies are longer than 124 days.
For more details regarding standard deviation, visit:
https://brainly.com/question/23907081
#SPJ1
●
• What pattern can you use to describe how the
numerator and denominator change in the fraction
models above?
we can say that the pattern for how the numerator and denominator change in the fractions model is that they are multiplied or divided by the same non-zero integer.
How is this so ?Let's consider the fraction 2/ 3.
If we multiply both the numerator & the denominator by 2, we get 4 /6.
Also multiplying both by 3, we will get 6 /9
In general, if we multiply the numerator and the denominator by the same non-zero integer, we get an equivalent fraction.
On the other hand, if we divide both the numerator and the denominator by the same non-zero integer,
we also get an equivalent fraction. For example if we divide 6/9 by 3, we get 2/3 again.
Hence , the above conclusion is correct.
Learn mor about fractions;
https://brainly.com/question/10354322
#SPJ1
Full Question:
Fraction 2/ 3.
What pattern can you use to describe how the numerator and denominator change in the fraction models above?
Use grid paper to find the median of the data. Then find the median of the lower half and the median of the upper half of the data.
82, 62, 95, 81, 89, 51, 72, 56, 97, 98, 79, 85
The median is
.
The median of the lower half of the data is
.
The median of the upper half of the data is
.
.
The median is 81.5.
The median of the lower half of the data is 67.
The median of the upper half of the data is 92.
Given a data set,
82, 62, 95, 81, 89, 51, 72, 56, 97, 98, 79, 85
Median of a data set is the middle element when the data are arranged in a order.
Arranging in ascending order,
51, 56, 62, 72, 79, 81, 82, 85, 89, 95, 97, 98
There are even number of data sets.
So, Median = Average of the middle two elements.
Median = (81 + 82) / 2 = 81.5
Lower half of the data set is,
51, 56, 62, 72, 79, 81
Median = (62 + 72) / 2 = 67
Upper half of the data set is,
82, 85, 89, 95, 97, 98
Median = (89 + 95) / 2 = 92
Hence the median is 81.5, lower half median is 67 and upper half median is 92.
Learn more about median here :
https://brainly.com/question/28060453
#SPJ1
Pls help me I really nee it pls pls pls pls
22. Florida has a population of about
2 x 107. The Earth has a population
of about 8 x 10⁹. About how many
times more populated is the Earth
than Florida? Express your answer as a
whole number.
s
Answer:7
Step-by-step explanation:
an amount of R1965,00 is invested in an account paying 11,50% interest per year, compounded semi-annually at the time of withdrawal the amount of interest earned is R 633,75 . the number of years that the money was invested rounded to two decimal places is
The value of number of years that the money was invested rounded to two decimal places is, 2.5 years
We have to given that;
An amount of R1965,00 is invested in an account paying 11,50% interest per year, compounded semi-annually at the time of withdrawal the amount of interest earned is R633,75
Hence, We get;
Interest = P ( (1 + r/2)ⁿ - 1965)
R633.75 = 1965 (1 + 11.5%/2)ⁿ - 1965
1965 × 1.0575ⁿ - 1965 = 633.75
1965 × 1.0575ⁿ = 2598.75
1.0575ⁿ = 1.3225
n = log₁.₀₅₇₅ (1.3225)
n = 5
Hence, Number of years is, 5/2 = 2.5
Learn more about the multiplication visit:
https://brainly.com/question/10873737
#SPJ1
PQ is tangent to Circle O at Point P with arc lengths 160° and 60° as shown below.
The measure of the angle m∠PQR is equal to 50° using the secant tangent angle formula. So option A is correct.
What is the secant tangent angleThe secant tangent angle is the angle formed by a tangent and a secant that intersect outside of a circle. The measure of the secant tangent angle can be found using the following formula:
θ = 1/2 (arc EB - arc BD)
where arc EB and arc BD are the measures of the arcs intercepted by the secant and tangent, respectively.
From the question,
θ = m∠PQR
arc EB = 160°
arc BD = 60°
m∠PQR = 1/2(160° - 60°)
m∠PQR = 1/2 × 100°
m∠PQR = 50°
Therefore, the measure of the angle m∠PQR is equal to 50° using the secant tangent angle formula.
Read more about secant tangent here:https://brainly.com/question/9132922
#SPJ1
1. Expand and simplify the following:
a) (x+3)(x + 5)
b) (x-6) (x + 7)
2. Common factor each of the following.
a) 2x+6
b) 9x² - 12x
3. Factor the following difference of squares.
a) x²-121
b) 4x² - 49
4. Factor each of the following trinomials.
a) x² - 10x + 16
b) x²-5x-24
c) (2x-3)(5x-4)
c) 24x² + 16x-2
c) 144-25x²
c) x² +8x-20
5. Factor the following quadratics using the appropriate factoring method (s).
a) 3x² + 18x+24
b) 99-11x²
c) 6x²-48x-54
The Common factor:
a) 2x+6 = 2(x+3)
b) 9x² - 12x = 3x(3x - 4)
How to solveExpand and simplify:
a) [tex](x+3)(x+5) = x^2 + 5x + 3x + 15 = x^2 + 8x + 15[/tex]
b) [tex](x-6)(x+7) = x^2 + 7x - 6x - 42 = x^2 + x - 42[/tex]
Common factor:
a) 2x+6 = 2(x+3)
b) 9x² - 12x = 3x(3x - 4)
Factorization is the process of expressing a number or equation in terms of its factors, which are integers or individual terms that when combined together generate the original number or expression. This is an essential concept in algebra and number theory.
Read more about factorization here:
https://brainly.com/question/25829061
#SPJ1
Are △ABC and △DEF similar triangles? Choose all that apply.
No, the corresponding angles are not congruent.
No, the corresponding angles are not congruent.,
No, the corresponding sides are not proportional.
No, the corresponding sides are not proportional.,
Yes, the corresponding sides are proportional.
Yes, the corresponding sides are proportional.,
Yes, the corresponding angles are all congruent.
Answer:
Step-by-step explanation:
No, the corresponding angles are not congruent.,
They have to be EXACTLY the same.
Lol i am learning this to.
The Bearing of X from Y is 35° Find the bearing of Y from X
Using the Law of Cosines, the angle between the lines PX and PY is found to be approximately 101.5°. Subtracting this angle from the bearing of Y from P (125°) and the bearing of X from P (35°) gives a bearing of approximately 54.5° from X to Y.
We can use the Law of Cosines to find the angle between the lines PX and PY, and then add this angle to the bearing of X from P to find the bearing of Y from X.
Let A be the angle between the lines PX and PY, and let C be the distance between X and Y. Then we have
C² = PX² + PY² - 2(PX)(PY)cos(A)
Substituting the given values, we get
950² = 420² + PY² - 2(420)(PY)cos(A)
Solving for cos(A), we get
cos(A) = (PY^2 - 950^2 - 420^2) / (-2)(420)(950)
cos(A) = -0.186
Since A is an acute angle, we can take the inverse cosine to find its measure
A = cos⁻¹ (-0.186)
A ≈ 101.5°
The bearing of X from P is 35°, so the bearing of Y from X is
125° - 35° - A ≈ 54.5°
Therefore, the bearing of Y from X is approximately 54.5 degrees to the nearest minute.
To know more about Law of Cosines:
https://brainly.com/question/17289163
#SPJ1
--The given question is incomplete, the complete question is given
" The bearings from a point P of two landmarks X and Y are 35° and 125° and their distances from P are 420 m and 950 m respectively. Find the bearing of Y from X (to the nearest minute)."--
NEED HELP ASAP PLS AND THX PIC ATTACHED
The Area of Triangle is 10 square unit.
We have,
base = 4 unit
Height = 5 unit
So, Area of Triangle
= 1/2 x base x height
= 1/2 x 4 x 5
= 2 x 5
= 10 square unit
Learn more about Area here:
https://brainly.com/question/27683633
#SPJ1
State Inc. decides to issue 10% annual coupon bonds with a maturity of 20 years.
a) Using $1,000 as the face value, what should you pay for this bond if the yield to maturity is 12%? If 10%? If 8%? If 6%. Explain the results.
b) Instead, they decide to borrow $50 million from a bank with a maturity of 5 years. If the interest rate is 8%, what is the monthly payment? What is the balance at the end of 28 months?
The bond price at 12% maturity is $435.42, at 10% maturity is $500.00, at 8% maturity is $607.28, and at 6% maturity is $748.65. The balance at the end of 28 months is approximately $41,097,019.67.
To determine the price of the bond at different yield to maturity rates, we need to use the bond pricing formula
Bond price = (Coupon payment / (1 + YTM)¹) + (Coupon payment / (1 + YTM)²) + ... + (Coupon payment + Face value) / (1 + YTM)ⁿ
Where Coupon payment = Annual coupon rate x Face value
YTM = Yield to maturity
n = Number of years to maturity x Number of coupon payments per year
Using $1,000 as the face value and an annual coupon rate of 10%, we have
At 12% yield to maturity
Coupon payment = 0.10 x $1,000 = $100
n = 20 x 2 = 40
Bond price = ($100 / (1 + 0.12)¹) + ($100 / (1 + 0.12)²) + ... + ($100 + $1,000) / (1 + 0.12)⁴⁰
Bond price = $435.42
At 10% yield to maturity
Coupon payment = 0.10 x $1,000 = $100
n = 20 x 2 = 40
Bond price = ($100 / (1 + 0.10)¹) + ($100 / (1 + 0.10)²) + ... + ($100 + $1,000) / (1 + 0.10)⁴⁰
Bond price = $500.00
At 8% yield to maturity
Coupon payment = 0.10 x $1,000 = $100
n = 20 x 2 = 40
Bond price = ($100 / (1 + 0.08)¹) + ($100 / (1 + 0.08)²) + ... + ($100 + $1,000) / (1 + 0.08)⁴⁰
Bond price = $607.28
At 6% yield to maturity
Coupon payment = 0.10 x $1,000 = $100
n = 20 x 2 = 40
Bond price = ($100 / (1 + 0.06)¹) + ($100 / (1 + 0.06)²) + ... + ($100 + $1,000) / (1 + 0.06)⁴⁰
Bond price = $748.65
To calculate the monthly payment and balance of the loan from the bank, we can use the formula for the monthly payment of an amortizing loan
P = (r × A) / (1 - (1 + r)⁻ⁿ)
where P is the monthly payment, r is the monthly interest rate (which is the annual interest rate divided by 12), A is the loan amount, and n is the total number of months in the loan.
First, we need to calculate the values of r, A, and n
r = 0.08 / 12 = 0.00667 (monthly interest rate)
A = $50,000,000 (loan amount)
n = 5 years × 12 months/year = 60 months (total number of months in the loan)
Now, we can plug these values into the formula to calculate the monthly payment
P = (0.00667 × $50,000,000) / (1 - (1 + 0.00667)⁻⁶⁰)
P ≈ $1,029,299.29
Therefore, the monthly payment on the loan is approximately $1,029,299.29.
To find the balance at the end of 28 months, we can use the formula for the remaining balance of an amortizing loan
B = (P * (1 - (1 + r)⁻ⁿ')) / r
where B is the remaining balance, r is the monthly interest rate, P is the monthly payment, and n' is the number of months remaining in the loan (which is equal to the total number of months minus the number of months already paid).
After 28 months, the number of months remaining in the loan is
n' = 60 - 28 = 32
We can now plug the values of P, r, and n' into the formula to find the balance
B = ($1,029,299.29 × (1 - (1 + 0.00667)⁻³²)) / 0.00667
B ≈ $41,097,019.67
Therefore, the balance at the end of 28 months is approximately $41,097,019.67.
To know more about bond price here
https://brainly.com/question/15518377
#SPJ1
LR
What is the mean of
89.93
94.51
68.90
97.66
97.57
86.05
98.35
89.15
80.71
91.46
84.82
Answer: 6
Step-by-step explanation:
How is y=4(2)^x-3 translated from the graph of y=4(2)^x
The graph of y=4[tex](2)^{x}[/tex]-3 is the same as the graph of y=4[tex](2)^{x}[/tex] shifted downwards by 3 units.
The function y=4[tex](2)^{x}[/tex] is an exponential function with base 2 and vertical intercept at (0, 4).
To translate this function to the graph of y=4[tex](2)^{x}[/tex]-3, we need to shift the graph downwards by 3 units. This can be achieved by subtracting 3 from the original function as follows:
y = 4[tex](2)^{x}[/tex] - 3
Now, the vertical intercept of the new function y=4[tex](2)^{x}[/tex]-3 is at (0, 1), which is 3 units below the intercept of the original function.
Notice how the entire graph has shifted down by 3 units, while maintaining the same shape as the original exponential function y=4[tex](2)^{x}[/tex].
To learn more about graph here:
https://brainly.com/question/30716175
#SPJ1
a)
b)
1. Convert the following Mayan numbers to
decimal (base 10).
: :|| :||
The given Mayan number which is : :|| :|| in decimal (base 10) is 42.
The Mayan number system is a base-20 system that uses three symbols: a dot (.), a horizontal bar (|), and a shell-like symbol (:). The symbol for zero is a shell-like symbol (:).
To convert the given Mayan number to decimal (base 10), we need to understand the positional value of each symbol. Each position in the number represents a power of 20, with the rightmost position being 20⁰, the next position to the left being 20¹, and so on.
The Mayan number given, : :|| :||, can be broken down as follows:
The leftmost position has no symbol, which represents a value of 0.
The second position from the left has two shell-like symbols (:), which represents a value of 2x20¹ = 40.
The third position from the left has two horizontal bars (||), which represents a value of 2x20⁰ = 2.
The given Mayan number in decimal (base 10) is 40 + 2 = 42.
To learn more about conversion click on,
https://brainly.com/question/30650712
#SPJ1
Complete question is:
Convert the following Mayan number to decimal (base 10).
: :|| :||
What is the sum of the interior angle
measures of a regular hexagon? Show
or explain how you can use the sum
of the interior angles of a triangle to
determine the answer.
The sum of the interior angle of the regular hexagon is S = 720°
Given data ,
Sum of Interior angles of a polygon with n sides is
nθ = 180 ( n - 2 )
where n is the number of sides
θ = angle in degrees
when n = 6 for a hexagon , we get
nθ = 180 ( 6 - 2 )
nθ = 180 x 4
nθ = 720°
Hence , the sum of interior angles of a hexagon is 720°
To learn more about sum of the interior angles of a polygon click :
https://brainly.com/question/14611583
#SPJ1
Points S and T are midpoints of the sides of trisngle FGH.
The length of GF is 4 cm minus half the length of side FH.
To do this, we can use the fact that point S is the midpoint of FH. This means that FS = 1/2 FH. Similarly, point T is the midpoint of GH, so TG = 1/2 GH. We can now use these equalities and the fact that SG = 4 cm and HT = 6 cm to set up an equation involving FH:
SG + GF + HT = ST + TG + FH
Substituting the given values and using the fact that TG = GH - TG = GH - 1/2 GH = 1/2 GH, we get:
4 cm + GF + 6 cm = 8 cm + 1/2 GH + FH
Simplifying and substituting FS = 1/2 FH and TG = 1/2 GH, we get:
10 cm + GF = 8 cm + FS + TG
GF = 8 cm + FS + TG - 10 cm
GF = 1/2 FH - 1/2 GH
Now, substituting the values we know, we get:
GF = 1/2 FH - 1/2 GH
GF = 1/2 (FS + SH) - 1/2 (GH)
GF = 1/2 (8 cm + SH) - 1/2 (GH)
GF = 1/2 (8 cm + FS) - 1/2 (GH)
GF = 1/2 (8 cm + 1/2 GH) - 1/2 (GH)
GF = 3 cm - 1/4 GH
We can now substitute TG = 1/2 GH and solve for GH:
TG = 1/2 GH
8 cm - FS = 1/2 GH
GH = 16 cm - 2 FS
Substituting this value into the expression for GF, we get:
GF = 3 cm - 1/4 (16 cm - 2 FS)
GF = 3 cm - 4 cm + 1/2 FS
GF = 1/2 FS - 1 cm
Finally, substituting FS = 8 cm - SH, we get:
GF = 1/2 (8 cm - SH) - 1 cm
GF = 4 cm - 1/2 SH
To know more about midpoint here
https://brainly.com/question/28224145
#SPJ1
Complete Question:
Points S and T are midpoints of the sides of triangle FGH
when HT = 6cm, ST = 8 cm, SG = 4CM
what is GF ?
A carpenter cuts a circle out of a piece of wood. the radius of the circle is about 23 inches. The carpenter cuts the circle into two semicircles. What is the area od one semicircle. Use 3.14 for pi
Answer:
830.53 in²
Step-by-step explanation:
Find the area of the full circle and divide it by 2:Use the circle area formula, A = r²Plug in 3.14 as pi, and plug in the radius:A = r²A = 3.14(23²)A = 1661.06Divide this by 2:1661.06 / 2= 830.53So, the area of one semicircle is 830.53 in²
Answer: The area of one semicircle is approximately 830.53 square inches.
Step-by-step explanation:
The area of a circle is given by the formula:
A = πr²
where A is the area of the circle and r is its radius.
The radius of the circle cut out of the piece of wood is about 23 inches. Therefore, its area is:
A = πr²
A = π(23)²
A = π(529)
A ≈ 1661.06 square inches
The carpenter cuts the circle into two semicircles. Therefore, the area of one semicircle is:
A/2 ≈ 830.53 square inches
Therefore, the area of one semicircle is approximately 830.53 square inches.
I hope this helps! Let me know if you have any other questions.
[-/5 Points]
DETAILS GHCOLALG12 4.4.026.
Write a third-degree polynomial function with real coefficients and the given zeros. (Use x as your variable.)
7, i
P(x) =
The value of a third-degree polynomial function with real coefficients and the given zeros are,
⇒ P (x) = x³ - (i + 14)x² + (49 + 14i)x - 49i
We have to given that;
Zeroes of the polynomial are,
⇒ 7, i
Now, The value of a third-degree polynomial function with real coefficients and the given zeros are,
⇒ P (x) = (x - 7)² (x - i)
⇒ P (x) = (x² + 49 - 14x) (x - i)
⇒ P (x) = (x³ - ix² + 49x - 49i - 14x² + 14ix)
⇒ P (x) = x³ - (i + 14)x² + (49 + 14i)x - 49i
Thus, The value of a third-degree polynomial function with real coefficients and the given zeros are,
⇒ P (x) = x³ - (i + 14)x² + (49 + 14i)x - 49i
Learn more about the function visit:
https://brainly.com/question/11624077
#SPJ1
8.1 CHECK YOUR UNDERSTANDING - TURN ME IN!
1. A recent Pew Research center poll asked a random sample of teens "In general, how much time would you say
you spend with your friends in person." 36 % of the 739 respondents said "too little". We will estimate the
population proportion with 99% confidence.
a) Interpret the confidence level.
36%
b) Construct and interpret a 99% confidence interval for the population proportion.
If you created a 95% confidence interval instead, would it be narrower or wider? Explain.
c) if you created a 95% confidence interval instead would it be narrower or wider
AP STATS
a) The confidence level of 99% means that we are 99% sure that the interval contains the true population proportion.
b) The 99% confidence interval for the population proportion is given as follows: (0.3145, 0.4055). It means that we are 99% sure that the true population proportion is between 0.3145 and 0.4055.
c) The 95% confidence interval would be narrower, as it would have a lower critical value, thus the margin of error would also be lower.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.
The parameters for this problem are given as follows:
[tex]\pi = 0.36, n = 739[/tex]
The lower bound of the interval is given as follows:
0.36 - 2.575 x sqrt(0.36 x 0.64/739) = 0.3145.
The upper bound of the interval is given as follows:
0.36 + 2.575 x sqrt(0.36 x 0.64/739) = 0.4055.
More can be learned about the z-distribution at https://brainly.com/question/25890103
#SPJ1
Solve for x:
-5 - 3(6x-8) = -5x + 19
Show your work
Answer: x = 0
Step-by-step explanation:
simplify the expression
−5−3(6x−8)=−5x+19
−5−18+24=−5+19
19−18x=−5x+19
−18+19=−5+19
−5−3(6x−8)=−5x+19
−18x+19=−5x+19
−5−3(6x−8)=−5x+19
−18x+19=−5x+19
−18+19−19=−5+19−19
−18x=−5x+19 − 19
−18x+19−19=−5x+19 − 19
−18x=−5x
−18x+5x=−5x+5x
x=−5x+5x−13
x−13=−5+5
−13x=0
−13x/−13 = 0/-13
x= 0/−13
x= 0
The number of milligrams D(h) of a certain drug that is in a patient's bloodstream h hours after the drug is injected is given by the following function.
D(h)=30e^-0.35h
When the number of milligrams reaches 11, the drug is to be injected again. How much time is needed between injections?
Round your answer to the nearest tenth, and do not round any intermediate computations.
When the number of milligrams reaches 11, the drug is to be injected again. We need approximately 6.7 hours between injections.
The given function is D(h)=30[tex]e^{-0.35h[/tex], which gives the number of milligrams D(h) of the drug in the patient's bloodstream h hours after it is injected.
When the drug is injected again, the number of milligrams in the bloodstream will be 11. Therefore, we need to find the value of h that satisfies the equation:
11 = 30[tex]e^{-0.35h[/tex]
To solve for h, we can first divide both sides by 30:
11/30 = [tex]e^{-0.35h[/tex]
Next, we take the natural logarithm of both sides:
ln(11/30) = ln([tex]e^{-0.35h[/tex])
Using the property of logarithms that ln(eˣ) = x, we can simplify the right side:
ln(11/30) = -0.35h
Finally, we can solve for h by dividing both sides by -0.35 and multiplying by -1:
h = (-1/0.35)ln(11/30)
Using a calculator, we get:
h ≈ 6.7
To learn more about function click on,
https://brainly.com/question/31059861
#SPJ1
Jack went for a mountain hike. On his way up, he traveled
at a speed of 2 mph. He reached the summit in 3 hours. On his
way back down, Jack jogged at a speed of 5 mph. Write
the formula that describes how the distance Jack covered during
the hike depends on the amount of time that he traveled.
Answer:
d = (20/7)t
Step-by-step explanation:
You want the distance traveled as a function of travel time if Jack's speed going up was 2 mph and going down was 5 mph.
TimeThe relation between time, speed, and distance is ...
t = d/s
If the total distance is d, the total travel time up and back is ...
t = t1 +t2
t = (d/2)/(2) +(d/2)/5 = d(1/4 +1/10) = 0.35d
Solving for distance, we have ...
d = t/0.35
d = (20/7)t . . . . miles, where t is in hours
<95141404393>
For her end of year party Adriana mixed 6 L of Brand A juice with 9 L of Brand B juice. Brand A contains 52% fruit and Brand B contains 12% fruit juice. What percent of the mixture is fruit juice?
A. 30%
B. 28%
C. 20%
D. 32%
The per cent of fruit juice in the mixture is 28%. The correct option is B.
To determine the percent of fruit juice in the mixture, we need to calculate the total amount of fruit juice in the 6 L of Brand A juice and the 9 L of Brand B juice, and then divide it by the total volume of the mixture.
The amount of fruit juice in 6 L of Brand A juice is:
0.52 x 6 L = 3.12 L
The amount of fruit juice in 9 L of Brand B juice is:
0.12 x 9 L = 1.08 L
The total amount of fruit juice in the mixture is:
3.12 L + 1.08 L = 4.20 L
The total volume of the mixture is:
6 L + 9 L = 15 L
So, the per cent of fruit juice in the mixture is:
(4.20 L / 15 L) x 100% = 28%
Therefore, the correct answer is (B) 28%.
To know more about the percentage follow
https://brainly.com/question/15804062
#SPJ1
What is the value of the expression 4 twelfths + 2 thirds
The value of the expression 4/12 + 2/3 is 1 1/12
What are fractions?A fraction is a part of a whole. A fraction consist of the upper part( numerator ) and the lower part ( denominator). Examples of fractions are; simple fraction , complex fraction, mixed fraction, improper fraction.
In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
Solving 4/12 + 1/3
= (9+4)/12
= 13/12
= 1 1/12
therefore the value of 4 twelfth + 2 third is 1 1/12
learn more about fractions from
https://brainly.com/question/78672
#SPJ1
When Steven was 3 years old (on his birthday), his grandmother decided to set up a trust account to pay for his college education. She wanted the account to grow
to $100,000 by his 18th birthday. If she was able to invest her money at 4% per year, how much did she have to deposit into this trust account? (Note: The
amount deposited is known as the present value of the investment. The $100,000 is known as the future value. Round your answer to the nearest cent.)
$
Using the future value,
Steven's grandmother needed to deposit $55,469.56 into the trust account.
We have,
We can use the formula for the future value of a present sum:
FV = PV(1 + r)^n
where FV is the future value, PV is the present value, r is the annual interest rate, and n is the number of years.
In this case, we have:
FV = $100,000
PV = unknown
r = 4% = 0.04
n = 15 years (18 - 3 = 15)
Substituting these values into the formula, we get:
$100,000 = PV(1 + 0.04)^15
Solving for PV, we get:
PV = $55,469.56
Thus,
Steven's grandmother needed to deposit $55,469.56 into the trust account.
Learn more about future value here:
https://brainly.com/question/14860893
#SPJ1
35% of those falled will find an excuse to avoid jury duty. if 10 people are called for jury duty, then what is the probability that 2 will find an excuse
The evaluated probability that 2 will find an excuse is 12.8%, under the condition that 35% of those failed will evaluate an excuse to avoid jury duty.
According to the data I found, about 23% of those evaluated to find an excuse (work, poor health, travel out of town, etc.) to avoid jury duty.
In the event 10 people are called for jury duty, then the evaluated probability that 2 will find an excuse can be found out using the binomial probability distribution formula.
The formula is:
[tex]P(X=k) = C(n,k) * p{^k }* (1-p)^{(n-k)}[/tex]
Here,
P(X=k) = successes probability of k in n trials
C(n,k) = combinations of number in n things taken k at a time
p= success probability of any one trial
n = trial number
For the given case
k = 2
n = 10
p = 0.23
Staging these values into the formula
[tex]P(X=2) = C(10,2) * 0.23^{2}* (1-0.23)^{(10-2)}[/tex]
= 45 × 0.0529 × 0.5225
= 0.128
Hence, the probability that exactly 2 out of 10 people will evaluate an excuse to avoid jury duty is 0.128 or approximately 12.8%.
To learn more about probability
https://brainly.com/question/13604758
#SPJ1
find the perimeter of the composite figure. 11 19.5 16 m 18m
The perimeter of the composite figure that is given above would be = 96.6m.
How to calculate the perimeter of the given figure?To calculate the perimeter of the given shape, it has to be divided into two.
First shape is a rectangle. Therefore the perimeter of a rectangle is calculated with the formula = 2(l+w)
Where ;
length = 16m
width = 11m
perimeter = 2(16+11)
= 2×27
= 54m
The second shape:
Perimeter of triangle = l+w+h
where;
length = 18-11 = 7m
width = 16m
height = 19.5m
perimeter = 7+16+19.5 = 42.5m
Therefore, the perimeter of the shape = 54+42.5 = 96.6m
Learn more about perimeter here:
https://brainly.com/question/31619854
#SPJ1
evaluate the following 12.45x11
Town A and Town were located close to each other, and recently merged into one city. Town A had a population with 12% whites. Town B had a population with 10% whitesAfter the merge, the new city has a total of 5000 residents, with 10.56% whitesHow many residents Town A and Town used to have?
The number of residents Town A used to have is 1400, and the number of residents Town B used to have is 3600, as shown by the simple equation below.
How to find the number of residentsLet x be the number of residents Town A used to have. The number of residents in Town B is:
5000 - x
We know that Town A had 12% whites and Town B had 10% whites. After the merge, the percentage of whites is 10.56%. With that in mind:
12%x+10%(5000-x) = 10.56%(5000)
0,12x + 500 - 0,1x = 528
0.02x = 28
x = 1400
Therefore, the number of residents Town A used to have is 1400. Now, the number of residents town B used to have is:
5000 - 1400 = 3600
With that in mind, we can conclude our answer is correct.
Learn more about equations here:
https://brainly.com/question/2972832
#SPJ1
Find the two perfect squares that each Integer is between. Then approximate the square root to one decimal place.
√47
pls i need it quick
Answer:
[tex] 36 < 47 < 49[/tex]
[tex] \sqrt{36} < \sqrt{47} < \sqrt{49} [/tex]
[tex]6 < \sqrt{47} < 7[/tex]
√47 is approximately 6.9