Answer:
A) $93,504.818
B) $40,000
C) $53,504.818
Step-by-step explanation:
Yearly contribution ( periodic payment) = $4000
Period (p) = 10years
Additional period(y) = 5years
Annual interest(r) = 9% = 0.09
Future value (FV) =
periodic payment [(1 + r)^y - 1] / r
4000 [(1 + 0.09)^10 - 1 / 0.09]
4000[1.09^10 - 1 / 0.09]
4000[1.3673636 / 0.09]
4000(15.192929)
= 60771.716
If left for five more years:
FV = 60771.716(1 + r)^n
FV = 60771.716(1 + 0.09)^5
FV = 60771.716(1.09)^5
FV = 60771.716(1.5386239549)
FV = $93,504.818
B) MR. HUGHES CONTRIBUTION :
Periodic payment × p ; $4000 was deposited annually for 10 years.
$4000 × 10 = $40,000
C) Interest = Future value - contribution
$93,504.818 - $40,000
= $53,504.818
Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean mu equals 247 days and standard deviation sigma equals 16 days. Complete parts (a) through (f) below.
Answer:
The answer is given below
Step-by-step explanation:
a) What is the probability that a randomly selected pregnancy lasts less than 242 days
First we have to calculate the z score. The z score is used to determine the measure of standard deviation by which the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Given that Mean (μ) = 247 and standard deviation (σ) = 16 days. For x < 242 days,
[tex]z=\frac{x-\mu}{\sigma}=\frac{242-247}{16}=-0.31[/tex]
From the normal distribution table, P(x < 242) = P(z < -0.3125) = 0.3783
(b) Suppose a random sample of 17 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies.
If a sample of 17 pregnancies is obtained, the new mean [tex]\mu_x=\mu=247,[/tex] the new standard deviation: [tex]\sigma_x=\sigma/\sqrt{n} =16/\sqrt{17} =3.88[/tex]
c) What is the probability that a random sample of 17 pregnancies has a mean gestation period of 242 days or less
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{242-247}{16/\sqrt{17} }=-1.29[/tex]
From the normal distribution table, P(x < 242) = P(z < -1.29) = 0.0985
d) What is the probability that a random sample of 49 pregnancies has a mean gestation period of 242 days or less?
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{242-247}{16/\sqrt{49} }=-2.19[/tex]
From the normal distribution table, P(x < 242) = P(z < -2.19) = 0.0143
(e) What might you conclude if a random sample of 49 pregnancies resulted in a mean gestation period of 242 days or less?
It would be unusual if it came from mean of 247 days
f) What is the probability a random sample of size 2020 will have a mean gestation period within 11 days of the mean
For x = 236 days
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{236-247}{16/\sqrt{20} }=-3.07[/tex]
For x = 258 days
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{258-247}{16/\sqrt{20} }=3.07[/tex]
From the normal distribution table, P(236 < x < 258) = P(-3.07 < z < 3.07) = P(z < 3.07) - P(z < -3.07) =0.9985 - 0.0011 = 0.9939
the area of a rectangular sandbox can be expressed as 72xy + 18x the width of the sandbox is 9x what is the perimeter of the sandbox
Answer:
18x +16y +4
Step-by-step explanation:
The area is the product of length and width, so the length is ...
A = LW
L = A/W = (72xy +18x)/(9x) = 8y +2
The perimeter is double the sum of length and width:
P = 2(L +W) = 2(8y +2 +9x)
P = 18x +16y +4 . . . . the perimeter of the sandbox
Trig work i don’t understand. pls help
Answer: A
Step-by-step explanation:
So we know that to find the area of a triangle you have to multiply the base times the height and divide it by two or multiply it by 1/2.Looking the information given it say that theta is equal to 26 degrees and the length of a or the hypotenuse is 25 and b which in this case is the base is 32. So the information gives us the base but now we need to find the height.
To find H we need to apply trigonometry solve for h the height.
As we could see theta which is 26 degrees is opposite the height and we know the hypotenuse length. So using soh cah toh we have to know that the length of h is going to be using the sin formula opposite over hypotenuse.
[tex]sin(26)=\frac{h}{25}[/tex] solve for h by multiplying both sides by 25.
h= 25 sin(26)
h= 10.96 is being rounded to the nearest hundredth because that is essential
Now we know H is equal to 10.96 which is the Height so now we have all the information we need the height and the base.
Multiply 10.96 by 32 and divide it by 2.
10.96 * 32 = 350.72
350.72 /2 = 176.36
The best answer is A because that is the only best approximation to 175.35.
how to find the angel in trigonometry when all the lengths of the right angled triangle already given.
Answer:
The three trigonometric ratios can be used to calculate the size of an angle in a right-angled triangle
Use rule ; SOHCAHTOA .Where sin x = opp/hyp
cos x = adj/hyp
tan x= opp/adj
Substitute the given values for the three sides
into any of the above rules
[tex]example = Hyp = 2\\opp = 1\\sin- x = 1/2\\x = sin^{-1} 1/2\\x = 30[/tex]
Step-by-step explanation:
I Hope It Helps :)
A company rounds its losses to the nearest dollar. The error on each loss is independently and uniformly distributed on [–0.5, 0.5]. If the company rounds 2000 such claims, find the 95th percentile for the sum of the rounding errors.
Answer:
the 95th percentile for the sum of the rounding errors is 21.236
Step-by-step explanation:
Let consider X to be the rounding errors
Then; [tex]X \sim U (a,b)[/tex]
where;
a = -0.5 and b = 0.5
Also;
Since The error on each loss is independently and uniformly distributed
Then;
[tex]\sum X _1 \sim N ( n \mu , n \sigma^2)[/tex]
where;
n = 2000
Mean [tex]\mu = \dfrac{a+b}{2}[/tex]
[tex]\mu = \dfrac{-0.5+0.5}{2}[/tex]
[tex]\mu =0[/tex]
[tex]\sigma^2 = \dfrac{(b-a)^2}{12}[/tex]
[tex]\sigma^2 = \dfrac{(0.5-(-0.5))^2}{12}[/tex]
[tex]\sigma^2 = \dfrac{(0.5+0.5)^2}{12}[/tex]
[tex]\sigma^2 = \dfrac{(1.0)^2}{12}[/tex]
[tex]\sigma^2 = \dfrac{1}{12}[/tex]
Recall:
[tex]\sum X _1 \sim N ( n \mu , n \sigma^2)[/tex]
[tex]n\mu = 2000 \times 0 = 0[/tex]
[tex]n \sigma^2 = 2000 \times \dfrac{1}{12} = \dfrac{2000}{12}[/tex]
For 95th percentile or below
[tex]P(\overline X < 95}) = P(\dfrac{\overline X - \mu }{\sqrt{{n \sigma^2}}}< \dfrac{P_{95}- 0 } {\sqrt{\dfrac{2000}{12}}}) =0.95[/tex]
[tex]P(Z< \dfrac{P_{95} } {\sqrt{\dfrac{2000}{12}}}) = 0.95[/tex]
[tex]P(Z< \dfrac{P_{95}\sqrt{12} } {\sqrt{{2000}}}) = 0.95[/tex]
[tex]\dfrac{P_{95}\sqrt{12} } {\sqrt{{2000}}} =1- 0.95[/tex]
[tex]\dfrac{P_{95}\sqrt{12} } {\sqrt{{2000}}} = 0.05[/tex]
From Normal table; Z > 1.645 = 0.05
[tex]\dfrac{P_{95}\sqrt{12} } {\sqrt{{2000}}} =1.645[/tex]
[tex]{P_{95}\sqrt{12} } = 1.645 \times {\sqrt{{2000}}}[/tex]
[tex]{P_{95} = \dfrac{1.645 \times {\sqrt{{2000}}} }{\sqrt{12} } }[/tex]
[tex]\mathbf{P_{95} = 21.236}[/tex]
the 95th percentile for the sum of the rounding errors is 21.236
Simple and easy question
please help
Answer:
Volume of a sphere = 4/3πr³
π = 3.14
r = radius which is 3in
Volume = 4/3 × 3.14 × 3²
= 37.68
= 38 cubic inches to the nearest hundredth
Hope this helps
Answer:
38 cubic inches
Step-by-step explanation:
Which of the following investments could be represented by the function A = 250(1 + 0.08/12)12 × 4?
hello,
the first term is 250 so this is the initial invested amount
[tex](1+\dfrac{0.08}{12})^{12}=(1+\dfrac{8\%}{12})^{12}[/tex]
is to compute 8% annual interest compounded monthly (there are 12 months in a year)
and then multiply by 4 means that it is computed for 4 years so
finally the answer is
$250 is invested at 8% annual interest compounded monthly for 4 years
hope this helps
Graph the relation shown in the table. Is the relation a function? Why or why not? {(-1, 9), (0, -1), (-1, 4), (4, 9)}
Answer:
Not a function
Step-by-step explanation:
For an equation to be a function, there should be only one y-coordinate per x-coordinate. Since this relation has both (-1,9) and (-1,4), this is not a function.
Answer:not a function
Step-by-step explanation:
because when you put the points on the coordinate plane your shape will come out as a v shaped object. In mathematics, a function is a binary relation over two sets that associates to every element of the first set exactly one element of the second set. Typical examples are functions from integers to integers or from the real numbers to real numbers
PLEASE HELP ASAP SHOE YOUR WORK!!!! Best answer gets brainliest :)
Answer:
Height = 3cm
Volume = 50.27cm^3
Step-by-step explanation:
Well to solve for the height with slant height and radius we can use the Pythagorean Theorem,
Which is [tex]a^2 + b^2 = c^2[/tex].
So we have c and a, so we have to fill those in.
(4)^2 + b^2 = (5)^2
16 + b^2 = 25
-16
b^2 = 9
[tex]\sqrt{b} \sqrt{9}[/tex]
b = 3cm
So to find the volume of a cone we use the following formula [tex]\pi r^2 \frac{h}{3}[/tex].
So we have the radius and height so we just fill those in.
(pi)(4)^2(3)/3
(pi)16(1)
pi*16
About 50.27cm^3
between which to whole numbers does the square root of 37 lie?
Between 6 and 7
6×6=36
7×7=49
hopefully this helped
The number √37 is lies between whole numbers 6 and 7.
We have to given,
A number is, √37
By the definition of square root, we get;
⇒ √37 = 6.08
And, We know that,
Number 6.08 is lies between whole number 6 and 7.
Hence, We get;
⇒ 6 < √37 < 7
Therefore, The number √37 is lies between whole numbers 6 and 7.
Learn more about Number system visit:
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Find the difference.
(3x4 - 5x2 - 4)-( 2x3 x2 + 1)
w
3x4 - 2x3 - 4x2-5
a
Answer:
(3x4 - 5x2 - 4)-( 2x3 x2 + 1) is equals to -15
3x4 - 2x3 - 4x2-5 is equals to -7
Step-by-step explanation:
1.) (3x4 - 5x2 - 4)-( 2x3 x2 + 1)
3 x 4 = 12 5 x 2 = 10 12 - 10 = 2 2 - 4 = -2
2 x 3 = 6 6 x 2 = 12 12 + 1 = 13
-2 - 13 = -15
2.)3x4 - 2x3 - 4x2-5 is eaquals to -7
3 x 4 = 12 2 x 3 = 6 12 - 6 = 6 4 x 2 = 8
6 - 8 = -2 -2 - -5 = -7
Those were my answers
If my score goes up 20,000 a day how long will it take me to reach 2,000,000
Answer:
It would take 100 days
Step-by-step explanation:
2,000,000 divided by 20,000 equals 100
So it would take 100 days
What is the value for y? Enter your answer in the box. y = An isosceles triangle A B C with horizontal base A B and vertex C is below the base. Side A C and C B are labeled with single tick mark. All the three angles are labeled. Base angles C A B is labeled as 34 degrees and angle C B A is labeled as left parenthesis x minus 5 right parenthesis degrees. The angle A C B is labeled as 4y degrees.
Answer:
28.
Step-by-step explanation:
I just did the question and I got it right. The answer above is right. The image below is where I did the question and has the picture attached next to it too.
*And I accidentally clicked the one star option, that's why it has such a low score.
An isosceles triangle is a triangle where two sides are equal and the angles opposite to the sides are also equal.
The value of y is 28.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
An isosceles triangle is a triangle where two sides are equal and the angles opposite to the sides are also equal.
m∠CAB = 34
m∠CBA = x - 5
m∠ACB = 4y
Triangle ABC is an isosceles triangle.
AC and BC are sides are equal.
This means,
m∠CAB = m∠CBA
34 = x - 5
34 + 5 = x
x = 39
Now,
The sum of the angles in a triangle is 180 degrees.
This means,
34 + (x -5) + 4y = 180
34 + (39 - 5) + 4y = 180
34 + 34 + 4y = 180
68 + 4y = 180
4y = 180 - 68
y = 112 / 4
y = 28
We can cross-check.
34 + 34 + 4 x 28 = 180
34 + 34 + 112 = 180
180 = 180
Thus,
The value of y is 28.
Learn more about triangles here:
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PLZ HELP!!!!WILL MARK BRAINLIEST AND 20 POINTS!!!
Answer: Find a common denominator on the right side of the equation
Step-by-step explanation:
You can see that they found the common denominator of 4 therefore that is the correct answer
I'll always give away 5 stars, thanks and Brainliest to the answer that's correct!
Naruto has a baseball card that is worth $45. The value of the card is increasing at the rate of 1.5% per year. How much will the card be worth in 15 years?
A: $366.17
B: $56.26
C: $89.21
D: $263.97
Answer:
a I believe sorry if I'm wrong
Answer:
I think its B: $56.26
The police department uses a formula to determine the speed at which a car was going when the driver applied the breaks, by measuring the distance of the skid marks.The equation d=0.03r^2+r models the distance, d, in feet, r miles per hour (r is the speed of the car) Factor the equation. d=?
Answer:
0.03 feet
Step-by-step explanation:
d = 0.03r² + r
When d = 0: 0.03r² + r = 0
r(0.03r + 1) = 0
∴ r = 0
When r = 0: d = 0.03 feet
Which statement is true about the equations –3x + 4y = 12 and 1/4x-1/3y=1
Answer: No solution
Step-by-step explanation:
This system of equation has no solution because...
-3x+4y=12
1/4x-1/3y=1
[tex]-3x+4y-4y=12-4y[/tex]
[tex]-3x=12-4y[/tex]
[tex]\frac{-3x}{-3}=\frac{12}{-3}-\frac{4y}{-3}[/tex]
[tex]\frac{12}{-3}-\frac{4y}{-3}[/tex]
[tex]x=-\frac{12-4y}{3}[/tex]
substitute
[tex]\frac{1}{4}\left(-\frac{12-4y}{3}\right)-\frac{1}{3}y=1[/tex]
[tex]-1=1[/tex]
-1=1 is false so therefore this system has no solution
Simplify this expression: 19 - (-8) - (-14) = ? A. 41 B. 25 C. -7 D. -3
Answer:
A. 41
Step-by-step explanation:
19 - (-8) - (-14) =
19+8+14
Remember: Two negatives=One positive ;)
27+14
41
A. 41
Answer:
[tex]\mathrm{A.} \: 41[/tex]
Step-by-step explanation:
[tex]19 - (-8) - (-14)[/tex]
[tex]\mathrm{Apply \: rule:} \: -(-a)=a[/tex]
[tex]19+8+14[/tex]
[tex]\mathrm{Add \: the \: numbers.}[/tex]
[tex]=41[/tex]
this diagram shows a scale drawing of a playground the scale is ___ 1:500 work out the perimeter of the real playground give your answer in meters
Answer:
The perimeter of the actual playground is 22000 units
Step-by-step explanation:
By measurement, the width of the scale drawing = 16 units
The breadth of the scale drawing = 6 units
Therefore, given that the scale is 1:500, we have that the actual dimensions of the playground are;
Actual width of the playground = 500×16 = 8,000 units
Actual breadth of the playground = 500×6 = 3,000 units
Therefore;
The perimeter of the actual playground = 2 × 8000 + 2 ×3000 = 22000 units.
simplifica: 49/90, se puede????
Answer:
49/90 is simplified
Step-by-step explanation:
Answer:
Step-by-step explanation:
49/90
In a game the average score was 60 time score was 5/2 of the average what was Tim’s score?
Answer:
in my own reasoning not sure if I am correct
Step-by-step explanation:
first it said Tim score was 5/2 of the of the average score
and the average score is 60
so that will be 5/2 × 60 which is
= 150
PLEASE HELP ME LAST QUESTION!!!!!!
Answer:
Angle 5
Step-by-step explanation:
Answer:
Angle 5
Step-by-step explanation:
Angle 8 is across from angle 5 meaning they have the same degrees.
The sides of an equilateral triangle measure 16 inches. The midpoints of the sides of the triangle are joined to form another equilateral triangle with sides that are half the length of the outer triangle. This process is continued until three triangles are inscribed in the first triangle. The sum of the perimeters of all four triangles is
Answer:
90 inches
Step-by-step explanation:
The perimeter of the inscribed triangle is 1/2 that of the enclosing triangle. So, the total of perimeters is ...
(3·16 in)(1 +1/2 +1/4 +1/8) = (48 in)(15/8) = 90 inches
The graph below shows a line of best fit for data collected on the number of toys sold at a toy store since the opening of the store. Based on the line of best fit, how many toys were sold 13 days after the store opened?
A.) 195
B.) 260
C.) 325
D.) 130
The answer that line of best fit, how many toys were sold 13 days after the store opened is A.) 195
The points A (-3, b), and B (1, 3) are 5 units apart. Find the value of b.
Answer:
b = 0
Step-by-step explanation:
To find the value of b, we will follow the steps below;
Using the distance formula:
D = √(x₂-x₁)² + (y₂-y₁)²
from the question given,
A (-3, b), this implies
(-3, b) = (x₁ ,y₁)
x₁=-3 and y₁ = b
similarly
B (1, 3)
(1, 3) = (x₂,y₂)
this implies
x₂ = 1 and y₂=3
D= 5
we can now proceed to insert the values into the formula and then solve for b
D = √(x₂-x₁)² + (y₂-y₁)²
5 = √(1+3)² + (3-b)²
5 = √4² + (3-b)²
5=√16 + (3-b)²
take the squares of both-side of the equation
5² = 16 + (3-b)²
25 = 16 + (3-b)²
subtract 16 from both-side of the equation
25 - 16 = (3-b)²
9 = (3-b)²
Take the square root of both-side
√9 = 3-b
3 = 3-b
add b to both-side of the equation
3 + b = 3 - b+ b
3 + b = 3
subtract 3 from both-side of the equation
3+b-3 = 3-3
b = 0
Therefore, the value of b is 0
4.- En una pastelería han preparado 30 pasteles. Los van a colocar en bandejas de forma que en cada bandeja haya el mismo número de pasteles y no sobre ninguno. ¿De cuántas formas los puede colocar?
Answer:
7 formas
Step-by-step explanation:
En la pastelería, se han preparado 30 pasteles.
Cada bandeja contendrá la misma cantidad de pasteles.
Para encontrar de cuántas maneras puedes ponerlos, tenemos que encontrar los factores de 30. Ellos son:
1, 2, 3, 5, 6, 10, 15, 30
Esto significa que podemos tener:
30 bandejas que contienen 1 bandeja cada una
15 bandejas con 2 tortas cada una
10 bandejas con 3 tortas cada una
6 bandejas con 5 tortas cada una
5 pasteles que contienen 6 pasteles cada uno
3 bandejas con 10 pasteles cada una
2 bandejas con 15 tortas cada una
Esto significa que hay 7 formas de colocar los pasteles.
Mrs. Brown has 11 more boys than girls in her class and has a total of 28 students. Which of the following systems of equations could be used to solve this problem?
Answer:
g=number of girls in the class b=number of boy in the class
g+b=28
g=11+b
Which expression is equivalent to
Answer:
Option 2) [tex]x^{\frac{1}{8}}y^8[/tex]
Step-by-step explanation:
=> [tex](x^{\frac{1}{4} } y ^{16} )^\frac{1}{2}[/tex]
=> [tex]x^{\frac{1}{4} * \frac{1}{2} } * y ^{16*\frac{1}{2} }[/tex]
=> [tex]x^{\frac{1}{8}}y^8[/tex]
y=(x+9)÷(x-3)
Find the value of y when x=5
solution,
X=5
[tex]y = \frac{x + 9}{x - 3} \\ = \frac{5 + 9}{5 - 3} \\ = \frac{14}{2} \\ = 7[/tex]
hope this helps...
Good luck on your assignment..
Answer:
When x=5
Y=(5+9)÷(5-3)
= 14 ÷2
= 7
If you are given the graph of h(x) = log6x, how could you graph M(x) = log6(x+3)?
Answer:
Translate 3 units to the left
Step-by-step explanation: