Hello,
I hope you and your family are doing well!
a. The variable t represents the number of years since 1999, so the constraints for t can be written as t ∈ {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.
b. To find the value of S(7), we substitute t = 7 into the function: S(7) = 1.084(7) + 17.392 = 22.688.
c. In context, the value of S(7) represents the amount of money, in billions of dollars, that the US government spent on science, space, and technology 7 years after 1999.
d. The key feature that is found when solving S(t) = 0 is the y-intercept of the graph of S(t). The y-intercept is the point where the graph crosses the y-axis.
e. The value for S(t) = 0 is not reasonable for the context because it represents the amount of money spent on science, space, and technology in 1999, which would be a negative number of years after 1999.
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Breaking strengths of a random sample of 28 molded plastic housing were measured, and a sample standard deviation of S=19.52 was obtained. A confidence interval (439.23, 460.77) for the average strength of molded plastic housings were constructed from these results. What is the confidence level of this confidence interval?
The confidence interval of this confidence level as calculate from the given data is 3.68 and 99% respectively.
Number of random sample (n)=28
Sample Standard deviation (S)=19.52
Confidence interval = 439.23 - 460.77 = 21.54
t = s/root of n
=19.52 /5.29
=3.68
v = n -1 = 27
now, confidence level
= 1 - alpha
= 99%
Confidence Interval, put simply, is a range within which we are confident that the genuine value exists. The probability that a confidence interval will contain the real parameter value depends on the confidence level that is chosen for the interval.
The phrase "Confidence Interval" refers to the range of values that is typically used to handle population-based data, extracting precise, important information with a given level of confidence.
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Devaughn's age is three times Sydney's age. The sum of their ages is 116. What is Sydney's age?
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I hope you and your family are doing well!
Let's call Sydney's age x and Devaughn's age y. We know that y = 3x and x + y = 116.
Substituting the first equation into the second equation gives:
3x + x = 116
4x = 116
x = 29
So Sydney's age is 29.
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PLS HELP! 70 POINTS!!
Mr. Mudd gives each of his children $2000 to invest as part of a friendly family competition. The competition will last 10 years. The rules of the competition are simple. Each child can split up his or her $2000 into as many separate investments as they please. The children are encouraged to do their research on types of investments. The initial investments made may not be changed at any point during the 10 years; no money may be added and no money may be moved. Whichever child has made the most money after 10 years will be awarded an additional $10,000.
The table shows the investment made by each of Mr. Mudd’s children, and what happened to their investment over the decade long friendly competition.
Child Performance of investments over the course of the competition
Albert $1000 earned 1.3% annual interest compounded monthly
$500 lost 3% over the course of the 10 years
$500 grew compounded continuously at rate of 0.7% annually
Marie $1500 earned 1.3% annual interest compounded quarterly
$500 gained 3% over the course of 10 years
Hans $2000 grew compounded continuously at rate of 0.8% annually
Max $1000 decreased in value exponentially at a rate of 0.6% annually
$1000 earned 1.9% annual interest compounded biannually (twice a year)
Make sure to show your work
1. What is the balance of Albert’s $2000 after 10 years?
2. What is the balance of Marie’s $2000 after 10 years?
3. What is the balance of Hans’ $2000 after 10 years?
4. What is the balance of Max’s $2000 after 10 years?
5. Who is $10,000 richer at the end of the competition?
Answer:
Albert = $2159.07; Marie = $2244.99; Hans = $2188.35; Max = $2147.40
Marie is $10 000 richer
Step-by-step explanation:
Albert
(a) $1000 at 1.2 % compounded monthly
A = P (1 + r/n )^nt
A = 1000(1 + 0.001)¹²⁰ = $1127.43
(b) $500 losing 2%
0.98 × 500 = $490
(c) $500 compounded continuously at 0.8%
A = Pe^rt
= 500e^0.008 * 10
= $541.64
(d) Balance
Total = 1127.43 + 490.00+ 541.64 = $2159.07
Marie
(a) 1500 at 1.4 % compounded quarterly
A = 1500(1 + 0.0035)⁴⁰ = $1724.99
(b) $500 gaining 4 %
1.04 × 500 = $520.00
(c) Balance
Total = 1724.99 + 520.00 = $2244.99
Hans
$2000 compounded continuously at 0.9 %
A = 2000e^0.009 * 10
= $ 2188.35
Max
(a) $1000 decreasing exponentially at 0.5 % annually
A = 1000(1 - 0.005)¹⁰= $951.11
(b) $1000 at 1.8 % compounded biannually
A = 1000(1 + 0.009)²⁰ = $1196.29
(c) Balance
Total = 951.11 + 1196.29 = $2147.40
Marie is $10,000 richer at the end of the competition.
Hope this helps!!! :)
(a) The diameter of Mars at its equator is approximately 6.79*10^3 kilometers. Write this number in standard notation.
Answer:
6790 km
Step-by-step explanation:
move the decimal 3 places to the right.
The owner of a factory wants to determine a confidence interval for the average wages at his factory. The population average wages is unknown. However, the owner was able to take a random sample of 64 workers. He found that the average salary for this sample of workers is $50,000. The population standard deviation is $3000. He calculated a 99% confidence interval for the population average wages at the factory. Which of the following choices is correct? Assume the distribution of wages is normally distributed.
4,034.06 ,5,965.94 are confidence interval for the population average wages at the factory.
What is confidence interval estimation?
Your estimate's mean plus and minus the range of that estimate's fluctuation is called a confidence interval.
If you repeat your test, you can expect your estimate to fall between these numbers with a reasonable degree of certainty. Another term for probability in statistics is confidence.
The formula for confidence interval estimation is:
μ = M ± Z(sM)
where:
M = sample mean
Z = Z statistic determined by confidence level
sM = standard error = √(s2/n)
M = 50000
Z = 2.58
sM = √(30002/64) = 375
μ = M ± Z(sM)
μ = 50000 ± 2.58*375
μ = 50000 ± 965.94
μ = 4,034.06 ,5,965.94
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"a. What was the population of the state in 2000 ?
b. When will the population of the state reach 28.3 million?
a. In 2000 , the population of the state was million."
In 2000, the population of the state was 23.1 million, After 13 years , the population of the state reach 28.3 million.
What is population?
The term "population" refers to all citizens who are present in a nation or who are temporarily absent from it, as well as all aliens who have made a nation their permanent home. The number of residents in a given area is depicted by this indicator. The annual changes in population brought on by births, deaths, and net migration are measured as growth rates.
Given:
[tex]A = 23.1e^0^.^0^1^5^2^t[/tex] models the population of US
where A is in million
t is years after 2000.
(a) We have to find the population in 2000.
In 2000, t = 0
Plug t = 0 in the above equation
[tex]A(0) = 23.1e^0^.^0^1^5^2^(^0^)\\A = 23.1[/tex]
Hence, in 2000 the population is 23.1 million.
(b) To find when the population of the state reach 28.3 million.
Plug A = 28.3 in above equation and solve for t.
[tex]28.3 = 23.1e^0^.^0^1^5^2^t\\e^0.0152t = \frac{28.3}{23.1} \\t*ln(0.0152) = ln( \frac{28.3}{23.1})\\t = 13.35718\\t = 13[/tex]
Hence, after 13 years the population of the state reach 28.3 million.
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In a lottery game, a player picks six numbers from 1 to 28. If the player matches all six numbers, they win 50,000 dollars. Otherwise, they lose $1.
What is the expected value of this game?
The expected value of this game will be 1,784.75.
What is the expected value?In parameter estimation, the expected value is an application of the weighted sum. Informally, the expected value is the simple average of a considerable number of individually determined outcomes of a randomly picked variable.
The expected value is given below.
E(x) = np
Where n is the number of samples and p is the probability.
In a lottery game, a player picks six numbers from 1 to 28. Assuming the player matches each of the six numbers, they win 50,000 bucks. In any case, they lose $1.
Then the probability of winning (p) and losing (q) is given as,
p = 1 / 28
q = 27 / 28
Then the expected value is given as,
E(x) = 50,000 (1 / 28) - 1 (27 / 28)
E(x) = 1785.714 - 0.964
E(x) = 1,784.75
The expected value of this game will be 1,784.75.
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In a video game, Clare scored 50% more points than Tyler. If c is the number of points that Clare scored and t is the number of points Tyler scored, which equations, are correct?
Answer:
c= 1.5t, c=t+0.5t and c=(1+0.5)t
Step-by-step explanation:
Given that, Clare scored 50% more points than Tyler, c is the number of points that Clare scored and t is the number of points that Tyler scored,According to question,c = 150% of tc = 1.5tHence, the correct options are c = 1.5t, c = t+0.5t and c = (1+0.5)t
Complete the square by adding the correct missing term on the left, then factor as indicated:
x²+x+_____________=(_____)²
The complete sentence will be;
⇒ x² + x + 1/4 = ( x + 1/2)²
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.
Given that;
The expression is,
⇒ x² + x + __ = (_____)²
Now,
Since, The expression is,
⇒ x² + x + __ = (_____)²
Hence, We can add the number to form the complete square as;
⇒ x² + x + 1/4 = x² + x + (1/2)²
= ( x + 1/2)²
Thus, The complete sentence will be;
⇒ x² + x + 1/4 = ( x + 1/2)²
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a hemispherical tank is filled with water and has a diameter of 10 feet. if the water weighs 62.4 pounds per cubic foot. what is the total weight of the water in a filled tank
The total weight of the water in a filled tank will be equal to 16,336 Pounds.
What is Volume?
Every three-dimensional item takes up space in some way. The volume of this area is what is used to describe it. The area covered within an entity's three-dimensional bounds is referred to as its volume. The object's size is another name for it.
As per the given data in the question,
Radius, r = 10/2 = 5 ft.
Use the equation of the volume of a sphere,
V = 4/3πr³
We only require half of it then,
V = 2/3πr³
V = 261.8 ft³
So, the total weight will be,
W = 261.8 × 62.4
W = 16,336 Pounds.
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WORD PROBLEM:
When the square of a certain number is added to the number, the resu;t is the same as when 48 is added to three times the number. Find the number.
Answer:
Step-by-step explanation:
Let x be the number.
The square of the number is x2
Increased by twice the number means add 2x.
So your equation is :
X2 +2x = 48.
Can you take it from here?
The asked number is 12.
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, When the square of a certain number is added to the number, the result is the same as when 48 is added to three times the number.
Let the number be x,
x²+x = 48X3 + x
x² = 144
x = 12
Hence, The asked number is 12.
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Question 5 (1 point)
Dev has a monthly food budget of $182. He maps the amount of money, x, he spends each month to the number of food items he buys.
What are the constrains on the domain?
O a
domain:x>182
Ob
domain: x20
Oc domain: x ≤182
Od domain: 0≤x≤182
For the function in the given case the constraint on domain can be written as x ≥ 182. The correct option is (a).
What is a function?A function y = f(x) is a one to one relationship between two sets X and Y where the set X is called the domain and Y the range of function f(x) ans x ∈ X and y ∈ Y.
Suppose the amount of money spent be x.
And, the number of food items be y.
Now, as per the question the function can be written as follows,
y = x/182
As the number of food items can only be positive integers, the values of x must be the multiples of 182.
Thus, the expression for the domain can be written as x ≥ 182.
Hence, the constraint on the domain is given as x ≥ 182.
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In a recent year 365 days a hospital had 5814 births. find the mean number of births per day
Answer:
ANS:- 15.9
Step-by-step explanation:
5814/365 = 15.9
What is the value of p in the equation p3=−0.027 ?
Answer:I hope this helpful mark me brainlist if correct then no if wrong
Step-by-step explanation:
P times 3 =-0.0027
Use the commutative property to reorder the terms
3p=-0.0027
Divide both sides of the equation by 3
p=-0.009 or p=-9/1000
M < a = ?
M < d = ?
please help!!
Answer:
m∠A = 60
m∠D = 60
Step-by-step explanation:
∆ABC and ∆DEF are congruent triangles
So,
m∠A = m∠D
x + 30 = 2x
2x - x = 30
x = 30
So,
m∠A = x + 30 = 30 + 30 = 60
m∠D = 2x = 2(30) = 60
Thus, m∠A and m∠D are 60°
Find m in equation, W=1/2*m*v squared?
Answer: To find the value of m in the equation W = 1/2 * m * v^2, you need to know the values of W and v. The variable m represents the mass of the object, and W represents the kinetic energy of the object. The equation states that the kinetic energy of an object is equal to 1/2 of its mass multiplied by its velocity squared.
If you are given the values of W and v, you can solve for m by rearranging the equation as follows:
m = 2 * W / v^2
Plugging in the values of W and v will give you the value of m.
For example, if W = 100 joules and v = 10 meters per second, the equation would be:
m = 2 * 100 joules / 10 m/s^2 = 20 kilograms
This is the mass of the object.
[tex]m=\frac{2W}{v^{2} }[/tex].
Step-by-step explanation:1. Write the expression.[tex]W=\frac{1}{2} mv^{2}[/tex]
2. Divide both sides of the equation by [tex]\frac{1}{2}[/tex] and [tex]v^{2}[/tex].[tex]\frac{W}{\frac{1}{2} v^{2} }=m\\ \\[/tex]
3. Rewrite and simplify.[tex]m=\frac{W}{\frac{1}{2} v^{2} }\\ \\m=\frac{2W}{v^{2} }[/tex].
After Becca's half-marathon, her pedometer showed 23, 580 steps, while Alex recorded
2.42 x 104 steps after the same race. What is the combined amount of their steps?
A
4.778 x 103 ; 4,778
B
2.3822 x 104 ; 23,822
C
4.778 x 104 ; 47, 780
D
4.808 x 104 ; 48,080
Answer:
Below
Step-by-step explanation:
2.42 x 10^4 = 24200
24200
+ 23580
47 780 or 4.778 x 10^4
A rectangle is 5 inches long and 2x inches wide. The value of the perimeter in inches) is equal to the value of the area (in square inches). Find x.
Answer:
the width of the rectangle is -5/3 inches.
Step-by-step explanation:
To find the perimeter of the rectangle, we add together the lengths of all four sides. Since the rectangle is 5 inches long and 2x inches wide, the perimeter is given by:
Perimeter = 5 + 2x + 5 + 2x = 10 + 4x
To find the area of the rectangle, we multiply the length by the width. The area is given by:
Area = 5 * 2x = 10x
Setting the perimeter equal to the area, we have:
10 + 4x = 10x
Subtracting 10 from both sides, we have:
4x = 10x - 10
Combining like terms, we have:
-6x = -10
Dividing both sides by -6, we have:
x = 10 / -6
Simplifying, we have:
x = -5/3
3. The diameter of an atom is 0.0000000001 inches. Which of these is an appropriate
estimate for the diameter of an atom?
1×10-10
A.
B.
1×10-9
C. 1×10¹0
D. 1×1019
in.
in.
in.
in.
Answer:
a. [tex]1 * 10^{-10}[/tex]
Explanation:
A converted to standard notation is the same number.
The vertices of a rectangle are W(1, 2) X(4, 2) Y(4, 23) and Z(1, 23) Find the perimeter of the rectangle. Use words, numbers, or models to justify your answer.
The vertices of a rectangle are W(1, 2) X(4, 2) Y(4, 23) and Z(1, 23) Find the perimeter of the rectangle is 16.
Step-by-step explanation:We could use the distance formula to find the distance between the points in this problem, but when we look we see that the sides of the rectangle are parallel to the x and y-axis for each pair of sides. The first two points have a distance of 3 because 4-1=3. Since it is a rectangle, the opposite side will have the same length. For the sides perpendicular, we look at the points with the same x coordinate. Using (4,2) and (4,-3), we can calculate the length of the side by finding the distance by adding the absolute values of the y coordinate. 2+3=5. This means that the triangle has two sides with a length of 5 and two sides with a length of 3. Adding these together, 5+5+3+3 = 16.
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5400 dollars is placed in an account with an annual interest rate of 6.75%. To the nearest tenth of a year, how long will it take for the account value to reach 11200 dollars?
The time needed for the account value to reach 11200 dollars is approximately 15.9 years.
What is the time required to reach the accrued amount?Simple interest formula is expressed as;
A = P( 1 + rt )
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given the data in the question;
Accrued amount A = $11200 Principal P = $5400Interest I = 6.75%Time r = ?Plug the given values into the above formula and solve for time t.
A = P( 1 + rt )
A/P = 1 + rt
( A/P - 1 ) = rt
t = ( A/P - 1 ) / r
t = ( $11200/$5400 - 1 ) / 6.75%
t = ( $11200/$5400 - 1 ) / 6.75/100
t = ( 56/27 - 1 ) / 0.0675
t = ( 29/27 ) / 0.0675
t = 15.9 years.
Therefore, the required time to reach the accrued amount is 15.9 years.
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What is the area of a semicircle with a diameter of 20?
Answer:
[tex]\huge\boxed{\sf 157.1 \ units^2}[/tex]
Step-by-step explanation:
Diameter = 20
Radius = Diameter/2 = 20/2 = 10
Area of semicircle:[tex]\displaystyle =\frac{\pi r^2}{2} \\\\r = 10\\\\= \frac{\pi (10)^2}{2} \\\\= \frac{100 \pi}{2} \\\\= \frac{314.2}{2} \\\\= 157.1 \ units^2\\\\\rule[225]{225}{2}[/tex]
Maximize: Profit = 20x + 30y
Constraints:
x + y <12
x + 2y<12
2x + y<12
x>0
y>0
Answer:
x> -10
Step-by-step explanation:
-6x+3y=24 in slope intercept form
Answer:
y=2x+8
Step-by-step explanation:
-6x+3y=24
-6x+6x+3y=24+6x ==> isolate the y variable
3y=6x+24 ==> simplify
(3y=6x+24)/3
y=2x+8 <== y=mx+b <== slope intercept form
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can someone help me with this circle question asap
The point which satisfies equation is (-2,4)
What is circle?
A circle could be a form consisting of all purposes during a plane that are at a given distance from a given point, the centre.
Main body:
The center of circle formula is also known as the general equation of a circle. In a circle, if the coordinates of the center are (h,k), r is the radius, and (x,y) is any point on the circle, then the center of circle formula is given below:
Formula of circle =
(x - h)² + (y - k)² = r²
According to question:
center of circle = (2,1)
diameter of circle = 10 units
radius = 5 units
equation of circle ⇒
(x - 2)² + (y - 1)² = 25
for a point to lie on circle , it need to satisfy the equation of circle:
A) (1,-3)
⇒(1 - 2)² + (3 - 1)²
⇒(-1)² +2²
⇒5
so it does not lie on circle.
B) (-2,4)
⇒(-2 - 2)² + (4 - 1)²
⇒-4²+3²
⇒ 25
so, it satisfies the equation.
hence, the point which satisfies equation is (-2,4)
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the manager of a theater wants to know whether the majority of its patrons are adults or children. One day, 5100 tickets were sold and the receipts totaled $29,484. The adult admission is $7.50, and the children's admission is $4.50. How many adult patrons were there
We can estimate the number of adult partons at 2187 by solving equations.
What do we mean by equations?The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions.
A function is an equation that has only one answer for y for every possible value of x.
When utilizing a function, each input of a specific type receives exactly one output.
A function is commonly referred to as f(x) or g instead of y. (x).
Because f(2) instructs us to do so, we should figure out the value of our function when x is equal to 2.
So, the total number of adults present was thus:
Let a be an adult, and b and c be kids.
Ticket totals:
a + c = 5200
c = (5200-a)
Total amount:
7.50a + 4.50c = 29961
In the first equation, swap out c with (5200-a).
7.5a + 4.5(5200-a) = 29961
7.5a + 23400 - 4.5a = 29961
7.5a - 4.5a = 29961 - 23400
3a = 6561
a = 6561/3
a = 2187
Therefore, we can estimate the number of adult partons at 2187 by solving equations.
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After going to your favorite restaurant for dinner and buying food for everybody the bill came to $145. You decide to leave 30% tip and the tax came to 10%.
How much was your total bill?
Answer:
203 dollars
Step-by-step explanation:
100 percent = 145
10 percent = 14.5
30 percent = 43.5
43.5 + 14.5 + 145 = 203
Which expression is equivalent to 5–√3⋅4–√5
5
3
⋅
4
5
?
The expression that is equivalent to ∛ 5 * [tex]\sqrt[5]{4}[/tex] is [tex]5^{1/3}*4^{2/5}[/tex]
What are radicals in math?A radical in mathematics is the opposite of an exponent, which is symbolized by the sign "n√" also known as root.
The number before the symbol or radical is regarded as an index number or degree, and it can either be a square root or a cube root and so on.
How to find the equivalent expressionThis equation represents exponents in fraction form and the basics for the calculation is from
x^(b/n)
[tex]\sqrt[n]{x}^{b}[/tex]
Rewriting the expression is done as below
∛ 5
= [tex]5^{1/3}[/tex]
and
[tex]\sqrt[5]{4}[/tex]
[tex]= 4^{2/5}[/tex]
combining both gives
∛ 5 * [tex]\sqrt[5]{4}[/tex]
[tex]5^{1/3}*4^{2/5}[/tex]
[tex]5^{1/3}*4^{2/5}[/tex] is the equivalent expression
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Solve the system of equations by graphing.
1. y = x - 1
y = 2x - 2
2. y = 4x
y = x + 3
3. y - x = 1
y = x - 2 + 3
Answer:
Step-by-step explanation:
1) x - 1 = 2x - 2
-x = -1
x = 1
2) 4x = x + 3
3x = 3
x = 1
3) x + 1 = x + 1
infinite solutions (parallel lines)
For graphing, just look at the y-intercept, in the equation y = mx + b.
b is the y-intercept, so, for you plot the y-intercpet on the y-axis. You look at m, which is the slope. For positive, you go up how many ever it says in the numerator and then to the right how many ever it says in the denominator. For a negative you do the same thing except you go down and then to the right, or up and to the left. For positive there is only up and then to the right. I hope this answers your question.
given the graph of f(x)on the right,determine the type of the function help for number 2
The type of the function for the given graph f(x) on the right is odd function.
What is meant by a function?An exact one of each element of Y is assigned to each element of X via a mathematical function from a set X to a set Y. The sets X and Y are denoted by the terms "domain" and "codomain," respectively.
The link between varying amounts and other variables was the foundational idea behind functions. The effect of time on a planet's position serves as an example of this. The infinitesimal calculus was used to develop the concept in the past, beginning at the end of the 17th century and continuing through the 19th century.
An odd function's graph possesses rotational symmetry with respect to the origin, which means that it doesn't change after being rotated by 180 degrees around the origin.
Therefore, The type of the function for the given graph f(x) on the right is odd function.
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