If 1/6 of the boys joined the basketball team, there are 160 boys in the soccer team.
If 1/6 of the boys joined the basketball team, then 5/6 of the boys did not join the basketball team. Similarly, if 2/9 of the boys joined the soccer team, then 7/9 of the boys did not join the soccer team.
Let's first find out how many boys did not join the soccer team:
7/9 x 540 = 380
Therefore, 380 boys did not join the soccer team.
To find out how many boys did join the soccer team, we can subtract the boys who did not join from the total number of boys:
540 - 380 = 160
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Find the inverse for each relation: 4 points each
1. {(1,‐2), (2, 3),(3, ‐3),(4, 2)}
2. {(4,2),(5,1),(6,0),(7,‐1)}
Find an equation for the inverse for each of the following relations.
3. Y=-8x+3
4. Y=2/3x-5
5. Y=1/2x+10
6. Y=(x-3)^2
Verify that f and g are inverse functions.
7. F(x)=5x+2;g(x)=(x-2)/5
8. F(x)=1/2x-7;g(x)=2x+14
The inverse relation is {(‐2,1), (3, 2),(‐3, 3),(2, 4)}, {(2, 4),(1, 5),(0, 6),(‐1, 7)}, the inverse equation is: y = (-x + 3)/8, y = (3/2)x - (15/2), y = (1/2)x + 10,
x = sqrt(y) + 3 or x = -sqrt(y) + 3 and f(g(x)) = g(f(x)) = x, f and g are inverse functions.
1.To find the inverse of the relation, we need to switch the x and y values of each point and solve for y:
{(‐2,1), (3, 2),(‐3, 3),(2, 4)}
2. Following the same process as above:
{(2, 4),(1, 5),(0, 6),(‐1, 7)}
So the inverse relation is {(2, 4),(1, 5),(0, 6),(‐1, 7)}.
3.To find the equation of the inverse, we can solve for x:
y = -8x + 3
x = (-y + 3)/8
So the inverse equation is: y = (-x + 3)/8.
4. Following the same process as above:
y = (2/3)x - 5
x = (3/2)y + 5
So the inverse equation is: y = (3/2)x - (15/2).
5. Following the same process as above:
y = (1/2)x + 10
x = 2(y - 10)
So the inverse equation is: y = (1/2)x + 10.
6.To find the inverse equation, we need to solve for x:
y = (x-3)^2
x = sqrt(y) + 3 or x = -sqrt(y) + 3
So the inverse equation is: x = sqrt(y) + 3 or x = -sqrt(y) + 3.
7,To verify that f and g are inverse functions, we need to show that f(g(x)) = x and g(f(x)) = x.
f(x) = 5x + 2
g(x) = (x-2)/5
f(g(x)) = 5((x-2)/5) + 2 = x - 2 + 2 = x
g(f(x)) = ((5x + 2)-2)/5 = x/5
Since f(g(x)) = g(f(x)) = x, f and g are inverse functions.
8.Following the same process as above:
f(x) = (1/2)x - 7
g(x) = 2x + 14
f(g(x)) = (1/2)(2x+14) - 7 = x
g(f(x)) = 2((1/2)x - 7) + 14 = x
Since f(g(x)) = g(f(x)) = x, f and g are inverse functions.
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A bag contains 4 red marbles, 7 blue marbles and 8 green marbles. If two marbles are drawn out of the bag, what is the probability, to the nearest 10th of a percent, that both marbles drawn will be green?
The probability that both marbles drawn will be green is 16.4%.
The probability of drawing a green marble on the first draw is 8/19.
Since there are no replacements, the probability of drawing another green marble on the second draw is 7/18 (since there are now only 18 marbles left in the bag, including 7 green marbles).
Therefore, the probability of drawing two green marbles in a row is:
(8/19) × (7/18)
= 56/342
To convert this to a percentage, we can divide 56 by 342 and multiply by 100:
(56/342) × 100 = 16.37%
Therefore, the probability that both marbles drawn will be green is 16.4%.
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Use the ratio test to find the radius of convergence of the power series 3x+36x^2+243x^3+1296x^4+6075x^5+
The radius of convergence is 1/3. To find the radius of convergence for the power series using the ratio test, we need to analyze the general term of the series. The given series is:
Σ(an * x^n)
where an is the coefficient of the term with x raised to the power n. The coefficients in the given series are:
a1 = 3
a2 = 36
a3 = 243
a4 = 1296
a5 = 6075
...
Notice that each coefficient is a multiple of 3^n. Thus, we can write the general term as:
an = 3^n
Now, we apply the ratio test. The ratio test states that the series converges if the limit as n approaches infinity of the absolute value of the ratio of consecutive terms is less than 1:
lim (n → ∞) |(a(n+1) * x^(n+1)) / (an * x^n)|
= lim (n → ∞) |(3^(n+1) * x^(n+1)) / (3^n * x^n)|
To simplify, divide 3^(n+1) by 3^n:
= lim (n → ∞) |(3 * x)|
The series converges when |3 * x| < 1. To find the radius of convergence, solve for |x|:
|x| < 1/3
The radius of convergence is 1/3.
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Problem
Yoshi is a basketball player who likes to practice by attempting the same three-point shot until he makes the shot. His past performance indicates that he has a
30
%
30%30, percent chance of making one of these shots. Let
X
XX represent the number of attempts it takes Yoshi to make the shot, and assume the results of each attempt are independent.
Is
X
XX a binomial variable? Why or why not?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Each trial isn't being classified as a success or failure, so
X
XX is not a binomial variable.
(Choice B)
B
There is no fixed number of trials, so
X
XX is not a binomial variable.
(Choice C)
C
The trials are not independent, so
X
XX is not a binomial variable.
(Choice D)
D
This situation satisfies each of the conditions for a binomial variable, so
X
XX has a binomial distribution
There is no fixed number of trials, so X is not a binomial variable. (Choice B) B is the right response.
Discrete random variables are within the category of binomial random variables. A binomial random variable keeps track of how frequently an event occurs over a predetermined number of trials. ALL of the following prerequisites have to be satisfied for a variable to qualify as a binomial random variable:
A predetermined sample size (number of trials) is used.
The relevant occurrence either takes place or doesn't in every trial.
On each trial, the likelihood of occurrence (or not) is the same.
Trials run separately from one another.
While Yoshi has a 30% chance of success for each shot and the trials are independent, the number of attempts is not fixed, as he continues until he makes the shot.
Thus, the correct answer is (Choice B) B. There is no fixed number of trials, so X is not a binomial variable.
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At the craft store, Stefan bought a bag of yellow and brown marbles. The bag contained 40 marbles, and 10% of them were yellow. How many yellow marbles did Stefan receive?
The number of yellow marbles Stefan received is 4.
To find out how many yellow marbles Stefan received, we need to calculate 10% of the total number of marbles, which is 40.
Percentage calculations involve finding a part of a whole, and in this case, we are looking for the part that represents the yellow marbles. To find 10% of 40 marbles, you simply multiply the total number of marbles (40) by the percentage value (10%) as a decimal. To convert 10% to a decimal, you divide by 100, giving you 0.1.
Now, multiply the total marbles by the decimal value:
40 marbles * 0.1 = 4 marbles
So, Stefan received 4 yellow marbles in the bag he bought from the craft store.
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Rectangle ABCD is graphed in the coordinate plane. The following are
the vertices of the rectangle: A(-6,-4), B(-4,-4), C(-4,-2), and
D(-6, -2).
What is the perimeter of rectangle ABCD?
units
Stuck? Review related articles/videos or use a hint.
Report a problem
Answer:
The perimeter of rectangle ABCD can be calculated by adding up the lengths of its sides. Using the distance formula, we can find that AB has a length of 2 units, BC has a length of 2 units, CD has a length of 2 units, and AD has a length of 4 units. Therefore, the perimeter of rectangle ABCD is 10 units.
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What is the quotient of 1. 892×10^8 and 4. 3×10^3
expressed in scientific notation? Please tell me the answer!
The quotient of 1.892×10^8 and 4.3×10^3 expressed in scientific notation is 4.4×10^4.
The quotient is determined by dividing any two numbers. In this case, the two numbers are 1.892×10^8 and 4.3×10^3. In order to calculate the quotient here, we will divide 1.892×10^8 by 4.3×10^3. Hence,
1. Divide the coefficients: 1.892 ÷ 4.3 = 0.44
2. Subtract the exponents: (10^8) ÷ (10^3) = 10^(8-3) = 10^5
3. Combine the results: 0.44 × 10^5
To express this answer in scientific notation, we need to move the decimal point one place to the left and adjust the exponent accordingly:
0.44 × 10^5 = 4.4×10^4
Therefore, the quotient expressed in scientific notation is 4.4×10^4.
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Larray bought roses at the flower shop for $4.50 per dozen with a 90% markup. what is the final retail price
A markup refers to the amount that is added on top of the cost price of a product to arrive at the selling price. In this case, the cost price of the roses was $4.50 per dozen. Therefore, a 90% markup would mean that the selling price is 90% more than the cost price.
To calculate the markup, we can use the following formula:
Markup = Cost Price x Markup Percentage
Markup Percentage = 90% = 0.9 (in decimal form)
Markup = $4.50 x 0.9 = $4.05
This means that the markup on the roses is $4.05 per dozen.
To calculate the final retail price, we simply need to add the markup to the cost price:
Retail Price = Cost Price + Markup
Retail Price = $4.50 + $4.05 = $8.55
Therefore, the final retail price for the roses that Larray bought at the flower shop is $8.55 per dozen.
In conclusion, Larray bought roses at the flower shop for $4.50 per dozen with a 90% markup, which resulted in a final retail price of $8.55 per dozen. The markup was calculated by multiplying the cost price by the markup percentage of 90%, and then adding it to the cost price to arrive at the selling price.
This is a common practice in the flower industry, where flower shops add a markup to the cost of their products to make a profit.
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A building is 210 m tall. A scale model is built using a scale factor of 0. 5.
a) Determine the height of the model to the nearest centimeter, if necessary.
b) What are the actual dimensions of the bed, couch, and desk?
a) The height of the scale model is 105 m. b) The actual dimensions of the bed, couch, and desk are twice as large as their corresponding dimensions in the scale model.
a) To determine the height of the scale model, we multiply the height of the actual building by the scale factor of 0.5:
Height of scale model = 0.5 x 210 m = 105 m.
b) Since the scale factor is 0.5, the actual dimensions of the bed, couch, and desk are twice as large as their corresponding dimensions in the scale model.
For example, if the length of the couch in the scale model is 10 cm, then the actual length of the couch is 2 x 10 cm = 20 cm. Similarly, if the width of the desk in the scale model is 8 cm, then the actual width of the desk is 2 x 8 cm = 16 cm.
Therefore, to find the actual dimensions of the bed, couch, and desk, we simply multiply the corresponding dimensions in the scale model by 2.
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¿Cómo se escribe la multiplicación 713 × 49, descomponiendo ambos números?
The decomposition of 713 × 49 has been provided below
How to decompose the problemTo multiply 713 and 49, we can use the distributive property and decompose the second number as follows:
49 = 40 + 9
Then, we can multiply each part of the sum by 713:
713 × 40 + 713 × 9
To calculate this, we can use the multiplication table and then add the results:
713
x 40
28520
713
x 9
6417
Then, we add the two results:
713 × 40 = 28520
713 × 9 = 6417
34997
Therefore, the multiplication 713 × 49, decomposed as 713 × 40 + 713 × 9, equals 34,997.
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If pp and qq vary inversely and pp is 19 when qq is 30, determine qq when pp is equal to 95
When the value of pp=95 the value of qq will be equal to 6.
It is given that pp varies inversely with qq, so we can write that
pp=k/qq
where k is the proportionality constant.
here we can find the value of k by substituting the value of pp and qq with 19 and 30 in the relation that is given above, we get:
30=k/19
k=30*19
k=570
we the value of k to be 570 after putting the values in the relation.
Now if pp is changed to 95, and k is equal to 570 we can get the value of qq by putting the known values in the same relation.
pp=k/qq
qq=570/95
qq=6.
Therefore, when the value of pp is 95 the value for qq will be equal to 6.
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Anne is taking courses in both mathematics and English. She estimates her probability of passing mathematics at 0. 42 and passing English at 0. 47 , and she estimates her probability of passing at least one of the courses at 0. 7. What is the probability that Anne could pass both courses?
The probability that Anne could pass both mathematics and English courses is 0.19 or 19%.
To find the probability that Anne could pass both mathematics and English, we can use the formula for the probability of the union of two events: P(A ∪ B) = P(A) + P(B) - P(A ∩ B), where A is the event of passing mathematics, B is the event of passing English, and A ∩ B is the event of passing both courses.
We are given:
P(A) = probability of passing mathematics = 0.42
P(B) = probability of passing English = 0.47
P(A ∪ B) = probability of passing at least one course = 0.7
Now we need to find the probability of passing both courses, P(A ∩ B).
Using the formula, we have:
0.7 = 0.42 + 0.47 - P(A ∩ B)
To find P(A ∩ B), we rearrange the equation:
P(A ∩ B) = 0.42 + 0.47 - 0.7
Now, calculate the probability:
P(A ∩ B) = 0.19
So, the probability that Anne is 0.19 or 19%.
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|x-6|=-10
thanks in advance
Answer:
I guess you need the value of (x) if that's so then
x= -4
Step-by-step explanation:
These cones are similar. find the volume
of the smaller cone. round to the
nearest tenth.
2cm 3 cm
volume = [ ? ] cm3
volume = 66 cm3
The volume of the smaller cone is approximately [tex]5.5 cm^3[/tex], rounded to the nearest tenth
If the cones are similar, then the ratio of the corresponding dimensions of the cones is the same.
Let's denote the height and radius of the smaller cone as h and r, respectively. Then, the height and radius of the larger cone are 3h and 2r, respectively.
Since the volumes of the cones are proportional to the cube of their radii and heights, we can write:
(volume of smaller cone) / (volume of larger cone) = [tex](r^2 * h) / ((2r)^2 * 3h)[/tex]
Simplifying this expression, we get:
(volume of smaller cone) / (volume of larger cone) = 1/12
Since we are given that the volume of the larger cone is [tex]66 cm^3[/tex], we can solve for the volume of the smaller cone as follows:
(volume of smaller cone) =[tex](1/12) * (66 cm^3) = 5.5 cm^3[/tex]
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If Nori made 2% in interest on $5,000 and her brother Sean made 1% in interest
on $10,000, who made more money in interest?
Both Nori and her brother Sean made the same amount in interest, $100, assuming that their investments lasted 1 year.
What is interest?The interest refers to the income or payment received or made for giving or taking credit from a lender.
The interest is usually depicted using a rate, which is expressed over 100.
Nori's Investment = $5,000
Interest rate = 2%
Interest amount = $100 ($5,000 x 2%)
Sean's investment = $10,000
Interest rate = 1%
Interest amount = $100 ($10,000 x 1%)
Thus, Nori and Sean equally made $100 in interest from their investments.
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what is x^2-3x=70 in standard form?
Answer: x^2 + 3x - 70 = 0
Step-by-step explanation:
what the answear to y=4x-9
The ordered pairs of the linear expression y = 4x - 9 is (0, -9)
What are the ordered pairs of the linear expressionFrom the question, we have the following parameters that can be used in our computation:
The linear expression y = 4x - 9
To determine the ordered pairs of the linear expression, we set x to any value say x = 0 and then calculate the value of y
Using the above as a guide, we have the following:
y = 4(0) - 9
Evauate
y = -9
Divide both sides by 1
y = -9
This means that the value of y is equal to -9
So, we have (0, -9)
Hence, the ordered pairs of the linear expression is (0, -9)
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Simplify 3y(y^2-3y+2)
Step-by-step explanation:
if this factorisation because I think you alr simplified, but here's the answer for factorisation anyways.
you can text me below in the comments section if that's not you want, I will try to answer if I can!!!
Answer:
3y(y - 2)(y - 1)
Step-by-step explanation:
Simplify by factoring
3y(y² - 3y + 2)
= 3y(y - 2)(y - 1)
The figure below is made up of 1 centimeters cubes, What is the volume of the figure?
Answer:
15 cubic centimeters
Step-by-step explanation:
The figure is in the shape of a rectangular and the formula for volume of such a rectangular box is
V=lwh, where V is the volume, l is the length, and h is the height.
Since each cube is 1 cm, we see that the length is 5 cm (1 cm cube * 5 = 5 cm), the width is 3 cm (1 cm cube * 3 = 3 cm), and the height is 1 cm (1 cm cube * 1 = 1 cm).
Thus, we the product of our length, width, and height will give us the volume of the figure:
V = 5 * 3 * 1
V = 15 cubic centimeters
Emma has a wooden sculpture in the shape of a cuboid.
The sculpture is 2. 2 m high, 1. 1 m wide and 0. 55 m thick.
Emma plans to paint all the faces of the sculpture with
three coats of wood varnish.
a How many tins of wood varnish does Emma
need to buy?
b What is the total cost of the wood varnish?
varnish
$ 3. 99
(Size of tin: 100 ml)
20 m2 per litre
a) To find the total surface area of the cuboid, we need to find the area of each face and then add them up.
Area of one face = length x width
Area of top and bottom faces = 1.1 m x 0.55 m = 0.605 m² (2 faces)
Area of front and back faces = 2.2 m x 0.55 m = 1.21 m² (2 faces)
Area of side faces = 2.2 m x 1.1 m = 2.42 m² (2 faces)
Total surface area = (2 x 0.605) + (2 x 1.21) + (2 x 2.42) = 7.7 m²
Each tin of varnish covers 20 m², so Emma needs:
Number of tins = (total surface area x number of coats) / coverage per tin
Number of tins = (7.7 x 3) / 0.02 = 1155
Emma needs to buy 1155 tins of wood varnish.
b) The cost of each tin of varnish is $3.99 for 100 ml. To find the cost of 1155 tins, we first need to convert the volume of varnish needed into liters.
Volume of varnish needed = (total surface area x number of coats) / coverage per litre
Volume of varnish needed = (7.7 x 3) / 20 = 1.155 liters
The number of tins required to make up 1.155 liters of varnish is:
Number of tins = (1.155 / 0.1) = 11.55
So Emma needs to buy 12 tins of varnish. The total cost is:
Total cost = cost per tin x number of tins
Total cost = $3.99 x 12 = $47.88
The total cost of the wood varnish is $47.88.
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Mae lee is going to but a new car. The car she wants costs $24. 599. She has $5. 000 to use as a down payment and will take a loan out for the rest. The interest rate on the loan is 4. 25% for 5 years how much interest will mae lee pay in all? round your answer to the nearest cent show all your work and explain each step
The interest that has to be paid for the car is $ 4534.2.
What is compound interest?Compound interest is a type of interest calculation in which the interest earned is added to the principal amount.
The principal is the sum that is left to be paid after the down payment hence;
Principal = $24, 599 - $5, 000
= $19599
A = P(1 + r/n)^nt
A = amount
P =principal
r = rate
n = Number of times compounded
t = time
Then we have that;
A = 19599( 1 + 0.0425)^5
A = $24133.2
Then ;
Interest = Amount - Principal
Interest = $24133.2 - $19599
=$ 4534.2
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840x - x2 A company's revenue for selling x (thousand) items is given by R(x) = x2 +840 Find the value of x that maximizes the revenue and find the maximum revenue. X= maximum revenue is $ 2
The value of x that maximizes revenue is x 28.99 and maximum revenue is $1680 (thousand).
The revenue function for a company that sells x (thousand) items is R(x) = x² + 840. To find the value of x that maximizes revenue, we need to differentiate the revenue function, set it equal to zero and solve for x. The maximum revenue can then be calculated by substituting the value of x into the revenue function.
Revenue function: R(x) = x² + 840
To find the value of x that maximizes revenue, we differentiate the revenue function with respect to x:
dR/dx = 2x
Setting this equal to zero, we get:
2x = 0
x = 0
However, this value does not make sense in the context of the problem, as the company cannot sell 0 items. Therefore, we need to consider the critical points of the function, which occur when dR/dx = 0 or is undefined.
dR/dx = 0 when 2x = 0, so x = 0 is a critical point.
dR/dx is undefined when x = ±√840, so these are also critical points.
We can use the second derivative test to determine which critical point corresponds to a maximum. The second derivative of the revenue function is:
d²R/dx² = 2
At x = 0, d²R/dx² = 2 > 0, so this critical point corresponds to a minimum.
At x = ±√840, d²R/dx² = 2 > 0, so these critical points correspond to a minimum.
Therefore, the value of x that maximizes revenue is x = √840 ≈ 28.99 (thousand items).
To find the maximum revenue, we substitute x = √840 into the revenue function:
R(√840) = (√840)² + 840 = 1680
So the maximum revenue is $1680 (thousand).
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What’s the answer? I need help:)
Answer:
x=180-90-54, y=180-x,z=90
Step-by-step explanation:
the sum of the degree of a triangle will equal 180. the sum of the degree of a line will equal 180.
Target INT1: I can correctly antidifferentiate basic functions and identify antiderivatives nd the most general antiderivatives of each function. 1. y = 1 - x^2 + x^2 + 3x^4
2. g(x) = cos x + x
3. h(x) = 5
The antiderivative of h(x) is 5x + C.
We can simplify the function y as y = 1 + 3x^4. Now, we can integrate term by term as:
∫ y dx = ∫ (1 + 3x^4) dx
= x + (3/5)x^5 + C
So, the antiderivative of y is x + (3/5)x^5 + C.
The antiderivative of cos(x) is sin(x) and the antiderivative of x is (1/2)x^2. Therefore, we can integrate term by term as:
∫ g(x) dx = ∫ (cos x + x) dx
= sin(x) + (1/2)x^2 + C
So, the antiderivative of g(x) is sin(x) + (1/2)x^2 + C.
The antiderivative of any constant is the constant times x. Therefore, we can integrate h(x) as:
∫ h(x) dx = ∫ 5 dx
= 5x + C
So, the antiderivative of h(x) is 5x + C.
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In a group of students,
[tex] \frac{8}{13} [/tex]
of the group are scouts and the rest are police cadets. If
[tex] \frac{3}{8} [/tex]
of the scouts or 15 of them are prefects, calculate the number of police cadets in the group
The calculated number of police cadets in the group is 25
Calculating the number of police cadets in the groupFrom the question, we have the following parameters that can be used in our computation:
Scouts = 8/13
Police cadets = the rest
This means that
Police cadets = 1 - 8/13
Evaluate
Police cadets = 5/13
Also, we have
Prefects = 3/8 or 15 of scouts
This means that
3/8 * Scouts = 15
Scouts = 40
So, we have
Total = 40/(8/13)
Total = 65
Recall that
Police cadets = 5/13
So, we have
Police cadets = 5/13 * 65
Evaluate
Police cadets = 25
Hence, the number of police cadets in the group is 25
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Unit v performance task: percents (7. Rp. A. 3)
black friday deals
holy stone drone with live video and
adjustable wide-angle camera.
best buy
best buy is offering this drone for 20% off for
black friday.
pc richard and son
pc richard and son is offering the same drone
for 10% off plus an extra $20 off to the first 100
customers.
you only have time to go to one store. Which store will give you the
cheaper price? (assume that you are one of the first 100 customers at pc
richard and son. )
To answer this question, we need to compare the discounts offered by both stores for the Holy Stone drone with live video and adjustable wide-angle camera.
Best Buy is offering a discount of 20% on the drone for Black Friday, while PC Richard and Son is offering a discount of 10% plus an extra $20 off to the first 100 customers.
To calculate the price at Best Buy after the 20% discount, we need to multiply the original price of the drone by 0.8 (100% - 20%). Let's assume the original price of the drone is $200. So, the price at Best Buy after the discount will be:
Price at Best Buy = $200 x 0.8 = $160
To calculate the price at PC Richard and Son after the discount, we need to first calculate the 10% discount and then subtract the extra $20 off. Let's assume the original price of the drone is still $200. So, the price at PC Richard and Son after the 10% discount will be:
Price after 10% discount = $200 x 0.9 = $180
Then, we need to subtract the extra $20 off for the first 100 customers:
Price at PC Richard and Son = $180 - $20 = $160
So, both stores are offering the drone at the same price of $160 after the discounts. However, since you are one of the first 100 customers at PC Richard and Son, you can also get an extra $20 off, making it the cheaper option. Therefore, you should go to PC Richard and Son to get the cheaper price.
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Suppose we were to gather a random sample of 28 observations from a population and wished to calculate a 95% confidence interval for the mean, µ, in the case where the population standard deviation, σ, is unknown. Enter the value from the Student's t distribution that we would use, to three decimal places
The value from the Student's t distribution that we would use to calculate a 95% confidence interval is 2.048
When the population standard deviation, σ, is unknown, we use the sample standard deviation, s, to estimate it. The t-distribution is used to calculate the confidence interval when we have a small sample size (less than 30) and the population standard deviation is unknown.
The value from the t-distribution that we would use to calculate a 95% confidence interval for the mean with a sample size of 28 is the t-value with 27 degrees of freedom, denoted by t(0.025,27) is 2.048.
This value can be obtained from a t-distribution table or calculator, and it represents the number of standard errors away from the mean that corresponds to a 95% confidence interval.
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According to a simple physiological model, an athletic adult male needs 20 calories per day per pound of body weight to maintain his weight. If he consumes more or fewer calories than those required to maintain his weight, his weight changes at a rate proportional to the difference between the number of calories consumed and the number needed to maintain his current weight; the constant of proportionality is 1/3500pounds per calorie. Suppose that a particular person has a constant caloric intake of HH calories per day. Let W(t)be the person's weight in pounds at time t (measured in days).
(a) What differential equation has solution W(t)? dWdt=
(Your answer may involve W, H and values given in the problem.)
(b) If the person starts out weighing 180 pounds and consumes 3200 calories a day. What happens to the person's weight as t→[infinity]? W→?
(a) The differential equation that has solution W(t) is:
dW/dt = (1/3500) * (HH - 20W)
This is because the rate of change of weight with respect to time is proportional to the difference between the person's constant caloric intake and the number of calories needed to maintain their current weight, which is 20 calories per day per pound of body weight. The constant of proportionality is 1/3500 pounds per calorie.
(b) To find out what happens to the person's weight as t→[infinity], we can look at the long-term behavior of the solution to the differential equation. As t gets very large, the weight W(t) approaches a limiting value W∞ such that dW/dt = 0. This means that the person's weight is no longer changing, and is therefore at a steady state.
To find this steady state weight, we set dW/dt = 0 in the differential equation:
(1/3500) * (HH - 20W∞) = 0
Solving for W∞, we get:
W∞ = HH/20
So as t→[infinity], the person's weight approaches W∞ = HH/20.
This means that if the person starts out weighing 180 pounds and consumes 3200 calories a day, their weight will eventually stabilize at W∞ = 3200/20 = 160 pounds.
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Is Figure A'B'C'D' a reflection of Figure ABCD? Explain.
Trapezoid A B C D graphed in Quadrant 1 of a coordinate plane with vertices A, 2, 2, B, 4, 4, C, 8, 4, and D, 10, 2. Trapezoid A prime B prime C prime D prime graphed in Quadrant 4 of a coordinate plane with vertices A prime, 2, negative 4, B prime, 4, negative 6, C prime, 8, negative 6, and D prime, 10, negative 4. The horizontal line y equals negative 1 is graphed and is equidistant between the bases of the trapezoids.
Yes; it is a reflection over the x-axis.
Yes; it is a reflection over the y-axis.
Yes; it is a reflection over line y = –1.
No; it is not a reflection.
Where the above is given, it is correct to state that "Yes; it is a reflection over line y = –1." (Option C)
What is reflection in math?A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. The line of reflection is formed when an image reflects through a line. A figure is said to mirror another figure when every point in one figure is equidistant from every point in another figure.
Note that in the above prompt, Since the horiztonal line y = -1 is equidistant between the bases of the trapezoids, ABCD and A'B'C'D and the corresponding coordinates are therefore equidistant from the line.
Hence Option C is correct.
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4. You decide to purchase a home for $225,000. The bank requires a 10% down payment.
You take out a 30-year, fixed rate mortgage at 4. 5%.
a. How much is the down payment?
b. How much is the mortgage (In other words, how much money are you
borrowing?)
c. What is your monthly mortgage payment?
a. The down payment is $22,500.
b. The mortgage is $202,500.
c. The monthly mortgage payment is $1,027.
a. The down payment is 10% of the home price, which is $225,000 x 0.1 = $22,500.
b. The mortgage is the remaining amount that you need to pay, which is $225,000 - $22,500 = $202,500.
c. The monthly mortgage payment can be calculated using the formula for a fixed-rate mortgage:
Monthly Payment = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]
where P is the principal amount (the mortgage), i is the monthly interest rate (4.5% / 12 = 0.375%), and n is the total number of monthly payments (30 years x 12 months/year = 360).
Plugging in the values, we get:
Monthly Payment = $202,500 [ 0.00375(1 + 0.00375)^360 ] / [ (1 + 0.00375)^360 – 1] = $1,027.
Therefore, your monthly mortgage payment will be $1,027.
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