To estimate the proportion of cyanobacteria in algae samples with a 99% confidence level and a margin of error ≤ 0.01, Ian would need a sample size of at least 12111.
To determine the required sample size (n) for estimating the proportion of cyanobacteria in the algae samples with a margin of error of at most (0.01) and a (99%) confidence level, you can use the formula for the margin of error in estimating a population proportion:
[tex]\[ E = Z \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \][/tex]
Given:
- Margin of error (E) = 0.01
- Confidence level = (99%), which corresponds to a Z-score of approximately 2.576
- Estimated proportion [tex](\(\hat{p}\)) = \(\frac{38}{50} = 0.76\)[/tex] (from the given sample)
Now, the formula can be rearranged to solve for (n):
[tex]\[ n = \frac{\hat{p}(1-\hat{p})}{\left(\frac{E}{Z}\right)^2} \][/tex]
Substitute the given values:
[tex]\[ n = \frac{0.76 \times (1 - 0.76)}{\left(\frac{0.01}{2.576}\right)^2} \][/tex]
Now calculate:
[tex]\[ n \approx \frac{0.76 \times 0.24}{\left(\frac{0.01}{2.576}\right)^2} \][/tex]
n ≈ 12111
Therefore, Ian would need a sample size of at least 12111 algae samples to estimate the proportion of cyanobacteria with a margin of error of at most (0.01) in a (99%) confidence interval.
Ian would require a sample size of approximately 12,102 algae to estimate the proportion of cyanobacteria with a margin of error of at most 0.01 in a 99% confidence interval.
To determine the required sample size for estimating the proportion of algae samples that are cyanobacteria with a margin of error of at most 0.01 and a 99% confidence level, we can use the formula for the confidence interval for a proportion:
[tex]\[ n = \left(\frac{z_{\alpha/2} \cdot \sqrt{p(1-p)}}{E}\right)^2 \][/tex]
where:
- n is the sample size,
- [tex]\( z_{\alpha/2} \)[/tex] is the z-score corresponding to the desired confidence level (for 99%, [tex]\( z_{\alpha/2} = 2.576 \),[/tex]
- p is the estimated proportion of the population that has the characteristic of interest (in this case, being cyanobacteria),
- E is the margin of error.
The estimated proportion p can be taken from the initial sample of 50 algae, where 38 were cyanobacteria. Thus, pis estimated as:
[tex]\[ p = \frac{\text{Number of cyanobacteria}}{\text{Total sample size}} = \frac{38}{50} = 0.76 \][/tex]
Now, we plug in the values into the formula:
[tex]\[ n = \left(\frac{2.576 \cdot \sqrt{0.76(1-0.76)}}{0.01}\right)^2 \][/tex]
[tex]\[ n = \left(\frac{2.576 \cdot \sqrt{0.76 \cdot 0.24}}{0.01}\right)^2 \][/tex]
[tex]\[ n = \left(\frac{2.576 \cdot \sqrt{0.1824}}{0.01}\right)^2 \][/tex]
[tex]\[ n = \left(\frac{2.576 \cdot 0.427}{0.01}\right)^2 \][/tex]
[tex]\[ n = \left(\frac{1.101}{0.01}\right)^2 \][/tex]
[tex]\[ n = (110.1)^2 \][/tex]
[tex]\[ n \ = 12101.01 \][/tex]
Since we cannot have a fraction of an algae sample, we round up to the nearest whole number:
[tex]\[ n \ = 12102 \][/tex]
Please help!!
What is the equation of the line that represents the initial climb?
Answer:
y = (5/2)x
Step-by-step explanation:
The rise is 5 squares and the run is 2 squares between the two marked points. That means the slope is 5/2. The line starts at (0, 0), so the equation is ...
y = (5/2)x
3 friends share the cost of a gift. The gift costs $70, but the store manager takes $10 off the market price. What amount should they each pay? What is the answer
Answer:
Amount each friend pays for the gift = $20
Step-by-step explanation:
Market price of a gift = $70
The store manager takes $10 off the market price.
Marked down amount = $10
New cost price = Marked price - Marked down amount [tex]=\$70-\$10=\$60[/tex]
The cost of the gift is divided among three friends.
This means that the cost of gift which is $60 is divided by three to get each one's contribution in the gift.
∴ Amount each friend pays for the gift [tex]=\frac{60}{3}=\$20[/tex]
What are the period and amplitude of the function?
The given graph displays a periodic function with a [tex]5[/tex]-unit period and a [tex]3[/tex]-unit amplitude. Therefore, option C is correct, accurately describing the function's characteristics based on the observed graph.
The given graph indicates a periodic function with repeating patterns. The period is the horizontal distance between two successive peaks or troughs. In this case, the graph repeats every [tex]5[/tex] units horizontally, so the period is indeed [tex]5[/tex]. The amplitude is the vertical distance from the midline to the peak or trough.
Here, the vertical distance is [tex]3[/tex] units, confirming the amplitude as [tex]3[/tex].
Therefore, according to the graph, option C is correct with a period of [tex]5[/tex] and an amplitude of [tex]3[/tex], aligning with the observed characteristics of the function's periodicity and vertical range.
The mathematical theory behind linear programming states that an optimal solution to any problem will lie at a(n) ________ of the feasible region.
a) interior point or center
b) maximum point or minimum point
c) corner point or extreme point
d) interior point or extreme point
e) None of these
Answer:
Option C) corner point or extreme point
Step-by-step explanation:
Linear Programming:
Linear programming is an optimization(maximization or minimization) technique for a system of linear equations and a linear objective function. The objective function defines the quantity to be minimized or maximized.The goal of linear programming is to find the values of the variables that maximize or minimize the objective function.Corner Point Theorem:
The corner point theorem states that the optimum value of the feasible region occurs at the corner point of the feasible region, thus the minimum or maximum value will occur at the corner point or the extreme point.Thus,
The mathematical theory behind linear programming states that an optimal solution to any problem will lie at corner point or extreme point of the feasible region
Suppose you pay $1.00 to play the following game. A card is drawn from a standard deck. If it is an ace, you recieve $5.00, if it is a king, queen, or jack, you receive $3.00. Otherwise you recieve no money. Find the expected value of your net winning. Use decimal notation for your answer.
Answer:
0.08
Step-by-step explanation:
A standard deck contains 52 cards. There are 4 aces and 12 kings/queens/jacks. This means that there is a 4/52 (or 1/13) chance of you winning 5$, and a 12/52 (or 3/13) chance of you winning 3$. To find the expected value, we can simply find the average amount of winnings. This can be done by adding the possible winning values for each card.. Since there is a 1/13 chance that you win 5$, we can add 5*1=5 to the sum. For the kings/jacks/queens, we can add 3*3=9 to the sum. Then, since we win nothing for anything else, we can find the expected value to be 14/13 = 1.08 (approximately). Subtracting the 1$ pay, the expected net winning is 0.08, or 8 cents.
Julia makes friendship bracelets. She was recently given nine bracelets from different people. At Christmas, she plans to give away ome third of her bracelets. She will be left with 23. With how many did she start?
Answer:
The number of bracelets with she start are 48.
Step-by-step explanation:
Given:
Julia was recently given 9 bracelets. She plans to give 1/3 of her bracelets. She will be left with 23.
Now, we need to find with how many did she start.
Let the bracelets with she start be [tex]x[/tex].
She plans to give [tex]\frac{1}{3}ofx[/tex] = [tex]\frac{x}{3}[/tex].
According to question:
[tex]x-9-\frac{x}{3}=23[/tex]
On solving the equation:
[tex]\frac{3x-27-x}{3} =23[/tex]
Multiplying both sides by 3 we get:
[tex]3x-27-x=69[/tex]
[tex]2x-27=69[/tex]
Adding both sides by 27 and then dividing by 2 we get:
[tex]x=48[/tex]
Therefore, the number of bracelets with she start are 48.
Which of the following is NOT a requirement to conduct a goodness-of-fit test? Question 1 options: a) For each category, the observed frequency is at least 5. b) The sample data consist of frequency counts for each of the different categories c) The sample is simple random sample. d) For each category, the expected frequency is at least 5.
The statement that is NOT a requirement to conduct a goodness-of-fit test is (a) For each category, the observed frequency is at least 5
How to determine the false statement?To conduct a goodness-of-fit test, only the expected frequency must be at least 5.
This means that it is false that the observed frequency is at least 5
Hence, the statement that is NOT a requirement to conduct a goodness-of-fit test is (a)
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4x^3+26x^2-15x-74x3+26x 2 −15x−7 is divided by x+7x+7? If there is a remainder, express the result in the form q(x)+\frac{r(x)}{b(x)}q(x)+ b(x) r(x) .
Answer:
4x^2 -2x -1
Step-by-step explanation:
Synthetic division works well for dividing by a linear binomial. See the attached for the working and the interpretation of the result.
The mean score of a placement exam for entrance into a math class is 80, with a standard deviation of 10. Use the empirical rule to find the percentage of scores that lie between 60 and 80. (Assume the data set has a bell-shaped distribution.)
Answer:
47.5%
Step-by-step explanation:
A baseball player strikes out three times for every two hits he gets if the player strikes out 15 times how many hits does he get if the player gets 46 hit how many times does he strike out
The player will get 10 hits for 15 times strikes out.
The player will strike out 69 times for 46 hits.
Step-by-step explanation:
Given,
Ratio of strike out to hits = 3:2
Condition 1: If the player gets 15 strikes out;
Let,
x be the hits for 15 times strikes out.
Using proportion;
Strike out : hit :: strike out : hit
[tex]3:2::15:x[/tex]
Product of mean = Product of extreme
[tex]15*2=3*x\\3x=30[/tex]
Dividing both sides by 3;
[tex]\frac{3x}{3}=\frac{30}{3}\\x=10[/tex]
The player will get 10 hits for 15 times strikes out.
Condition 2: if the player gets 46 hits
Let,
y be the strikes out.
Using proportion,
Strike out : hit :: strike out : hit
[tex]3:2::y:46[/tex]
Product of mean = Product of extreme
[tex]2*y=46*3\\2y=138[/tex]
Dividing both sides by 2;
[tex]\frac{2y}{2}=\frac{138}{2}\\y=69[/tex]
The player will strike out 69 times for 46 hits.
Keywords: Ratio, proportion
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Answer:The player will get 10 hits for 15 times strikes out.
The player will strike out 69 times for 46 hits.
Step-by-step explanation:
Given,
Ratio of strike out to hits = 3:2
Condition 1: If the player gets 15 strikes out;
Let,
x be the hits for 15 times strikes out.
Using proportion;
Strike out : hit :: strike out : hit
Product of mean = Product of extreme
Dividing both sides by 3;
The player will get 10 hits for 15 times strikes out.
Condition 2: if the player gets 46 hits
Let,
y be the strikes out.
Using proportion,
Strike out : hit :: strike out : hit
Product of mean = Product of extreme
Dividing both sides by 2;
The player will strike out 69 times for 46 hits.
Keywords: Ratio, proportion
Step-by-step explanation:
The distance from the centroid of a triangle to its vertices are 16cm, 17cm, and 18cm. What is the length of the shortest median
Answer:
[tex]24[/tex] [tex]\text{cm}[/tex]
Step-by-step explanation:
Given: The distance from the centroid of a triangle to its vertices are [tex]16\text{cm}[/tex], [tex]17\text{cm}[/tex], and [tex]18\text{cm}[/tex].
To Find: Length of shortest median.
Solution:
Consider the figure attached
A centroid is an intersection point of medians of a triangle.
Also,
A centroid divides a median in a ratio of 2:1.
Let G be the centroid, and vertices are A,B and C.
length of [tex]\text{AG}[/tex] [tex]=16\text{cm}[/tex]
length of [tex]\text{BG}[/tex] [tex]=17\text{cm}[/tex]
length of [tex]\text{CG}[/tex] [tex]=18\text{cm}[/tex]
as centrod divides median in ratio of [tex]2:1[/tex]
length of [tex]\text{AD}[/tex] [tex]=\frac{3}{2}\text{AG}[/tex]
[tex]=\frac{3}{2}\times16[/tex]
[tex]=24\text{cm}[/tex]
length of [tex]\text{BE}[/tex] [tex]=\frac{3}{2}\text{BG}[/tex]
[tex]=\frac{3}{2}\times17[/tex]
[tex]=\frac{51}{2}\text{cm}[/tex]
length of [tex]\text{CF}[/tex] [tex]=\frac{3}{2}\text{CG}[/tex]
[tex]=\frac{3}{2}\times18[/tex]
[tex]=27\text{cm}[/tex]
Hence the shortest median is [tex]\text{AD}[/tex] of length [tex]24\text{cm}[/tex]
A part of a line consisting of two endpoints and all points between them
Answer:
segment
Step-by-step explanation:
We know that a line has no end points.
If we take a part from the line then it is called line segment.
The line segment has starting point and end point.
A part of a line consisting of two endpoints and all the points between them is called segment.
Therefore, the answer is segment
Line segment
LineA line segment is a section of a line that is defined by two distinct end points and includes all points on the line between them. So, a part of a line made up of two ends and all points in between is known as a line segment.A line is a collection of points that extends in two opposite directions and is infinitely thin and long.A line is a one-dimensional figure with no thickness that extends in both directions indefinitely.Find out more information about line here:
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A rectangle is inscribed in an equilateral triangle so that one side of the rectangle lies on the base of the triangle. Find the maximum area the rectangle can have when the triangle has side length 14 inches.
Answer:
A(max) = 42.43 in²
Dimensions:
a = 7 in
b = 6,06 in
Step-by-step explanation: See annex
Equilateral triangle side L = 14 in, internal angles all equal to 60°
Let A area of rectangle A = a*b
side b tan∠60° = √3 tan∠60° = b/x b = √3 * x
side a a = L - 2x a = 14 - 2x
A(x) = a*b A(x) = ( 14 - 2x ) * √3 * x
A(x) = 14*√3*x - 2√3 * x²
Taking derivatives both sides of the equation
A´(x) = 14√3 - 4√3*x
A´(x) = 0 ⇒ 14√3 - 4√3*x = 0 ⇒ 14 - 4x = 0 x = 14/4
x = 3,5 in
Then
a = 14 - 2x a = 14 - 7 a = 7 in
b = √3*3,5 b = *√3 *3,5 b = 6,06 in
A(max) = 7 *6,06
A(max) = 42.43 in²
In his suitcase, Jack has 3 shirts, 4 pants, 2 socks (pairs of socks), and 2 shoes (pairs of shoes). How many unique ways can Jack get fully dressed? Show your work and explain.
Answer:
48
Step-by-step explanation:
the number of shirts are 3, number of pants 4, number of socks pairs 2 and 2 pairs of shoes.
first lets start with shirts and pants, number of unique combinations are,
(for each shirt there are 4 different pant combinations) = [tex](3)(4)[/tex]
=12
similiarly for each shirt pant pair there are 2 shoes and 2 socks pairs.
thus, total number of combinations are=
[tex](12)(2)(2)[/tex]
= 48
A rectangle has length x and width x – 3. The area of the rectangle is 10 square meters. Complete the work to find the dimensions of the rectangle. x(x – 3) = 10 x2 – 3x = 10 x2 – 3x – 10 = 10 – 10 (x + 2)(x – 5) = 0 What are the width and length of the rectangle?
Answer:
Step-by-step explanation:
Area of rectangle = Length × Width
The given rectangle has a length if x meters
The width of the triangle is (x-3) meters
The area of the rectangle is given as 10 square meters.
Area if rectangle = x(x-3) = 10
Multiplying each term in the parentheses,
x^2 -3x = 10
x^2 -3x -10 = 0
This is a quadratic equation
We will look for two numbers such that when they are multiplied, it will give us -10x^2 and when they are added, it will give -3x. It becomes
x^2 + 2x - 5x -10 = 0
x(x+2)-5(x+2) =0
( x + 2)(x-5) = 0
x = -2 or x = 5
The length of the rectangle cannot be negative so the length is 5 meters
Widith = x+3 = 5-3 = 2 meters
Final answer:
The dimensions of the rectangle are found by solving the quadratic equation derived from the area. The length is 5 meters, and the width is 2 meters, as negative dimensions are not possible.
Explanation:
To find the dimensions of the rectangle with an area of 10 square meters and the sides defined as x and x
- 3, we have derived a quadratic equation x^2 - 3x - 10 = 0 which factors down to (x + 2)(x - 5) = 0. This gives us two possible solutions for x: either x + 2 = 0 or x - 5 = 0. Solving these equations, we find x = -2 or x = 5. Since a rectangle cannot have a negative dimension, we disregard x = -2. Therefore, the length of the rectangle is x = 5 meters and the width is x - 3 = 2 meters.
helppppppppppppppppppp
Answer:
Option D: 2 . cos(90 + x) = -2a
Step-by-step explanation:
Given that:
sin x = a --------- eq1
As we know that trignometry says:
cos(90 + x) = -sinx-------- eq2
In option two we are given that:
cos(90 + x) = -2a ---------- eq3
So by equating both sides of eq2 and eq3:
-2a = -2sinx
By cancelling -2 from both sides we get:
sinx = a
That is given in eq1
hence proved
i hope it will help you!
The function f(x)=lnx is transformed into the equation f(x)=ln(9.2x). Select from the drop-down menus to correctly identify the parameter and the effect the parameter has on the parent function. The function f(x)=ln(9.2x) is a of the parent function by a factor of _________.
The function f(x)=ln(9.2x) is a horizontal compression of the parent function by a factor of 1/9.2
Step-by-step explanation:
The multiplication of a function by a number compresses or stretches the function vertically while to compress or stretch the function horizontally, the input variable is multiplied with a number.
i.e.
[tex]For\ f(x) => g = f(bx)[/tex]
where b is a constant.
Now
If b>0 then the function is compressed horizontally
The given function is:
[tex]f(x) = ln\ x\\Transformed\ to\\f(x) = ln\ (9.2x)[/tex]
As the variable in function is multiplied with a number greater than zero, the function will stretch horizontally.
The function f(x)=ln(9.2x) is a horizontal compression of the parent function by a factor of 1/9.2
Keywords: Transformation
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Answer:
The function f(x)=In (9.2x) is a horizontal compression of the parent function by a factor of 5/46
Step-by-step explanation:
I just took this test and that was the correct answer :( good luck everyone
FortyForty people purchase raffle tickets. Three winning tickets are selected at random. If first prize is $50005000, second prize is $45004500, and third prize is $500500, in how many different ways can the prizes be awarded?
To determine the number of different ways the prizes can be awarded, we need to use the concept of combinations.
Explanation:To determine the number of different ways the prizes can be awarded, we need to use the concept of combinations. Since there are 40 people purchasing raffle tickets, and 3 winning tickets are selected at random, we can find the number of ways the prizes can be awarded using the formula for combinations:
C(n, r) = n! / ((n-r)! * r!)
Where n is the total number of items and r is the number of items chosen at a time. In this case, n = 40 and r = 3:
C(40, 3) = 40! / ((40-3)! * 3!)
= 40! / (37! * 3!)
= (40 * 39 * 38) / (3 * 2 * 1)
= 9880
Therefore, there are 9,880 different ways the prizes can be awarded.
PLEASE HELP URGENT!!! 90 POINTS
One zero of the polynomial function f(x) = x3 − x2 − 20x is x = 0. What are the zeros of the polynomial function?
\Given :
x^{3} +x^{2} -20x
Solution:
x^{3} +x^{2} -20x
taking x common from the given polynomial
⇒x(x^{2} +x-20)=0
⇒x(x(x+5)-4(x+5))=0
⇒x(x+5)(x-4)=0
⇒ x=0 , x+5=0 , x-4=0
⇒x = 0 , x = -5 , x = 4
The zeros of the polynomial function f(x) = x³ - x² - 20x are x = 0, x = 5, and x = -4.
To find the remaining zeros, we can use polynomial division or factoring techniques. Since the given polynomial is already in its factored form, we can use the zero-product property to find the other zeros.
The given polynomial f(x) = x³ - x² - 20x can be factored as
f(x) = x(x² - x - 20).
Now, we have two factors: x and (x² - x - 20).
To find the zeros of the second factor, we can set it equal to zero and solve for x. So, we have
x² - x - 20 = 0.
We can factor this quadratic equation by splitting the middle term:
x² - x - 20 = (x - 5)(x + 4).
Now, we have three factors: x, (x - 5), and (x + 4). To find the zeros, we set each factor equal to zero and solve for x:
x = 0 (given) x - 5 = 0 => x = 5 x + 4 = 0 => x = -4
Therefore, the zeros of the polynomial function
f(x) = x³ - x² - 20x are x = 0, x = 5, and x = -4.
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Express the confidence interval 0.333 less than p less than 0.555 in the form Modifying Above p with caret plus or minus Upper E. Modifying Above p with caret plus or minus Upper E equals nothing plus or minus nothing
Answer: = [tex]0.444\pm 0.111[/tex]
Step-by-step explanation:
The confidence interval for population proportion(p) is given by :-
[tex]\hat{p}-E<p<\hat{p}+E[/tex] (1)
It is also written as : [tex]\hat{p}\pm E[/tex] (*)
The given confidence interval for population proportion :
[tex]0.333<p<0.555[/tex] (2)
Comparing (1) and (2) , we get
Lower limit = [tex]\hat{p}-E=0.333[/tex] (3)
Upper limit = [tex]\hat{p}+E=0.555[/tex] (4)
Adding (3) and (4) , we get
[tex]2\hat{p}=0.888\\\Rightarrow\ \hat{p}=\dfrac{0.888}{2}=0.444[/tex]
Put value of [tex]\hat{p}=0.444[/tex] in (2) , we get
[tex]0.444+E=0.555\\\\\Rightarrow\ E=0.555-0.444=0.111[/tex]
Put values of [tex]\hat{p}=0.444[/tex] and E= 0.111 in (*) , we get
Required form = [tex]0.444\pm 0.111[/tex]
The confidence interval 0.333 to 0.555 can be written in the form 0.444 +/- 0.111 This helps to clearly represent the sample proportion and its margin of error.
The confidence interval 0.333 less than p less than 0.555 can be expressed in the form Modifying Above p with caret plus or minus Upper E. To do this, we need to find the middle point of the interval, which represents the sample proportion and the margin of error (E").
Find the midpoint:The confidence interval can be written as 0.444 plus or minus 0.111.
Please please help me with this
Answer:
Step-by-step explanation:
First find the equations of the lines, then fill in the proper inequality sign. The upper line has a y-intercept of 1 and a slope of 1/2, so the equation, in slope-intercept form is
[tex]y=\frac{1}{2}x+1[/tex]
Since the shading is below the line, the inequality sign is less than or equal to. The inequality, then, is
[tex]y\leq \frac{1}{2}x+1[/tex]
But the solutions are in standard form, so let's do that:
[tex]-\frac{1}{2}x+y\leq 1[/tex]
AND they do not like to lead with negatives, apparently, so let's change the signs and the way the inequality is facing, as well:
[tex]\frac{1}{2}x-y\geq -1[/tex]
Let's do the sae with the lower line. The equation, in slope-intercept form is
[tex]y=\frac{3}{2}x-3[/tex] since the slope is 3/2 and the y-intercept is -3. Now, since the shading is above the line, the inequality is greater than or equal to:
[tex]y\geq \frac{3}{2}x-3[/tex]
In standard form:
[tex]-\frac{3}{2}x+y\geq -3[/tex] and not leading with a negative gives us
[tex]\frac{3}{2}x-y\leq 3[/tex]
Those 2 solutions are in choice B, I do believe.
Trevor is making payments on a car that cost $26,555 he makes 36 equal payments if he runs to equal payments up to the nearest whole dollar about how much will he overpay after 36 months
Answer:
The over payment amount after 36 months is $ 0.37
Step-by-step explanation:
Given as :
The cost of the Car = $ 26,555
The number of times payment done for 36 month = 36
So, The the cost of car for 36 equal payment = [tex]\dfrac{\textrm Total cost of car}{\textrm number of times payment done }[/tex]
i.e The the cost of car for 36 equal payment = [tex]\frac{26,555}{36}[/tex]
∴ The the cost of car for 36 equal payment = $ 737.6389
Now rounding this value to nearest whole dollar = $ 738
Note - A) If after decimal , number are above 4 then round it to 1 above digit
B) If after decimal , number 4 or less then simply remove all number after decimal
So, The over payment after 36 months = $ 738 - $ 737.63 = $ 0.37
Hence The over payment amount after 36 months is $ 0.37 Answer
Mr. Lynch buys some turkey slices, wheat rolls, and cheese for $45. The ratio of the amount of money he spends on cheese to the amount of he spends on turkey slices is 2:3
Given a ratio of cheese to turkey slices is 2:3, Mr. Lynch spent $18 on cheese and $27 on turkey slices out of a total of $45.
Explanation:Mr. Lynch is faced with a real-world example of the concept of ratios. In this case, the ratio of cheese to turkey slices is 2:3, meaning for every 2 parts of cheese, he's spending on 3 parts of turkey slices. The total amount spent is $45. We can solve this ratio problem to identify the individual costs for cheese and turkey slices by using a simple mathematical method.
Firstly, let's understand how a ratio works. It's a way to compare amounts of different things. Given the ratio 2:3 (cheese to turkey), add the ratio numbers together to get the total parts, i.e., 2 + 3 = 5. These 5 parts represent the total amount of $45 spent.
Next, we need to find the value of one part. To do this, divide the total amount spent by the total parts: $45/5 parts gives us 9: this determines that each part is worth $9.
Finally, to find the amounts spent on cheese and turkey slices, multiply the number of parts each item has in the ratio by the value of one part. So, for cheese, it's 2 parts x $9 = $18, and for turkey slices, it's 3 parts x $9 = $27.
In conclusion, Mr. Lynch spent $18 on cheese and $27 on turkey slices.
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The previous triangular prism had a surface area of 288 square units. What happens to the surface area of your prism when you double all four measurements?
If all four dimensions of triangular prism having surface area as 288 is doubled than new surface area will be four times than the initial prism that is 1152 square unit.
Solution:Given that
Surface area of a triangular prism = 288 square unit
Need to evaluate new surface area if all four measurement of triangular prism is double.
Relation between surface area and the four dimensions of the triangular prism is given by following formula
Surface Area of triangular prism = bh + 2ls + lb
Where h is height of the prism , b is length of base of the prim , l is length of the prism and s is side length of the prism.
Given that Area of triangular prism = 288 square unit
=> bh + 2ls +lb = 288
Doubling the four dimensions means replace b by 2b, l by 2l , s by 2s and h by 2h in formula of Surface area of triangular prism.
[tex]\text { We get Surface area of new triangular prism }=2 b \times 2 h+2 \times 2 l \times 2 s+2 l \times 2 b[/tex]
[tex]\begin{array}{l}{=4 \times b h+4 \times 2 l s+4 \times l b} \\\\ {=4(b h+2 l s+l b)}\end{array}[/tex]
=> Surface area of new triangular prism = 4 (bh + 2ls +lb)
=> Surface area of new triangular prism = 4 x 288 = 1152 square unit.
Hence we can conclude that if all four dimensions of triangular prism having surface area as 288 is doubled than new surface area will be four times than the initial prism that is 1152 square unit.
Answer: C, the surface area increases by 4 times
Step-by-step explanation:
Triangle $ABC$ has sides of $6$ units, $8$ units, and $10$ units. The width of a rectangle, whose area is equal to the area of the triangle, is $4$ units. What is the perimeter of this rectangle, in units
Answer:
20
Step-by-step explanation:
Given that the area of the rectangle is equal to that of the triangle
Area of triangle $ABC$
= 1/2 (bh)
Given that the sides of the triangle are $6$ units, $8$ units, and $10$ units,
The base and the heights are $6$ units and $8$ units. The $10$ units is the hypotenuse
From Pythagoras theorem,
6^2 + 8^2 = 10^2
Therefore, area of triangle
=1/2 (6 × 8)
= $24$ units^2
Area of rectangle = L × W
Where L = Length, W = Width
Area of the rectangle = area of triangle
L × 4 = 24
L= 24/4
L = $6$ Units
Perimeter of rectangle
=2 (L + B)
= 2(6 + 4)
= $20$ Units
Answer:
20
Step-by-step explanation:
We use the Pythagorean Theorem to verify that triangle $ABC$ is a right triangle, or we recognize that $(6,8,10)$ is a multiple of the Pythagorean triple $(3,4,5)$. The area of a right triangle is $\frac{1}{2}bh$ where $b$ and $h$ are the lengths of the two legs, so the area of triangle $ABC$ is $\frac{1}{2}(6)(8)=24$. If the area of the rectangle is $24$ square units and the width is $4$ units, then the length is $\frac{24}{4}=6$ units. That makes the perimeter $6+6+4+4=\boxed{20}$ units.
A quality control technician checked a sample of 30 bulbs. Two of the bulbs were defective. If the sample was representative, find the number of bulbs expected to be defective in a case of 450.
36
45
30
24
Answer:
if sample of 30 bulbs has 2 defective bulbs so,
there is one defective bulb every
[tex] \frac{30}{2} = 15[/tex]
bulbs.
total defective bulbs in 450 bulbs =
[tex] \frac{450}{15} = 30[/tex]
Write a quadratic equation with the given roots. Write the equation in the form ax^2+bx+c=0 , where a, b, and c are integers. –7 and –2
Answer:
x² +9x +14 = 0
Step-by-step explanation:
Since the roots are integers, we can write the equation in the given form using a=1. Then b is the opposite of the sum of the roots:
b = -((-7) +(-2)) = 9
And c is the product of the roots:
c = (-7)(-2) = 14
So, the desired quadratic equation is ...
x² +9x +14 = 0
_____
The attached graph confirms the roots of this equation.
_____
Another way
For root r, a factor of the equation is (x -r). For the given two roots, the factors are ...
(x -(-7))(x -(-2)) = (x +7)(x +2)
When expanded, this expression is ...
x(x +2) +7(x +2) = x² +2x +7x +14
= x² +9x +14
We want the equation where this is set to zero:
x² +9x +14 = 0
___
If a root is a fraction, say p/q, then the factor (x -p/q) can also be written as (qx -p). In this case, expanding the product of binomial factors will result in a value for "a" that is not 1.
Miguel earns 2,456.75 every month he also earns an extra 4.75 every time he sells a new gym membership last month Miguel sold 32 new gym membership how much money did Miguel earn last month
Answer: Total amount of money earned last month = $2608.75
Step-by-step explanation:
Miguel earns 2,456.75 every month. This is his constant pay for the month. He also earns an extra 4.75 every time he sells a new gym membership.
Last month, Miguel sold 32 new gym membership. This means that the extra money that he earned for last month will be the number of new gym membership sold times the amount her earns per new gym membership sold. It becomes
32 × 4.75 = 152
Total amount of money earned last month will be sum of his monthly salary + the extra earned. It becomes
2456.75 + 152 = $2608.75
PLEASE HELP!!!! WILL GIVE BRAINLIEST!!!!!!!
Matthew picks flowers and sells them to tourists. The function s(t) approximates how many flowers Matthew picks per hour. The function W(h) represents how hours per week Matthew spends picking flowers. What are the units of measurement for the composite function s(W(h))?
a. flowers/hour
b. hours/week
c. flowers/week
d. weeks/flower
Answer:
c Flower/ Week
Step-by-step explanation:
think about it like this
hours (flowers)
____. x. _______
Weeks hours
Both of the hours cancel out similar to unit conversions in chemistry and you are left with flowers per week. since the value of flowers you get per hour you work, and x is dependant on the amount of hours you work in a week. These two functions work in conjuction to give flowers per week picked, this crossing off happens diagonally from left down to the right.
The units of measurement for the composite function s(W(h)) is Option(C) flowers/week.
What is the given unit of the composite function ?Given that the function s(t) approximates how many flowers Matthew picks per hour.
Unit of function s(t) is flowers/hours.
Also given that the function W(h) represents how many hours per week Matthew spends picking flowers.
Unit of W(h) = hours/week .
The composite function s(W(h)) will have unit -
= Flowers/hours * hours/week
= Flowers/week
The units of measurement for the composite function s(W(h)) is Option(C) flowers/week.
To learn more about Units and dimensions, refer -
https://brainly.com/question/28464
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What is the original message encrypted using the RSA system with n = 43 · 59 and e = 13 if the encrypted message is 0667 1947 0671? (To decrypt, first find the decryption exponent d which is the inverse of e = 13 modulo 42 · 58.)
Answer:
Ik sorry but you can
Step-by-step explanation:
search in internet
The student needs to find the decryption exponent 'd' for the RSA algorithm by computing the modular multiplicative inverse of e modulo φ(n), and then use that to decrypt the message.
Explanation:The student is asking how to decrypt a message that was encrypted using the RSA algorithm. The given public key consists of n = 43 · 59 and e = 13, and the encrypted message is 0667 1947 0671. To decrypt the message, we need to find the private key, which includes the decryption exponent d. The decryption exponent is the modular multiplicative inverse of e modulo φ(n), where φ(n) is the Euler's totient function of n. Since n is the product of two primes, 43 and 59, φ(n) is (43-1)(59-1) which equals 42 · 58. Now, we need to find d such that it satisfies the congruence ed ≡ 1 (mod φ(n)), which will be d = 13⁻¹ mod 42 · 58. Once d is computed, we can decrypt each part of the message using the formula M = C^d mod n, where M is the original message and C is each part of the encrypted message.