(a) The probability of an infant has a low birth weight is equal to 1540.
(b) Won't find a probability that the event is not less than 27 and are not independent. So we need to answer that we will have to find a low both by given less than equal to the 27 point.
(c) Probability in less than equal to 36 and 8, given problem the 1 now for the probability the we have found already equal to 0692 point and for the time it will be the sum of the 3 of them.
The length of the gestation 123 under 4, and the first 1 will be small and then the came 3 weeks, and this 1 will be from the 22. The 27 weeks- and this will be the 28 to the 36 weeks- this will be the greater than the 36 weeks and we have the probability for each of them, for the first 1 will be. The 1 will be 59 point. This 1 will be the 855, and this 1 will be the ebon 9 to 82 and the next 1. We will have the call this. The means that the will be the frame is not the lowest weight, so condition will be low, and this 1 will be no more, which makes it easier now and no more no more. It will be, and this will be no more.
It will again now and then no more so from the question here even to win be less than 20, with the probability low weight equal to 1540, the common among 1 minus that equal to 46 point the next 1 for the 2227 point, the probability equal to the 1, is 13, the common 1 equals to 1 minus 0 upon , 131 minus upon 13 ease and the next 1 will on 3791 minus 379 to 621, and the last 1 will be the 1351 minus 35 o 965, and that will be the summary of The question here the question: find the probability that an infant has a child, so we have the lobed and we want to root the. By going to the first plan, and this 1 . I got you this 1 and then got you. got the last 1 and then got to the low, so we multiply them like a pair and then we add them up. So if we do it, we should get the tiptoe. We keep going like this until the last value will be on 982 time 35, and if we compute it, we will have the 4 times 4 plus 59 times upon a 13 plus 3855 times 379 plus upon 9082 times 35 equal to 0692 point for the question B, won't you find a probability that the event is not less than 27 and are not independent. So we need to answer that we will have to find a low both by given less than equal to the 27 point, so it will be between the both of them here. So we will end up the first and second 1, so we will have. It will be equal to. I will try to find the probability, the al and the less than equal to 27 point. So we'll add up this 1 and this 1 together. So we get on 5 , 59 and 10 times 13, and if we compare the 54 plus 5910 on a 135127 point and then we want to find a probability of the time with the probability point probably the end. We have equal to the 1692 we found in the time when the problem is the last time question to 27 will be the sum of the all be the 59, and we can equal to the 59 times 4 equal to the 2152 times 10 to the power. Minus 6 and it's a different form, the 127 point, so the form they are not independent and for of question c 1251 is the probability of the testation will be less than equal to the thirty. Sixth, given that this 1 by the formula equal probability in less than equal to 36 and 8, given problem the 1 now for the probability the we have found already equal to 0692 point and for the time it will be the sum of the 3 of them here on together, so it will be easy adjacent to her .0692 l minus the last 1 here will be minus 982 times 35 and if we compute it, we go have on in 82 times 35006. So let me compute again. 0.9082100. .035 point. the son from here, so let me compare again time, 5 or so 59 times upon it: 13 plus 55 times 3 on 982 times upon 35, then this 1 equal to the point 6 p. This will be correct here, 692 point. So this 1 minus 82 times 5692 point and if we compute we can equal to the 0.54071.
To learn more about length of the gestation visit here : brainly.com/question/17892801
#SPJ1
What value of d makes the equation -4-11i+2i= 3i-(4-di) true?
Answer:
d = -12
Step-by-step explanation:
[tex]3i-4-di = -4-11i+2i\\3i-4-di = -4-9i\\3i-\left(4-di\right)-3i = -4-9i-3i\\-\left(4-di\right)=-4-12i\\\frac{- 4 - di}{-1} = -\frac{4}{-1}-\frac{12i}{-1}\\\frac{-\left(4-di\right)}{-1}\\= \frac{\left(4-di\right)}{1}\\=4-id\\=\frac{- 4 - 12i}{-1}\\=-\frac{- 4-12i}{1}\\=-( - 4)-( - 12i)\\=-\left(-4\right)-\left(-12i\right)\\= 4 + 12i\\4-(id) = 4 + 12i\\4 - id - 4 = 4 + 12i - 4\\- id=12i\\\frac{-id}{-i} = \frac{12i}{-i}\\\frac{id}{i}\\= d\\- \frac{12i}{i}\\= - 12[/tex]
Evaluate. Write your answer as a fraction in simplest form. 1/2 + 7/18 + 5/6 please help me asap
Answer:
31/18 which is changed to 1³¹/¹⁸
Step-by-step explanation:
9/18+7/18+15/18 I found the lcm or the lowest common multiple of all the three and multiplied it by each fraction first then u can add all of them and put it over 18 or add each
(35 POINTS!!) Given f of x is equal to 1 over the quantity x minus 3 and g of x is equal to the square root of the quantity x plus 3, what is the domain of f (g(x))?
[–3, ∞)
[–3, 6) ∪ (6, ∞)
(–∞, 3) ∪ (3, ∞)
ℝ
Answer:
the second option
[–3, 6) ∪ (6, ∞)
Step-by-step explanation:
f(x) = 1/(x - 3)
the domain is every value of x that does not turn the denominator to 0. so, x <> 3.
g(x) = sqrt(x + 3)
the domain is every value of x that does not turn (x+3) into a negative value. so, x >= -3.
f(g(x)) = 1/(sqrt(x + 3) - 3)
the domain is all values of x that are valid for g(x) AND that do not generate range values of g(x) that violate the domain of f(x).
so, it is (x >= -3) AND (sqrt(x + 3) <> 3).
and sqrt(x + 3) = 3, if (x + 3) = 9.
that means x = 6.
so, 6 is forbidden, every other value of x is allowed here.
therefore, the domain of f(g(x)) is
(x >= -3) AND (x <> 6)
and that is equivalent to
[-3, 6) u (6, infinity)
everything larger or equal to -3 and different from 6.
Income Tax Expenses (at 25%= 4,375 and if income tax expense had been23% what would the net income have been
Based on the calculation below, the net income would have been 13,475 if income tax expense had been 23%.
How do we calculate net income?The net income when the tax rate is 23% can be calculated as follows:
Income before tax = Income tax expenses at 25% tax rate / Tax tax rate = 4,375 / 25% = 17,500
Net income at 23% tax rate = Income before tax * (100% - Tax rate of 23%)
Net income at 23% tax rate = 17,500 * (100% - 23%)
Net income at 23% tax rate = 17,500 * 77%
Net income at 23% tax rate = 13,475
Learn more about net income here: https://brainly.com/question/10207673.
#SPJ1
What is “a/b -c+d” if “a=7/8, b=-7/16, c=.8, and d=1/4”
Answer:
(7-8) / (-7/16) = -2 -(.8) + (1/4) = -.55 -2+ -.55= -2.55
Step-by-step explanation:
Target had 8x10⁹ dollars in sales last year. Explain how to find the product 8x10⁹.
Using scientific notation, The value of 8x10⁹ is 8000000000
How should a scientific notation be written?In scientific notation, the correct format is an x 10 b, where an is an integer or decimal number whose absolute value is more than or equal to one and less than ten, or 1 |a| 10. In order for the scientific notation to be mathematically identical to the original number, b must be a power of 10.
The given problem is written in scientific notation,
The multiplication of the given number will be-
8x10⁹ = 8000000000
To learn more about scientific notation from given link
https://brainly.com/question/1767229
#SPJ9
A retaining wall requires 36.8 cu yd of concrete. The combined amounts of cement, sand, and gavel should be 1 1/2 times the of concrete needed. What total amount of cement, sand, and gavel will be required?
Using proportions, it is found that the total amount of cement, sand, and gavel required is of 55.2 cubic yards.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
The decimal equivalent to the mixed number 1 1/2 is given by:
1 + 1/2 = 1 + 0.5 = 1.5.
1.5 times 36.8 cubic yards is:
1.5 x 36.8 = 55.2.
The total amount of cement, sand, and gavel required is of 55.2 cubic yards.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
Tom developed the following scientific question Do boys score higher on IQ than girls He gives the same IQ tests to two 12 years old boys and two 12 years old girls. After checking the IQ scores on the tests he realizes that the two girls had a much higher average score than the two boys He concluded that girls have higher IQs than boys
What is wrong with the experiment:
Not Ethical
not a random example
biased replication needed sample size too small
needs a control
did not use safety skills
more than one independent variable
Data does not make sense with problem statement
Conclusion does not make sense with the data and problem statement
Name:
Independent Variable
Dependent Variable
Constant
Control
How can you improve the experiment
1. The experiment conducted by Tom is wrong because of the following:
Not a random example (sample)Sample size is too small.2. The independent variable is the IQ test while the dependent variables are the IQ scores of the four boys and girls. The constant is the number of testers. There is no control.
3. To improve the experiment, Tom needs to increase the sample sizes of boys and girls to at least 50 boys and 50 girls to make the generalization reasonable. He should obtain the IQ scores of girls as a control to compare the IQ scores of boys.
What is an experiment?An experiment is a scientific study conducted to support or refute a hypothesis.
An experiment involves observations and actions performed to solve a problem or make a discovery.
Thus, Tom's experiment should be improved with research methodologies.
Learn more about experiments at https://brainly.com/question/17274244
#SPJ1
Use the graph of f to determine each of the following.
(a) the domain of f
(b) the range of f
(c) the zero(s) of f
(d) f(-3.5)
(e) the intervals on which f is increasing
(f) the intervals on which f is decreasing
(g) the values for which f(x) ≤0
(h) any relative maxima or minima
(i) the value(s) of x for which f(x) = 3
() Is f(0) positive or negative?
(a) the domain of f would be an interval (−3,6]
(b) the range of f would be an interval (−6,3]
(c) the zero(s) of f are x = −0.5 and x=6.
(d) the value of f(-3.5) would be 2
(e) the intervals at (−3,3) which f is increasing
(f) the intervals at (3,6] which f is decreasing
(g) the values are (−3,−0.5] for which f(x) ≤0
(h) x = 3 which is a relative maximum point
(i) the value of x is 3 for which f(x) = 3
(j) the function would be positive if f(0)
What are the domain and range of the function?The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.
The domain of the function shown in the graph is given by the set of values x that has a point on the graph.
In other words, by launching the graph onto the x-axis we will cover the interval (−3,6]
The range of the function shown in the picture is given by the set of values y that has a point on the graph.
In other words, by launching the graph onto the y-axis we will cover the interval (−6,3]
The zeros of the function are the x-intercepts of the function, so the zeros are x = −0.5 and x=6.
The value of f(-3.5) is given by the y- coordinate of the point of intersection of the graph with the vertical line x=-3.5 So, f(-3.5)≈2.
The function is increasing whenever the y- coordinate increases if we trace the graph in the direction of positive x values.
So, the graph is increasing on (−3,3), where x=3 corresponds to the x- coordinate of the turning point on the graph.
The function is decreasing whenever the y- coordinate decreases if we trace the graph in the direction of positive x values.
So, the graph is decreasing on (3,6].
The values of x where f(x) ≤0, correspond to the points where the graph is below the x-axis, so the values of x for which f(x) ≤0 are (−3,−0.5].
The relative maxima or minima are the x-coordinate points where the continuous function has a turning point, like x=3 which is a relative maximum point
.
There are no relative minimum points for the given function.
The value of x for f(x)=3 is the x- coordinate of the point of intersection of the graph with the horizontal line y=3
So, x≈3.
we will determine the y = coordinate of the point of intersection of the graph with the vertical line
x=0, which is above 2, so f(0) is positive.
Therefore, the domain of the function is interval (−3,6], and the range of the function is interval (−6,3].
Learn more about the domain and the range here:
brainly.com/question/21027387
#SPJ1
5. Look at the model and fill in each blank with the correct answer.
bigger
smaller
?
5526
3496
?
(a) The smaller number is
(b) The difference between the two numbers is
(c) The sum of the two numbers is_
The smaller number is 3496
The difference between the two numbers is 2030
The sum of the two numbers is 9022
Given no.
5526,3496
The difference between the two numbers is 5526-3496=2030
The sum of the two numbers is 5526+3496=9022
The process of combining two or more objects is known as addition. The procedure of determining the sum of two or more integers in mathematics is known as addition. It is a basic mathematical operation that we all employ on a daily basis. When we work with money, compute our shopping bills, or calculate the time, we employ addition frequently.
Addition is a mathematical procedure that is used to add numbers. The sum of the provided numbers is the outcome of adding the supplied numbers. For instance, if we add 2 and 3, (2 + 3), the result is 5. We used the addition function on two integers, 2 and 3, to produce the sum, 5.
To learn more about Addition from the given link:
https://brainly.com/question/14092461
#SPJ9
Megan wants to purchase 2
1/2
pounds of chocolate pretzels for lunch this week. If each pound cost $3.48, how much will she
spend on pretzels?
PLEASE WORK OUT ANSWER
Answer: $8.70
Step-by-step explanation: $3.48 x 2 for the 2 pounds. You divide 3.48/2 to get the half pound. 3.48 x 2 = 6.96. 3.48/2=1.74. 1.74 + 6.96 = $8.70
Answer:
Step-by-step explanation:
$3.48 x 2 for the 2 pounds. You divide 3.48/2 to get the half pound. 3.48 x 2 = 6.96. 3.48/2=1.74. 1.74 + 6.96 = $8.70
The median annual salary for an event planner is $60,900. If the event planner pays an
8% income tax, how much money in dollars and cents will the event planner pay for
income tax?
Sunt
Answer:
$4,872.00
Step-by-step explanation:
Convert 8% into a decimal and multiply
$60,900.00 x 0.08 = $4,872.00
-4ca: use a = 2. and c = -5
Answer:
40
Step-by-step explanation:
For this equation, all we do is simply plug in the values.
-4 (c) (a)
-4 (-5) (2)
-4*-5*2
Now, multiply, and you get your answer.
-4 * -5 = 20
20 * 2 = 40
40 is your answer
Triangle BCD has the following side lengths: BC = 60, CD = 50
Triangle RST has the following side lengths: RS = 11x-4, ST = 70
What is the value of x?
What is the length of the side RS
Answer:
c.x=9sr=95
THATS THE ANSWER PO.
The value of the variable x will be 88. Then the length of the side RS will be 84.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
If two triangles are similar, then the ratio of the corresponding sides will remain constant.
Triangle BCD has the following side lengths: BC = 60, CD = 50.
Triangle RST has the following side lengths: RS = 11x-4, ST = 70.
The triangle BCD and RST are similar triangles. Then we have
RS / ST = BC / CD
11x - 4 / 70 = 60 / 50
11x - 4 = 84
11x = 88
x = 8
Then the length of the side RS will be
RS = 11x - 4
RS = 11 × 8 - 4
RS = 88 - 4
RS = 84
The value of the variable x will be 88. Then the length of the side RS will be 84.
More about the triangle link is given below.
https://brainly.com/question/25813512
#SPJ2
Divide. (6x³ + 2x² + 3x −4) ÷ (x² + 3x +4)
6x³ + 2x² + 3x - 4 is not exactly divisible by x² + 3x - 4.
Given,
The expression : 6x³ + 2x² + 3x - 4
We have to divide the given expression by x² + 3x - 4.
Let's take 6x³ + 2x² + 3x - 4 as p(x) and x² + 3x - 4 as g(x).
If p(x) is divisible by the factors of g(x), then p(x) is divisible by g(x).
So, let's factorize x² + 3x - 4
x² + 3x - 4 = (x - 1) (x + 4)
Now,
p(x) = 6x³ + 2x² + 3x - 4
By using remainder theorem,
If p(1) = 0 and p(4) = 0, then p(x) is divisible by g(x).
So,
p(1) = 6 × 1³ + 2 x 1² + 3 x 1 -4
p(1) = 6 + 2 + 3 - 4
p(1) = 11 - 4
p(1) = 7
Next,
p(4) = 6 x 4³ + 2 x 4² + 3 x 4 - 4
p(4) = 6 x 64 + 2 x 16 + 12 - 4
p(4) = 384 + 32 + 12 - 4
p(4) = 424
Here, p(1) and p(4) is not 0.
So, p(x) is not divisible by g(x).
That is, 6x³ + 2x² + 3x - 4 is not exactly divisible by x² + 3x - 4.
Learn more about divisibility here:
https://brainly.com/question/1591815
#SPJ1
the value of 86 in a dataset with the mean 101 and the standard deviation 19
The z-score of the value is -0.79
How to determine the z-score of the value?The given parameters are
Value = 86
Mean = 101
Standard deviation = 19
The z-score of the value is calculated using
z= (Value - Mean)/Standard deviation
This gives
z = (86 - 101)/19
Evaluate
z = -0.79
Hence, the z-score of the value is -0.79
Read more about z-score at:
https://brainly.com/question/25638875
#SPJ1
The mass of flour in a bag is about 141.6 grams. You add about 10.19 grams of flour to the bag. What is the mass of flour in the bag to the nearest tenth of a gram
The tenth of a gram closest to it is 151.79 grams.
The flour's mass is 141.6 grams.
10.19 grams are added.
The amount of flour in the bag =141.6+ 10.19
= 151.79.
A physical quantity is mass. The weight of a body serves as the unit of mass measurement. It can be measured in normal mass quantities such grams, kilograms, and pounds. Although grams are used to measure smaller objects, the kilogram is the SI unit of mass.
In the metric measurement system, a gram is a unit of weight that is one thousandth of a kilogram. When something is extremely light, its weight is measured in grams.
Therefore, 151.79 grams of flour, to the nearest tenth of a gram, are in the bag.
To learn more about mass, visit:
brainly.com/question/941818
#SPJ1
Select all that have a value of 0.
cos π/2
cos 0
sin 0
sin 3π/2
tan π
Answer:
cos(π/2)sin(0)tan(π)Step-by-step explanation:
You want to know which trig functions on the given list have a value of zero.
Trig functionsSine
The sine function is zero at x=0 and multiples of π.
Cosine
The cosine function is zero at x = π/2 and for odd multiples of π.
Tangent
The tangent function is zero at x=0 and multiples of π. It is zero in the same places the sine function is zero.
List valuesThese values are zero:
cos(π/2)sin(0)tan(π)These function values are something different:
cos(0) = 1sin(3π/2) = -1find the 31st term 2,10,18
Answer:
242
Step-by-step explanation:
Help please with my math
The percentage of the actual salary that actual mortgage is is 30%.
What is the percentage of actual mortgage?Percentage is the fraction of an amount that is expressed as a number out of hundred. Percentage is a measure of frequency. The sign used to show percentage is %.
In order to transform a number into a percentage, express it as a fraction of a total amount and multiply by 100. So, actual mortgage would be divided by actual budget, the fraction would then be multiplied by 100.
Percentage of actual salary that is actual mortgage = (actual mortgage / actual salary) x 100
(1080 / 3600) x 100 = 30%
To learn more about percentages, please check: https://brainly.com/question/25764815
#SPJ1
Angela is arranging 32 framed pictures on a wall. How
can she arrange her pictures in equal rows? Find all
possible arrangements.
Answer:
1×32
2×16
4×8
8×4
16×2
32×1
Step-by-step explanation:
This question about arranging pictures is just trying to get you to explore the factors of 32, maybe for practicing the math ideas of factoring, or area, or max/min, or matrices.
Think of what numbers go into 32:
1, 2, 4, 8, 16, 32
Pair them up!
1×32 and 32×1 will look differently if they are pictures on a wall. So we'll list them separately. Then there's also 2×16 and 16×2, and 4×8 and 8×4.
Fill in the blanks below in order to justify whether or not the mapping down represents a function
Answer:
The mapping diagram above represents a function since there is one number in Set A (the input) where there is only one mapping to Set B (the output).
Step-by-step explanation:
For each number in set A, there is one mapping from set A (input) to set B (output), so the mapping represents a function.
NB. The relation is a function IF AND ONLY IF each input value has only 1 output value.
The domain of f(x) is all real numbers & satisfies f(x+1)=2f(x).
For [tex] \sf x \in(0,1],[/tex] f(x)=x(x+1). For value [tex]\sf x \in( - \infty ,m],[/tex] f(x)[tex] \geq \dfrac{ - 8}{9}. [/tex] What is the value of m?
The domain of f(x) is all real numbers & satisfies function f(x+1)=2f(x).
For x∈(0,1], the function f(x)=x(x-1). For value x∈(-[tex]\infty[/tex],m], f(x)≥[tex]\frac{-8}{9}[/tex]. What is the value of m?
the smallest value m=[tex]\frac{7}{3}[/tex].
Given that, for x∈(0,1], f(x)=x(x-1)
Let's plot this function
We'll go from 0 to 1 and let's graph what this function is look like
f(x)=x(x-1) will be a parabola and it's going to go between the points (0,0) and (1,0).
Will graph it in figure1 we can see.
The minimum value of this parabola is right in the middle and it is
f(0.5)=-0.25
Now, let try and graph the function in the other intervals
We know f(x+1)=2f(x)
Now we can evaluate couple of points
f(0+1)=2f(x)
f(0.5+1)=2f(0.5)
f(1+1)=2f(1)
And we quickly deduce that the graph in(1,2] is twice the height of the graph in (0,1].
We will graph a parabola in figure 2 we can see.
This parabola is going to have a graph of 2 between its twice as tall and this can be multiplied by the quantity of (x-1) multiplied by the quantity of (x-2).
It is 2(x-1)(x-2).
We graph next interval twice the height of the graph in the interval from 2 to 3. We can see the graph in figure3.
This parabola will have an equation 4 times the quantity of (x-2) and (x-3).
We can also shift this graph to the left and it going to be half the height.
Looking at this graph we want f(x)≥[tex]\frac{-8}{9}[/tex].
In the 3 interval from 2 to 3 its going to intersect .
we want to look for the points where f(x)≥[tex]\frac{-8}{9}[/tex].
We are looking for m which f(x)≥[tex]\frac{-8}{9}[/tex].
parabolas equation =[tex]\frac{-8}{9}[/tex].
4(x-2)(x-3)=[tex]\frac{-8}{9}[/tex]
[tex]x^{2} -5x+6=\frac{-2}{9} \\(x-\frac{7}{3})(x-\frac{8}{3})=0\\ x= \frac{7}{3},\frac{8}{3}\\\\[/tex]
Therefore, We will take the smallest value m=[tex]\frac{7}{3}[/tex].
To learn more about function visit:https://brainly.com/question/12183687
#SPJ1
Today, Sarah counted all of the wheels of all of the cycles in the shop. She found that there were 30 wheels in all. There were the same number of bikes as there were trikes. How many bikes were there? How many trikes were there? Show how you figured it out.
Answer:
Step-by-step explanation:
Bicycles have two wheels whereas Trikes have 3 wheels. Let x be the number of bicycles2x=30[tex]\frac{2x}{2} =\frac{30}{2} \\x=15[/tex]There were 15 bicyclesLet y be the number of trikes3x=30 since there were same number of trikes as bicycles[tex]\frac{3y}{3} =\frac{30}{3} \\y=10[/tex]There were 10 Trikes-3x+2<8 and 1/2x-5<-3
The values of x in the inequalities are x< -2 and x < 4
How to determine the valuesGiven the inequalities;
-3x+2<81/2x-5<-3To determine the value of x for each, we have;
-3x + 2 < 8
collect like terms
-3x < 8 - 2
-3x < 6
Make 'x' the subject
x < 6/ -3
x< -2
1/2x - 5 < -3
Find the Lowest common multiple
x - 10 / 2 < -3
cross multiply
x - 10 < -3 × 2
x - 10 < -6
collect like terms
x < - 6 + 10
x < 4
Thus, the values of x in the inequalities are x< -2 and x < 4
Learn more about inequalities here:
https://brainly.com/question/25275758
#SPJ1
please help
please hurry
Hay 12 estudiantes en una clase que se presentan en el concierto de la escuela. Esto representa el 40% de la clase. ¿Cuántos estudiantes hay en la clase?
Mediante el uso de porcentajes, concluimos que la clase tiene una población total de 30 estudiantes.
¿Cuál es la cantidad de estudiantes de la clase?
En este problema tenemos a 12 estudiantes procedentes de una clase que participan en un evento cultural de su escuela y también se conoce que equivalen al 40 por ciento de su clase. El total de estudiantes de la clase se obtiene al dividir el número de estudiantes por el porcentaje:
x = 12 / 40 %
x = (12 · 100) / 40
x = 30
La clase tiene una población total de 30 estudiantes.
Para aprender más sobre porcentajes: https://brainly.com/question/23935688
#SPJ1
Find the angle of elevation of the sun from the ground to the top of a tree when a tree that is 10 yards tall casts a shadow 14 yards long. Round to the nearest degree.
The angle of elevation of the sun from the ground to the top of a tree is 36°.
We are given that:
The sun from the ground to the top of a tree when a tree that is 10 yards tall casts a shadow 14 yards long.
Now by using the trigonometric identity .
tan θ = P / B
As figure is given below .
AB = Perpendicular = 10 yards
BC = Base = 14 yards
Putting all the values in the trigonometric identity .
tan θ = 10 / 14
θ = 36°
Therefore, the angle of elevation of the sun from the ground to the top of a tree is 36°.
Learn more about angle of elevation here:
https://brainly.com/question/1851601
#SPJ9
Suppose that between the ages of 22 and 40, you contribute $3000 per year to a 401(k) and your employer contributes $1500 per year on your behalf. The interest rate is 8.3% compounded annually. What is the value of the 401(k) rounded to the nearest dollar after 18 years? b) Suppose that after 18 years of working for this firm, you move on to a new job. However, you keep your accumulated retirement funds in the 401(k). How much money to the nearest dollar, will you have in the plan when you reach 65? c) What is the difference between the amount of money you will have accumulated in the 401(k) and the amount you contributed to the plan?
The amount of money accumulated after 18 years at compound interest is $192429.71 . At 65 there will be $1412484.01 in the account.
Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
The compounding interest formula when there are annual contributions is:
[tex]A=P(1 + r)^Y + c[ ((1 + r)^Y - 1) / r ][/tex]
Where P is the principal amount which is 4500,
r is 8.3% = 0.083
Y is the number of years which is 18 .
and C is the annual contributions which is equal to P
Therefore:
[tex]A=4500(1 + 0.083)^{18} + 4500[ ((1 + 0.083)^{18} - 1) / 0.083 ]\\\\A=192429.71[/tex]
Hence the amount of money in the account is $192429.71
Now the principal is $192429.71 and the rate is 0.083 , now it is a compound interest and time is 65 - 40 = 25 years.
[tex]A = P(1+0.083)^{25}[/tex]
[tex]A = 192429.71(1+0.083)^{25}\\\\A= 1412484.01[/tex]
Hence the total money accumulated is $1412484.01
c) Total money put in the account = 3000 × 18 = 54000
Difference = $1412484.01 - $ 54000 = $ 1358484.01
To learn more about compound interest visit:
https://brainly.com/question/13155407
#SPJ1
Write as a Rate.
2 teachers for every 19 students
