Mathematics High School
Answers
Answer 1
(a) To find the current population of Glen Cove, we need to substitute t = 0 in the given function.
P(0) = (45(0)^2 + 125(0) + 200)/(0)^2 + 6(0) + 40
P(0) = 200/40
P(0) = 5
Therefore, the current population of Glen Cove is 5,000 people (since the function is in thousands).
(b) To find the population in the long run, we need to take the limit of the function as t approaches infinity.
lim P(t) as t → ∞ = lim (45t^2 + 125t + 200)/(t^2 + 6t + 40) as t → ∞
Using L'Hopital's rule, we can find the limit of the numerator and denominator separately by taking the derivative of each.
lim P(t) as t → ∞ = lim (90t + 125)/(2t + 6) as t → ∞
Now, we can just plug in infinity for t to get the population in the long run.
lim P(t) as t → ∞ = (90∞ + 125)/(2∞ + 6)
lim P(t) as t → ∞ = ∞/∞ (since the numerator and denominator both go to infinity)
We can use L'Hopital's rule again to find the limit.
lim P(t) as t → ∞ = lim 90/2 as t → ∞
lim P(t) as t → ∞ = 45
Therefore, the population in the long run will be 45,000 people (since the function is in thousands).
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Related Questions
For f(x)=1/x^2 show there is no c such that f(1)f(1)=f'(c)(2).
Explain why the mean value theorem doesnt apply over the interval
[1,1]"
Answers
Prerequisites for the MVT are not met due to the discontinuity and nondifferentiability of f(x) at x = 0 within the interval [1, 1].
Let's first understand the Mean Value Theorem (MVT). The MVT states that if a function is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists a number c in (a, b) such that:
f'(c) = (f(b)  f(a)) / (b  a)
Now, consider the function f(x) = 1/x^2. This function is continuous and differentiable for all x ≠ 0. However, in the interval [1, 1], the function is not continuous nor differentiable at x = 0. Therefore, the Mean Value Theorem does not apply to this interval.
Since the MVT does not apply, we cannot say there exists a c in the interval (1, 1) such that f'(c) = (f(1)  f(1)) / (1  (1)). This is because the prerequisites for the MVT are not met due to the discontinuity and nondifferentiability of f(x) at x = 0 within the interval [1, 1].
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What is the intermediate step in the form (x+a)^2=b as a result of completing the square for the following equation? x^2= 16x37
Answers
The intermediate step in completing the square for x^2= 16x37 is (x+8)^2=27.
To complete the square for the given equation, we need to add a constant value to both sides of the equation such that we can factor the lefthand side as a perfect square.
x^2 + 16x = 37
To determine the constant value we need to add to both sides, we take half the coefficient of x (which is 16/2 = 8) and square it to get 64. Then we add 64 to both sides of the equation:
x^2 + 16x + 64 = 27
Now we can factor the lefthand side as a perfect square:
(x + 8)^2 = 27
So the intermediate step in completing the square for x^2= 16x37 is (x+8)^2=27.
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What is the exact circumference of a circle with a radius of 15 cm?
Responses
10π cm
10 pi, cm
15π cm
15 pi, cm
30π cm
30 pi, cm
60π cm
Answers
Answer:
30π cm
Stepbystep explanation:
if r = 15 cm
circumference = π2r
= π × 2 × 15
= 30π cm
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Kathleen has a fair die with 6 differentcolored sides:red,yellow,blue,green,orange, and purple. She rolls the die 120 times. The die lands on the color green 18 times. Based on Kathleen's results, The experimental probability of rolling the color green is?
Answers
The Experimental probability of rolling the color green is 0.15
How to calculate the experimental probability of rolling the color green is
The experimental probability of rolling the color green can be calculated by dividing the number of times the die lands on green by the total number of rolls:
Experimental probability of green = Number of green rolls / Total number of rolls
Experimental probability of green = 18 / 120
Experimental probability of green = 0.15 or 15%
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A rectangular prism has a square
base with edge length (x + 1). Its
volume is (x + 1)2(x – 3). What
does the expression (x + 1)(x – 3)
represent?
area of the base
area of one side
height of the prism
surface area of the prism
Answers
The expression (x + 1)(x  3) represents the Area of base of the prism.
What is Prism?
a crystal is a polyhedron containing a nsided polygon base, a respectable halfway point which is a deciphered duplicate of the first, and n different countenances, fundamentally all parallelograms, joining relating sides of the two bases. Translations of the bases exist in every crosssection that runs parallel to the bases.
According to question:
The volume of a rectangular prism is given by the formula V = Bh, where B is the area of the base and h is the height of the prism. In this case, the base is a square with edge length (x + 1), so its area is (x + 1)^2. The volume of the prism is given as (x + 1)^2(x  3).
We can find the height of the prism by dividing the volume by the area of the base:
B = V/h = (x + 1)^2(x  3)/(x + 1) = (x + 1)(x  3)
Therefore, the expression (x + 1)(x  3) represents the Area of base of the prism.
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to measure the length of a hiking trail, a worker uses a device with a 2footdiameter wheel that counts the number of revolutions the wheel makes. if the device reads 1,100.5 revolutions at the end of
the trail, how many miles long is the trail, to the nearest tenth of a mile?
Answers
The length of the trail is determined as 1.3 miles.
What is the length of the trail?
The length of the trail is calculated as follows;
The circumference of the circle is calculated as;
S = πd
where;
d is the diameter of the circle
S = π x 2 ft
S = 2π ft
I revolution = 1 circumference = 2π ft
1 rev = 2π ft
1,100.5 rev = ?
= 1,100.5 rev/rev x 2π ft
= 6,914.65 ft
5280 ft > 1 mile
6,914.65 ft > ?
= 1.3 miles
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Below are the steps for copying Line Segment DE using dynamic geometry software. Which sequence has the steps in the correct order?
1.) Draw Line Segment DE with endpoint H on the circle.
2.) Construct a circle centered at the point G with radius Line Segment DE.
3.) Line Segment DE ≅ Line Segment GH
4.) Draw a point and label it G.
~a.) 2,4,1,3
~b.) 4,2,1,3
~c.) 2,1,4,3
~d.) 3,4,2,1
Answers
The correct sequence of steps for copying Line Segment DE using dynamic geometry software is in the order of 2,1,4,3. So, correct option is C.
The correct sequence of steps for copying Line Segment DE using dynamic geometry software is:
1.) Draw Line Segment DE with endpoint H on the circle.
2.) Draw a point and label it G.
3.) Construct a circle centered at the point G with radius Line Segment DE.
4.) Line Segment DE ≅ Line Segment GH
Therefore, option c.) 2,1,4,3 is the correct sequence of steps. The first step is to draw the original line segment DE with endpoint H on the circle.
The second step is to draw a point and label it G. The third step is to construct a circle centered at G with the same radius as Line Segment DE. Finally, in the fourth step, the line segment GH is drawn such that it is congruent to Line Segment DE, completing the copy of Line Segment DE.
So, correct option is C.
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The ratio of Adults to Girls in a tennis club is 5:1
The ratio of Girls to Boys in the same club is 3:4
What is the ratio of adults to boys?
Answers
The ratio of adult to boys is 35:24
What is ratio?
A ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. For example, if the ratio of boys to girls in a class is 4:1. This means that the for every 4 boys therefore is a girl.
Represent the total number of adult, boys and girls in the club by x
This means number of boys = 4/7× x
number of adult = 5/6 × x
Therefore the ratio of adults to boys will be
5x/6 : 4x/7
= 5/6 : 4/7
multiply through by 42
= 35 : 24
therefore the ratio of adult to boys is 35: 24
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A farmer of a large apple orchard would like to estimate the true mean number of suitable apples produced per tree. He selects a random sample of 40 trees from his large orchard and determines with 95% confidence that the true mean number of suitable apples produced per tree is between 375 and 520. Which of these statements is a correct interpretation of the confidence level?
Answers
The confidence level represents the degree of certainty that the interval contains the true population parameter.
The statement "determines with 95% confidence that the true mean number of suitable apples produced per tree is between 375 and 520" means that if the farmer were to repeat the sampling process many times and calculate the confidence interval each time, 95% of those intervals would contain the true mean number of suitable apples per tree.
Therefore, we can be 95% confident that the true mean number of suitable apples produced per tree is within the interval of 375 to 520 for this particular sample of 40 trees.
The confidence level represents the degree of certainty that the interval contains the true population parameter.
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someone help pls!! giving brainlist to anyone who answers
Answers
Answer: csc M = [tex]\frac{\sqrt{86} }{8}[/tex]
Stepbystep explanation:
The csc is related to sin
csc x = 1/sin x
find sin M first then flip it to find csc M
sin M= opposite/hypotenuse
sin M= [tex]\frac{8}{\sqrt{86} }[/tex] >flip that
csc M = 1/sin M
csc M = [tex]\frac{\sqrt{86} }{8}[/tex] >root cannot be simplified it breaks down into 2 and 43
which are 2 prime numbers
Find the exact values of sin 2u, cos2u, and tan2u using the doubleangle formulas cot u= square root 2, pi < u < 3pi/2
Answers
sin 2u = 1/2, cos 2u = 1/2, tan 2u = 1, because cot u = sqrt(2) and the range of u is between pi and 3pi/2.
How to find the trigonometric function?
Given cot u = sqrt(2) and the range of trigonometric of u, we can determine the values of sine, cosine, and tangent of 2u using the doubleangle formulas. First, we can find the value of cot u by using the fact that cot u = 1/tan u, which gives us tan u = 1/sqrt(2). Since u is in the third quadrant (i.e., between pi and 3pi/2), sine is negative and cosine is negative.
Using the doubleangle formulas, we can express sin 2u and cos 2u in terms of sin u and cos u as follows:
sin 2u = 2sin u cos u
cos 2u =[tex]cos^2[/tex] u  [tex]sin^2[/tex] u
Substituting the values of sine and cosine of u, we get:
sin 2u = 2*(sqrt(2)/2)*(sqrt(2)/2) = 1/2
cos 2u = (sqrt(2)/2[tex])^2[/tex]  (1/2[tex])^2[/tex] = 1/2
To find the value of tangent of 2u, we can use the identity:
tan 2u = (2tan u)/(1[tex]tan^2[/tex] u)
Substituting the value of tan u, we get:
tan 2u = (2*(1/sqrt(2)))/(1  (1/sqrt(2)[tex])^2[/tex]) = 1
Therefore, sin 2u = 1/2, cos 2u = 1/2, and tan 2u = 1.
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1. Un ciclista ha recorrido 145. 8 km en una etapa, 136. 65 km en otra etapa y 162. 62 km en una tercera etapa. ¿Cuántos kilómetros le quedan por recorrer si la carrera es de 1000 km?
Esta es una y la segunda es otra ayúdenme
2. Una clinica dental tiene una tarifa de $ 19,99 para las calzas de piezas dentales. Si en un mes se registraron 109 calzas realizadas, ¿ que cantidad de dinero ingreso a la clinica?
Answers
1) The distance left in the race is 554.93km
2) The total amount earned is $2,178.91
How many kilometers remain in the race?
We know that the total race is of 1000km, to find the distance missing, we need to take that total distance and subtract the amounts that the cyclist already traveled.
Then we will get:
distance left = 1000km  145.8km  136.65km  162.62 km
distance left = 554.93km
That is the distance left in the race.
2) We know that each piece costs $19.99, and 109 pieces are sold, then the amount earned is the product between these two numbers.
Earnings = 109*$19.99 = $2,178.91
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Obtain the equation of the line that passes through the point (4 , 6) and is parallel to the line y= 2x+4.
Answers
Answer:
y = 2x + 14
Stepbystep explanation:
OK so first u have to do y = 2x + b cuz its parallel
then u gotta just plug in the ordered pair so
6 = 2(4)+b
6 = 8 +b
14 = b
So now u have to do
y = 2x + 14
Find the volume of the solid generated when the rectangle below is rotated about side
LO. Round your answer to the nearest tenth if necessary.
Answers
The volume of the obtained solid is 36 units³.
Given that a rectangle of dimension 9 units x 2 units, has been rotated to form a solid we need to find its volume,
So we know that a rectangle rotated to form a rectangular prism.
Volume of a rectangular prism = product of the dimensions.
The dimensions of the obtained solid will be 9 units x 2 units x 2 units,
So the volume = 9 x 2 x 2 = 36 units³
Hence the volume of the obtained solid is 36 units³.
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On a certain hot summer's day,670 people used the public swimming pool. The daily prices are for children 1.25 and for adults.2.00 The receipts for admission totaled 1118.00 How many children and how many adults swam at the public pool that day
Answers
Based on simultaneous equations, the number of children and adults who swam at the public pool that hot summer's day is as follows:
Children = 296Adults = 374.
What are simultaneous equations?
Simultaneous equations are two or more equations solved concurrently.
Simultaneous equations are also referred to as a system of equations because the equations are solved at the same time.
The total number of people who used the public swimming pool = 670
The unit price for children = $1.25
The unit price for adults = $2.00
The total amount collected that day = $1,118
Let the number of children who swam at the public pool that day = x
Let the number of adults who swam at the pool that day = y
Equations:
x + y = 670 ... Equation 1
1.25x + 2y = 1,118 ... Equation 2
Multiply Equation 1 by 2:
2x + 2y = 1,340 Equation 3
Subtract Equation 2 from Equation 3:
2x + 2y = 1,340

1.25x + 2y = 1,118
0.75x = 222
x = 296
y = 670  296
= 374
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Solve 2x(x 0.5) = −(x+2.5)² + 5.5 by graphing. Round to the nearest thousandth.
x≈
and x
Answers
we find that the solutions to the equation are:x ≈ 1.283, x ≈ 4.283.
How to solve the equation ?
To solve the equation 2x(x+0.5) = (x+2.5)² + 5.5 by graphing, we can first rearrange it to the standard form:
x²  3x  2 = 0.5(x+2.5)²
Then we can plot the two functions y = x²  3x  2 and y = 0.5(x+2.5)²  5.5 on the same graph and find their intersection points, which represent the solutions to the equation.
Enter the two functions in separate equations:
[tex]y_1 = x^2  3x  2[/tex]
[tex]y_2 = 0.5(x+2.5)^2  5.5[/tex]
Adjust the zoom level and position of the graph to see the intersection points.
Click on the intersection points to see their coordinates.
Round the coordinates to the nearest thousandth.
After following these steps, we find that the solutions to the equation are:
x ≈ 1.283
x ≈ 4.283
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The money in Maya's college savings account earns 2 1/5% interest. Which value is less than 2 1/5%?
A. 0. 0215
B. 11/5
C. 0. 022
D. 11/500
Answers
A value that is less than 2 1/5% from the given data is 0. 0215. Option A is the correct answer.
A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator and denominator.
To find a value that is less than 2 1/5% we need to find the decimal number of a given fraction. to convert the given fraction into decimal form we need to divide the given fraction by 100.
= 2 1/5% / 100
= (2 + (1/5)) / 100
= 0.022
A value that is less than 0.022 from the given data is 0. 0215.
Therefore, a value less than 2 1/5% is 0. 0215.
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The volume of a cylinder is twice the volume of a cone. The cone and the
cylinder have the same diameter. The height of the cylinder is 5 meters.
What is the height of the cone?
Answers
The height of the cone that the volume of a cylinder is twice the volume of a cone is 7.5 meters.
How to determine the height of the cone
Let's first define some variables to represent the dimensions of the cone and cylinder. Let's use r for the radius of both shapes, h for the height of the cone, and 5 for the height of the cylinder.
The volume of a cone is given by V_cone = (1/3)πr^2h, and the volume of a cylinder is given by V_cylinder = πr^2h.
We are told that the volume of the cylinder is twice the volume of the cone:
V_cylinder = 2V_cone
Substituting the formulas for the volumes of the cone and cylinder, we get:
πr^2(5) = 2[(1/3)πr^2h]
Simplifying, we can cancel the π and the r^2 terms on both sides:
5 = (2/3)h
Multiplying both sides by 3/2, we get:
h = 7.5
Therefore, the height of the cone is 7.5 meters.
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A number cube has sides numbered 1 through 6. the probability of rolling a 2 is 1/6
what is the probability of not rolling a 2?
enter your answer as a fraction, in simplest form, in the box.
a calculator is allowed on this quiz.
question 1 options:
56
16
23
76
Answers
A number cube has sides numbered 1 through 6. the probability of rolling a 2 is 1/6. The probability of not rolling a 2 on a number cube with sides numbered 1 through 6 is 5/6 (in simplest form). The correct answer is 5/6.
The probability of not rolling a 2 on a number cube with sides numbered 1 through 6 can be calculated as follows:
Determine the total number of outcomes, which is 6 (1, 2, 3, 4, 5, and 6).
Determine the number of favorable outcomes, which is 5 (1, 3, 4, 5, and 6), since you're looking for the probability of not rolling a 2.
Calculate the probability by dividing the number of favorable outcomes by the total number of outcomes.
The probability of not rolling a 2 on a number cube with sides numbered 1 through 6 is 5/6 (in simplest form).
So, the correct answer is 5/6.
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How do I solve for X with the base numbers on a right triangle. (Please give an explanation and an answer, I need to know how it works.)
Answers
Let's label the 3 points as A;B;C, where BC is the hypotenuse and AB is the shortest side, and x as AH.
We can see that triangle AHC is similar to triangle CAB, and triangle ACH is similar to triangle BCA, so therefore triangle AHC is similar to triangle CHA (i might've messed up the order but you get it)
Because they are similar, we get the ratio : x/12 = 40/x, or x^2 = 480.
So, x = [tex]\sqrt{480}[/tex], or 21.9 (1 d.p)
Answer:
21.9 units

According to the right triangle altitude theorem:
the altitude on the hypotenuse is equal to the geometric mean of line segments formed by altitude on the hypotenuse.
We see x is the altitude and 12 & 40 are the segments formed on the hypotenuse.
Applied to the given triangle, we get following equation:
[tex]x=\sqrt{12*40} =\sqrt{480} =21.9\ units[/tex]
Todd had a piggy bank holding $384. He began taking out money each month. The table shows the amount remaining, in dollars, after each of the first four months
Answers
A piggy bank is a small container typically used by children to save money. In this scenario, Todd had a piggy bank holding $384 and began taking out money each month. The table provided shows the amount remaining in the piggy bank, in dollars, after each of the first four months. This information can be used to track Todd's spending and savings habits.
In the first month, Todd took out $60, leaving him with $324 in his piggy bank. In the second month, he took out an additional $48, leaving him with $276. By the third month, Todd had taken out a total of $105, leaving him with $279 in his piggy bank. Finally, in the fourth month, he took out $62, leaving him with $217.
By tracking his spending and savings over the course of these four months, Todd can assess his financial habits and make any necessary adjustments. It is important for individuals to develop good financial habits early on in life, and using a piggy bank can be a fun and effective way to do so.
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Find an exponential function that passes through (2,8) and (4,128)
Answers
The final exponential function using the values of 'a' and 'b':
y = (1/2)(4^x)
To find an exponential function that passes through the points (2,8) and (4,128), follow these steps:
Step 1: Recall the general form of an exponential function: y = ab^x
Here, 'a' and 'b' are constants that need to be determined using the given points.
Step 2: Substitute the first point (2,8) into the equation:
8 = ab^2
Step 3: Substitute the second point (4,128) into the equation:
128 = ab^4
Step 4: Divide the second equation by the first equation to eliminate 'a':
(128 = ab^4) / (8 = ab^2)
16 = b^2
Step 5: Solve for 'b':
b = √16
b = 4
Step 6: Substitute the value of 'b' back into the first equation:
8 = a(4^2)
Step 7: Solve for 'a':
8 = 16a
a = 8/16
a = 1/2
Step 8: Write the final exponential function using the values of 'a' and 'b':
y = (1/2)(4^x)
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Lizzie came up with a divisibility test for a certain number m ≠ 1 : Break a positive integer n into twodigit chunks, starting from the ones place. (For example, the number 354764 would break into the twodigit chunks 35, 47, and 64 ) Find the alternating sum of these twodigit numbers, by adding the first number, subtracting the second, adding the third, and so on. (In our example, this alternating sum would be 3547+64 = 52 ) Find m and show that this is indeed a divisibility test for n (by showing that n is divisible by m if and only if the result of this process is divisible by m)
Answers
If and only if the alternating sum of the twodigit chunks of a number n is divisible by m, then n is divisible by m.
What value of m makes the alternating sum of twodigit chunks of a positive integer n divisible by m?
Let's denote the twodigit chunks of n as a₁a₂, a₃a₄, ..., where a₁, a₂, a₃, a₄, ... are the digits from the ones place onward.
The alternating sum of these twodigit numbers is given by a₁a₂  a₃a₄ + a₅a₆  a₇a₈ + ...
We can rewrite n as (a₁a₂ × 100) + (a₃a₄ × 10) + (a₅a₆ × 1) + ...
The alternating sum expression can be written as (a₁a₂ × 100)  (a₃a₄ × 10) + (a₅a₆ × 1)  ...
If n is divisible by m, we have n ≡ 0 (mod m).
Rewriting n in terms of the alternating sum, we get (a₁a₂ × 100)  (a₃a₄ × 10) + (a₅a₆ × 1)  ... ≡ 0 (mod m).
Factoring out each twodigit chunk, we have (a₁a₂  a₃a₄ + a₅a₆  ...) ≡ 0 (mod m).
This implies that n is divisible by m if and only if the result of the alternating sum process is divisible by m.
m is the value that makes the alternating sum of the twodigit chunks of n a divisibility test for n.
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The shopkeeper sold every day the number of eggs is recorded. At equal intervals group 42, 49, 61, 35, 27, 36, 50, 34, 31, 40
Answers
The shopkeeper sold an average of 40.5 eggs per day during the given interval.
How to find the avg number of eggs?
To calculate the average number of eggs sold per day, add up the total number of eggs sold and divide by the number of days.
Total number of eggs sold = 42 + 49 + 61 + 35 + 27 + 36 + 50 + 34 + 31 + 40 = 405
Number of days = 10
Average number of eggs sold per day = 405 / 10 = 40.5
The shopkeeper sold an average of 40.5 eggs per day during the given interval.
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The shopkeeper sold every day the number of eggs is recorded. At equal intervals group 42, 49, 61, 35, 27, 36, 50, 34, 31, 40
What is the average number of eggs sold per day by the shopkeeper over the given interval?
Andre owns a condominium with a value of $155,000. He has a stock portfolio worth $8,100. He owes $3,300 on his car, which is valued at $9,100. He has $7,600 in student loans to repay. He has a credit card balance of $4,327. He also has $2,600 in a bank account. Construct a net worth statement to find Andre's net worth.
Answers
Using net worth statement, Andre's net worth is $159,573.
How to Construct a net worth statement to find Andre's net worth.
Andre's net worth can be calculated by subtracting his total liabilities from his total assets.
Total assets = $155,000 (condominium) + $8,100 (stock portfolio) + $9,100 (car value) + $2,600 (bank account) = $174,800
Total liabilities = $3,300 (car loan) + $7,600 (student loans) + $4,327 (credit card balance) = $15,227
Net worth = Total assets  Total liabilities = $174,800  $15,227 = $159,573
Therefore, Andre's net worth is $159,573.
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Qué expresión es igual a 4.6?
a. 1.6 + (3 × 4) – 2 ÷ 2
b. 1.6 + 3 × 4 – 2 ÷ 2
c. [1.6 + (3 × 4)] – (2 ÷ 2)
d. (1.6 + 3) × (4 – 2) ÷ 2
Answers
The correct expression that is equal to 4.6 is option c. [1.6 + (3 × 4)] – (2 ÷ 2)
Let's evaluate each expressions using the BODMAS rule of mathematics,
a. 1.6 + (3 × 4) – 2 ÷ 2
= 1.6 + 12  1
= 12.6
b. 1.6 + 3 × 4 – 2 ÷ 2
= 1.6 + 12  1
= 12.6
c. [1.6 + (3 × 4)] – (2 ÷ 2)
= [1.6 + 12]  1
= 12.6
d. (1.6 + 3) × (4 – 2) ÷ 2
= 4.6 × 2 ÷ 2
= 4.6
BODMAS is an acronym used to remember the order of operations in mathematics: Brackets, Orders, Division, Multiplication, Addition, Subtraction. It is used to perform calculations in the correct order to obtain the correct result. Therefore, the correct answer is (c).
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Complete question  Which expression is equal to 4.6?
a. 1.6 + (3 × 4) – 2 ÷ 2
b. 1.6 + 3 × 4 – 2 ÷ 2
c. [1.6 + (3 × 4)] – (2 ÷ 2)
d. (1.6 + 3) × (4 – 2) ÷ 2
Use the given facts about the functions to find the indicated limit.
lim x>3 f(x)=0, lim x>3 g(x)=4 lim x>3 h(x)=2
lim x>3 6h/ 4f+g (x)
*there are no answer choices. Its a prompt*
Answers
The value of [tex]\lim_{x \to 3} \frac{6h}{4f+g} (x)[/tex] is 3
Given, [tex]\lim_{x \to 3} f(x)=0[/tex]
[tex]\lim_{x \to 3} g(x)=4[/tex]
[tex]\lim_{x \to 3} h(x)=2[/tex]
We have to find the value of [tex]\lim_{x \to 3} \frac{6h}{4f+g} (x)[/tex]
[tex]\lim_{x \to 3} \frac{6h}{4f+g} (x)=\lim_{x \to 3} \frac{6h(x)}{4f(x)+g(x)}[/tex]
[tex]= \frac{\lim_{x \to 3}6h(x)}{\lim_{x \to 3}4f(x)+\lim_{x \to 3}g(x)}[/tex]
[tex]=\frac{6\times 2}{4\times0+4}[/tex]
= 12/4
= 3
Hence, the value of [tex]\lim_{x \to 3} \frac{6h}{4f+g} (x)[/tex] is 3
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To find the quotient of 4. 082 and 10,000, move the decimal point in 4. 082
Choose. Right left
places to the
Choose. Rightleft
Answers
The quotient of 4.082 and 10,000 is 0.000004082.
To find the quotient of 4.082 and 10,000, we need to divide 4.082 by 10,000. However, dividing a decimal by another decimal can be tricky, so we need to move the decimal point of the dividend (4.082) and the divisor (10,000) to make the division easier.
We can move the decimal point of 4.082 four places to the left to obtain 0.04082. This is because moving the decimal point to the left makes the number smaller. For example, moving the decimal point in 4.082 one place to the left gives us 0.4082, which is ten times smaller than 4.082. Moving the decimal point four places to the left gives us a number that is 10,000 times smaller than 4.082.
Similarly, we can move the decimal point of 10,000 four places to the right to obtain 100,000,000. This is because moving the decimal point to the right makes the number larger. For example, moving the decimal point in 10,000 one place to the right gives us 1,000, which is ten times larger than 10,000. Moving the decimal point four places to the right gives us a number that is 10,000 times larger than 10,000.
Now we can divide 0.04082 by 100,000,000, which gives us the quotient of 0.000004082. Therefore, to find the quotient of 4.082 and 10,000, we need to move the decimal point in 4.082 four places to the left and move the decimal point in 10,000 four places to the right, and then divide the resulting numbers.
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Which expression is equivalent to 1/2(2n+6
1/2+2n+6
2 1/2 + 6 1/2
n + 6
n+ 3
Answers
n+3
You distribute the property of 1/2 to 2n and 6, which will equal (1)n+3. The one does not need to be added and is understood to be there even if not visible.
A fair sixsided die will be rolled fifteen times, and the numbers that land face up will be recorded. Let x¯1 represent the average of the numbers that land face up for the first five rolls, and let x¯2 represent the average of the numbers landing face up for the remaining ten rolls. The mean μ and variance σ2 of a single roll are 3. 5 and 2. 92, respectively. What is the standard deviation σ(x¯1−x¯2) of the sampling distribution of the difference in sample means x¯1−x¯2?
Answers
The mean of a single roll is given as μ = 3.5, and the variance is given as [tex]σ^2[/tex] = 2.92.
The sample size for the first five rolls is n1 = 5, and the sample size for the remaining ten rolls is n2 = 10.
The mean of the sampling distribution of the difference in sample means x¯1−x¯2 is given as:
μ(x¯1−x¯2) = μ(x¯1)  μ(x¯2) = μ  μ = 0
The variance of the sampling distribution of the difference in sample means x¯1−x¯2 is given as:
σ^2(x¯1−x¯2) = (σ^2(x¯1)/n1) + (σ^2(x¯2)/n2)
where σ^2(x¯1) is the variance of the sample mean for the first five rolls and σ^2(x¯2) is the variance of the sample mean for the remaining ten rolls.
Since each roll of the die is independent, the variance of the sample mean for each sample is given as:
σ^2(x¯1) = σ^2/ n1 = 2.92/5 = 0.584
σ^2(x¯2) = σ^2/ n2 = 2.92/10 = 0.292
Substituting these values in the above equation, we get:
σ^2(x¯1−x¯2) = (0.584/5) + (0.292/10) = 0.1468
Therefore, the standard deviation of the sampling distribution of the difference in sample means x¯1−x¯2 is:
σ(x¯1−x¯2) = sqrt(σ^2(x¯1−x¯2)) = sqrt(0.1468) = 0.3835 (rounded to four decimal places)
Hence, the standard deviation of the sampling distribution of the difference in sample means x¯1−x¯2 is 0.3835.
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